systems: Influence of three phase conditions on drop size
distributions
vorgelegt von
Dipl.-Ing.
Lena Katharina Hohl
geb. in Nordhorn
von der Fakultät III - Prozesswissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
Dr.Ing.
-genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr.-Ing. Felix Ziegler Gutachter: Prof. Dr.-Ing. Matthias Kraume Gutachter: Prof. Alberto Brucato
Tag der wissenschaftlichen Aussprache: 25.05.2018
There are a lot of people who helped me preparing this thesis, either in a direct way via scientific discussions, experiments or contributions to the publications or in an indirect way by making me enjoy the spare time in life with festivities, fun, vacations, food and drinks and everything else.
I would like to thank Prof. Kraume for giving me the chance to work at his department and especially in this project. You gave me the trust and freedom to do as I thought best, but your door was always open for discussions. Thank you for the numerous opportunities to visit great conferences all around the world. Thanks also to Prof. Alberto Brucato for agreeing to review my thesis on such a short notice and for the great feedback during the defense.
Furthermore, thanks to Niklas Paul for convincing me that the project is interesting and that the department and the collaborative research center are crowded by nice and awesome people. Thank you for all the help and discussions in my first years and your relaxed attitude that made me feel like everything will work out eventually. Thanks to the other SFB members and especially to Dmitrij Stehl, Tina Skale and Anja Drews (the "Pickering people") and to the MLS team consisting of Tobias Pogrzeba, Marcel Schmidt and Markus Illner. Thanks also to Daniel Zedel who was always friendly, helpful and open for discussions and helped me find my way into both the department and the SFB. A big thanks to Cornelia Löhmann for being always friendly and helpful.
Furthermore, thanks to the Z64 (the best office in the world): Susanne Röhl, Marc Petzold and Markus Kolano for all the discussions, (pink) cocktails, cakes and all the fun we had together over the last years. Thanks also to Jörn for great times during numerous conferences. Thanks to Joschka for being one of the first members of the C4E2 fanclub, which we still need to establish by the way. Thanks to Mathilde, Frauke and Sherly for the trip to Indonesia and Deniz for hosting all the movie nights and the reminders to play beach volleyball. Thanks also to all the other current and former great people at the department that I like to spend my time with: Evgenia, Sissy, Lutz, David, Frederic, Max, Robert, Johannes, So, Philipp, Nico and Jan-Paul. Thanks also to Gabi, Ulla, Rainer and Johan for all the help with equipment, ordering chemicals and administrative stuff.
Another important group who made this thesis possible are the students who decided to trust me as a supervisor. Thanks to Maresa Kempin (twice), Bernhard Tontarra, Jens-Christian Gantert, Kexin Chen, Harris-Simon Baytelman, Anja Dahlitz, Maximilian Knossalla, Roman Eibauer, Corbinian Schwendele, Rick Rehmann and Vanessa Quaas. Additionally, thanks to my student research assistants: Felix Heitmann, Sascha Pietsch, Vanessa Quaas and Félix Delory. To the latter two I would like to also express my gratitude for all the work they spent during the preparation of my "real" defense.
Thanks to my family, especially my mom and dad. You were always supportive although you did not really have an idea what I was doing in the last years. Thanks to Simon for being the best big brother ever. Thanks to Christoph for your constant optimism concerning my work and for being who you are.
up to three liquid phases as a function of composition and process conditions. These innovative solvent systems are promising reaction media for processes such as the hydroformylation of long-chained olefins. In this work, the influence of the third phase on the drop size distributions and the phase separation behavior was investigated since these are crucial parameters to achieve high reaction rates and an efficient catalyst recycling. A methodology to identify the phases in agitated systems was developed using an in-situ endoscope technique. By analyzing phase behavior and physical properties of the systems in combination with drop size analysis, the influencing factors on the drop size distributions under two and especially three phase conditions were quantified. The prediction of the droplet sizes in three phase systems with population balance equations is a challenging task that mainly works for simple dispersion conditions and in a narrow process condition range. Although the predictive power is not yet satisfactory, this work provides an overview on how a change in process conditions affects all parameters relevant for drop breakage and coalescence. Furthermore, the impact of the dispersion conditions on the phase separation was investigated for two phase systems, simple three phase systems and also for the case of multiple emulsions. Experimental and simulation results indicate, that the phase separation process can be modeled under two phase and three phase conditions.
Zusammenfassung
Mikroemulsionssysteme bestehend aus Wasser, 1-Dodecen und nicht-ionischen Tensiden bilden je nach Zusammensetzung und Prozessbedingungen bis zu drei flüssige Phasen aus. Da diese Systeme vielverspre-chende Reaktionsmedien für die Hydroformylierung langkettiger Olefine und vergleichbare Prozesse sind, wurde der Einfluss der dritten Phase auf Dispersion und Phasentrennung untersucht. Beide Phänomene sind entscheidend für den Gesamtprozess, da sie sowohl die Reaktionsraten als auch die Effizienz des Katalysator-recyclings und die Reinheit des Reaktionsproduktes beeinflussen. Mittels einer in-situ Endoskopmesstechnik und Bildanalyse wurde in dieser Arbeit eine Methode entwickelt, um die flüssigen Phasen in gerührten Sys-temen zu identifizieren. Durch eine Kombination dieser Methodik mit einer Analyse des Phasenverhaltens und der physikalischen Eigenschaften wurden des Weiteren relevante Einflussgrößen auf Tropfenbruch und Koaleszenz unter zwei- und insbesondere dreiphasigen Bedingungen bestimmt. Die Vorhersage von Trop-fengrößen mittels Populationsbilanzen verläuft erfolgreich in zweiphasigen Mikroemulsionssystemen, jedoch ist die Vorhersagekraft unter dreiphasigen Bedingungen nur in eingeschränkten Prozessparametern sowie in vergleichbar einfachen Systemen ausreichend. Um eine weitere Optimierung der Vorhersage zu ermöglichen wurden unter anderem Bedingungen für die Bildung multipler Emulsionen sowieso zu erwartende Trends der Tropfengrößen als Funktion der Prozessbedingungen dargestellt. Darüber hinaus konnte der Einfluss der dreiphasigen Dispersionen auf die Phasentrennung aufgeklärt und quantifiziert werden. Dazu wurde ein be-stehendes Modell zur Phasentrennung auf den dreiphasigen Zustand erweitert. Ein Vergleich der Experimente und Simulationen zeigt ein hohes Potenzial dieses Modells für die Beschreibung dreiphasiger flüssig/flüssig Systeme.
1 Introduction 1
1.1 Microemulsion systems . . . 2
1.2 Application of microemulsion systems as reaction media . . . 3
2 Scope and outline of the thesis 5 2.1 General structure of the thesis . . . 5
2.2 Journal articles used for this thesis . . . 5
3 State of the Art 7 3.1 Phase behavior and physical properties . . . 7
3.1.1 Prediction and determination of phase behavior . . . 9
3.1.2 Interfacial phenomena . . . 10
3.1.3 Single phase and emulsion rheology . . . 12
3.2 Identification of the phases in agitated systems . . . 14
3.3 Droplet size distributions and Population balance equations . . . 15
3.3.1 Turbulence in agitated systems . . . 17
3.3.2 Drop breakage . . . 17 3.3.3 Drop-drop coalescence . . . 18 3.3.4 Fitting procedure . . . 19 3.3.5 Multiple emulsions . . . 20 3.4 Phase separation . . . 21 3.4.1 Henschke model . . . 22
3.4.2 Phase separation in microemulsion systems . . . 24
4 Materials and Methods 26 4.1 Chemicals and physical properties . . . 26
4.2 Determination of physical properties . . . 27
4.3 Determination of phase heights and separation behavior . . . 28
4.4 Determination of phase composition . . . 29
4.5 Image acquisition and analysis . . . 29
4.6 Stirred tank setups . . . 30
4.7 Drop size modeling . . . 30
4.8 Phase separation modeling . . . 31
5 Results and discussion 33 5.1 Phase behavior and physical properties . . . 33
5.1.1 Phase behavior in systems with water, 1-dodecene and Marlipal 24/70 . . . 34
5.1.2 Phase behavior in systems with water, 1-dodecene and Marlophen or Triton X100 . . . . 36
5.1.3 Phase behavior in systems with water, 1-dodecene and C4E2 . . . 37
5.1.4 Hysteresis effects . . . 39
5.1.5 Summary of phase behavior results in water, 1-dodecene, surfactant systems . . . 40
5.2 Identification of the phases in agitated systems . . . 41
5.2.1 Interfacial tension and free energy . . . 41
5.2.2 Fluid dynamics in the stirred tank . . . 42
5.3 Drop size distributions in two phase systems . . . 44
5.3.1 Two phase systems without surfactant . . . 44
5.3.2 Two phase systems with surfactant . . . 47
5.4 Drop size distributions in three phase systems . . . 52
5.4.1 Experimental results for Marlophen, Triton X100 and Marlipal systems . . . 52
5.4.2 Experimental results and prediction approaches for C4E2 systems . . . 53
5.5 Emulsion rheology . . . 63
5.5.1 Viscoelasticity . . . 63
5.5.2 Influence of composition . . . 63
5.6.1 Validation of the model implementation . . . 67
5.6.2 Impact of the fitting parameter on the modeling results . . . 67
5.6.3 Simulation without settling experiment . . . 69
5.7 Phase separation in three phase systems . . . 73
5.7.1 Sedimentation . . . 73
5.7.2 Experimental and modeling results in three phase systems . . . 75
6 Summary and Outlook 80 References 81 List of Figures 90 List of Tables 94 A Appendix 95 A.1 Additional information and results . . . 95
A.1.1 CMC and MAC measurements . . . 95
A.1.2 Physical properties of the pure components and binary mixtures . . . 95
A.1.3 Evaluation of experimental errors of the endoscope technique . . . 96
A.1.4 Emulsion rheology . . . 98
A.1.5 Simulation results in water/1-dodecene systems . . . 99
A.2 List of supervised student projects . . . 101
A.2.1 Microemulsion systems . . . 101
A.2.2 Pickering emulsions* . . . 101
A.3 List of proceedings, posters and presentations . . . 102
A.3.1 Proceedings . . . 102
A.3.2 Posters . . . 102
A.3.3 Presentations . . . 103
A.4 List of own publications in peer-reviewed journals . . . 105
A.4.1 Articles with additional information . . . 105
Abbreviations
aq aqueous phase
C number of carbon atoms
CF D computational fluid dynamics
CM C critical micelle concentration
CST R continuous stirred tank reactor
C4E2 diethylene glycol monobutyl ether (short-chained amphiphilic molecule)
DLV O theory by Derjaguin, Landau, Verwey and Overbeek
DM F N,N-dimethylformamide
dpz dense-packed zone
E number of ethoxy groups
HLB hydrophilic-lipophilic balance
HLD hydrophilic-lipophilic deviation
InP ROM P T Intergrated chemical processes in liquid multiphase system (collaborative research center)
M AC minimum aggregation concentration
mi microemulsion phase
org organic phase
o/w oil-in-water emulsion
P BE Population balance equation
RCH/RP Ruhrchemie/Rhône-Poulenc process
T OC total organic carbon
T OF Turn-over-frequency
T P P T S tri(m-sulfonyl)triphenylphosphine, vulgo triphenylphosphine trisulfonated
w/o water-in-oil emulsion
1Φ one phase microemulsion system
2
̄Φ lower two phase microemulsion system 2
̄Φ upper two phase microemulsion system 3Φ three phase microemulsion system
Latin letters
a0 m−1 natural curvature of amphiphilic membrane a1,2 m−1 orthogonal curvature of amphiphilic membrane A m2 interfacial area
Ar − Archimedes number
ACN − alcane carbon number
B − salinity factor
b m stirrer bottom clearance ̇
Bb s−1 birth rate of droplets by breakage ̇
Bc s−1 birth rate of droplets with by coalescence c − number of inner droplets
C − empirical constant for Weber correlation (Eq. 10)
c1,b − first empirical constant for drop breakage c1,c − first empirical constant for drop coalescence c2,b − second empirical constant for drop breakage
Cic − constant for coalescence model by Rosen (Eq. 39)
C1 − factor for Henschke model (defined by Eq. 31) C2 − factor for Henschke model (defined by Eq. 32) CM C mg/L critical micelle concentration
cpα − critical point water/oil
cpβ − critical point water/surfactant
cs mol/L surfactant concentration
ct K−1 factor for the weakening of hydrogen bonds
cw − friction coefficient
d, d′, d′′ m drop diameter, differentiation between several drops by apostrophe(s)
dmax m maximum drop diameter
d1,0 m arithmetic mean diameter
d3,2 m Sauter mean diameter
d3,2(t=0) m inital Sauter mean diameter
d3,2(t=0),start m guessed inital Sauter mean diameter for iteration (Henschke model) d3,2,i m Sauter mean diameter at interface
dst m stirrer diameter
D m tank diameter
̇
Db s−1 droplet death rate by breakage
̇
Dc s−1 droplet death rate by coalescence
E J mol−1 activation energy for droplet collision
EACN − equivalent alcane carbon number
EON − number of ethoxy groups
f Hz frequency
F − number of state variables
F (d) s−1 drop coalescence rate
g ms−2 acceleration due to gravity
g(d) s−1 drop breakage rate
G J Gibbs free energy
G′ P a storage modulus
G′′ P a loss modulus
h m height
hc m height of sedimentation line
hcrit m critical distance between droplets
hd m height of dense-packed zone
hp m height of dense-packed zone during free sedimenation
hpy m running varaible for Henschke model
hst m height of stirrer blade
j − size category of distribution
H m filling height
Hc N m Hamaker coefficient
HLB − hydrophilic-lipophilic-balance
HLD − hydrophilic-lipophilic-deviation
j(A) − factor for the co-surfactants or alcohols
kdi − factor for dipole interactios
k1 − Einstein coefficient
Km P a elastic modulus of membrane
KG P a Gaussian modulus
KHR − Hadamard-Rybczynski factor
Lamod − modified Laplace number
Lg mm gap size
m kg mass
M − number of hydropobic monomers in surfactant molecules
M AC mol/L minimal aggregation concentration,
n rpm stirrer speed
N − number of hydrophilic monomers in surfactant molecules
Nd m−3 number of droplets per unit volume
N e − power number
NCa − capillary number
ns mol amount of substance
P kgm2s−3 power
P h − number of phases
q − function for Henschke model defined by Eq. 22
q0(d) m−1 probability density function of number (drop diameter)
q1 m◦C parameter to define Q (Eq. 46)
q2 s3m−1 parameter to define Q (Eq. 46) q3 m−1 probability density function of volume
Q m defined by Eq. 46
Q0 − cumulative function of number
Q3 − cumulative function of volume
r m drop radius
ra m length of the contour of the channel in dense-packed zone
rf m radius between two compressed droplets
rf i m radius between compressed droplet at interface
R J mol−1K−1 universal gas constant
Re − Reynolds number
Res − Reynolds number during sedimentation
Re∞ − Reynolds number for single droplet in infinitely expanded fluid
Ri N m−1 interfacial rigidity
r∗f,t m radius of the area between droplets in dense-packed zone
r∗f,t m radius between droplets in dense-packed zone
r∗
v − fitting parameter
r∗v,weighted − weighted fitting parameter (Eq. 43)
S g/ml salt concentration
Snorm − normed error parameter
S1 − error parameter for difference between experiment and simulation (Eq. 41) S2 − error parameter for difference between experiment and simulation (Eq. 46)
S3 s error parameter (Eq. 47)
S4 s error parameter (Eq. 53)
T ◦C temperature
tsep s overall separation time
T OF s−1 Turn-over-frequency
vrel ms−1 relative velocity
vs ms−1 sedimentation velocity
vs,∞ ms−1 sedimentation velocity of single droplet in infinite medium
vs,exp ms−1 experimental sedimentation velocity
vs,exp,opt ms−1 optical experimental sedimentation velocity
vs,sim ms−1 simulated sedimentation velocity
W et − stirred tank Weber number
x wt.% mass fraction z − correction factor Indices c continuous phase calc calculated d dispersed phase ef f effective exp experimental min minimum max maximum lip lipophilic n, N number of experiment norm normalized sim simulated ss steady state tot total Greek letters
α − mass fraction of 1-dodecene (in relation water + 1-dodecene)
β m−1 daughter drop size distribution
γ − mass fraction of surfactant (in relation to water, 1-dodecene and surfactant)
̇γ s−1 shear rate
Γ mol m−2 interface coverage
ϵ W kg−1 average energy dissipation rate
ζ − number of daughter droplets per breakage event
η P a s dynamic viscosity
θ − function of Henschke model
κ µScm−1 electrical conducitivty
λ(d) − coalescence efficiency
λk m Kolmogorov length
Λ m turbulence eddy size in macroscale
ν m2s−1 kinematic viscosity
ξopt m char. length of surfactant membrance at optimum formulation
σdsd − standard deviation of a drop size distribution
τi s drop/interface coalescence time
τt s drop/drop coalescence time
φ − phase fraction
φi − dispersed phase fraction in dense-packed zone
φp,o − average iniital volume fraction of drops in dense-packed zone
φp − dispersed volume fraction of drops in dense-packed zone
φo − initial dispersed phase fraction
1
Introduction
In respect to the future shortage of fossil resources and in compliance with the principles of "Green Chemistry" [7] it is crucial to enable an efficient and economically viable application of sustainable resources in industrial processes. Despite the use of renewable feedstock, other aspects like the reduction of waste products, energy consumption and the use of green solvents are examples for the principles stated by Anastas and Warner [7] to achieve a greener chemistry in comparison to most of today’s common processes [8, 117]. One example to follow these principles is to use homogeneously catalyzed liquid/liquid reactions, which offer several advantages in comparison to heterogeneous catalysis such as high reaction rates and selectivity under mild reaction conditions [130]. However, one basic disadvantage of homogeneous catalysis is the complicated separation of the product from the valuable catalyst since thermal operations like decomposition, distillation or rectification can negatively affect the active life span of the catalyst. In heterogeneous catalysis, the product separation is significantly easier to carry out since the catalyst is insoluble in the product phase and can be recycled without thermal stresses. Unfortunately, these processes usually exhibit lower reaction rates because the reaction only occurs at the educt/catalyst interface. Therefore, the reaction performance strongly depends on the polarity of the phases and the size of the interfacial area [51].
n-aldehyde (product) olefin iso-aldehyde (byproduct) R R R catalyst (polar)
Fig. 1: Hydroformylation of olefines
The hydroformylation of olefins (Fig. 1) is one example for a homogeneous catalysis where the problem of catalyst recycling is solved using liquid multiphase systems. In the established Ruhrchemie/Rhône-Poulenc (RCH/RP) process, the hydroformylation of short-chained olefins is performed by combining the unpolar organic educt phase with synthesis gas and a catalyst such as cobalt or rhodium solubilized in a polar phase. The solubilisation of the catalyst in the polar phase is achieved using specific ligands such as TPPTS1. The reaction takes place at the oil/water interface where the catalyst is located. The subsequent catalyst recycling can be achieved by phase separation in a decanter, as illustrated in (Fig. 2) [69, 129]. The resulting aldehydes are utilized for fragrances and comparable products in small quantities, but also as intermediates which are converted to alcohols, carboxylic acids or aldol condensation products in downstream processes [10]. The world-wide production of short and medium-chained aldehydes in 2009 already was 2.4 million tons (C ≤ 12) and 0.72 million tons for long-chained aldehydes (≥ C12) [43]. The global market for hydroformylation products is expected to be in the range of US$ 33.27 billion in 2025 [2]. The current state of the art in industrial hydroformylation processes and detailed reaction mechanisms including side products are described for example in [10, 11, 46, 137]. Unfortunately, this method fails if the hydrocarbon chain length of the olefins exceeds C ≈ 5. CO, H2 olefin reactor decanter product processing catalyst recycling unpolar phase polar phase
Fig. 2: Simplified schematic hydroformylation process using multiphase systems (RCH/RP process) 1TPPTS = tri(m-sulfonyl)triphenylphosphine, vulgo triphenylphosphine trisulfonated
reaction efficiency mechanical Emulsions
Pickering-Microemulsion systems homogeneous unpolar polar catalyst particles surfactant T1 T2 Thermomorphic systems phase separation
Fig. 3: Comparison of solvent systems
Due to their poor solubility in water, higher olefins lead to low reaction rates which prevents a profitable pro-cess [129]. To realize the conversion of long-chained olefins despite these obstacles, innovative solvent systems have been extensively investigated within the last years by numerous researchers [50, 74, 158]. Within the collaborative research center "Integrated chemical processes in liquid multiphase systems" (InPROMPT) [74] three different solvent systems are currently investigated: Pickering emulsions, thermomorphic systems and microemulsions [131, 148, 155]. Aim is to achieve a fundamental understanding of these systems by combining basic investigations on their specific characteristics directly with the hydroformylation process in lab and mini-plant scale. In the following section, a brief overview of these solvent systems is provided, followed by a more detailed description of the microemulsion systems which were investigated in this thesis.
In Figure 3 the three solvent systems are arranged according to their current performance in hydroformylation reaction and separation processes. All of these solvent systems inherit specific benefits and disadvantages concerning reaction rates, selectivity and catalyst recycling and a huge optimization potential. The mechanical dispersion (left) and homogeneous systems (right) either lead to low reaction rates or insufficient catalyst recycling, which prevents their use as solvent systems for economically viable processes. All of the remaining liquid/liquid systems can be applied as reaction media to realize the rhodium-catalyzed hydroformylation of long-chained olefins or similar reactions [65, 114, 128, 148, 158]. In Pickering emulsions, solid particles in a size range of 50 - 800 nm are used to generate stable emulsions and high interfacial areas [54, 134, 138]. The catalyst is located within the droplets of a polar (aqueous) phase which can be recycled using ultrafiltration [135, 148]. These systems currently provide the smallest reaction rates in comparison to the other approaches but the simplest one-step phase separation. The application of thermomorphic systems leads to higher reaction rates, since the reaction is performed in a liquid single phase system [28, 33, 65, 155]. For catalyst recycling a change of process temperature can be applied to induce a transformation into a two phase system. Since the catalyst loss after this first step still is high enough to cause economic problems, a subsequent organic solvent nanofiltration needs to be applied. The current process furthermore uses hazardous chemicals such as N,N-dimethylformamide (DMF), which is one disadvantage in comparison to the application of aqueous solvent systems.
In microemulsion systems the catalyst is solubilized in a polar phase during reaction and separation [42, 112, 114, 129, 130, 131]. To enhance the interfacial area of these systems and achieve higher reaction rates, amphiphilic molecules such as non-ionic surfactants are used. The phase behavior of these systems offers the possibility of efficient phase separation under specific process conditions despite the presence of high amounts of surfactant hindering coalescence [94]. The separation is performed in a decanter and leads to marginal catalyst loss, but a subsequent filtration of the organic phase might be necessary to remove residual amounts of surfactant [156].
1.1
Microemulsion systems
In this work, microemulsion systems consisting of water, oil and non-ionic surfactants were investigated. The composition of these systems can be described using the mass ratio of oil to oil and water α and the mass fraction of surfactant γ as depicted in Equation 1 and 2.
α = moil
moil+ mwater
γ = msurf actant
moil+ mwater+ msurf actant
(2)
The maximum number of phases in systems with three liquid components can be calculated according to Gibbs [37] using the state variables F which are temperature and external pressure (F = 2) and the number of components which are water, oil and non-ionic surfactant (Kc = 3) (Eq. 3).
F = Kc− P h + 2 (3)
This results in a maximum of three different phases (Ph = 3) which can occur in ternary water/oil/ surfactant systems. Plotting the phase behavior at constant α as a function of γ and temperature results in the phase conditions depicted in Figure 4 [67, 152]. All of the resulting conditions are microemulsion systems. At temperatures below Tmin and above Tmax of the respective composition, two phase systems occur with a
microemulsion phase and a corresponding excess phase which is organic for low temperatures (2
̄Φ) and aqueous for high temperatures (2̄Φ). At high surfactant concentrations, a single microemulsion phase (1Φ) is developed. An area with three liquid phases (3Φ) occurs between Tmin and Tmax for surfactant concentrations between γmin and γmax. If the complete 2
̄Φ, 2̄Φ or 3Φ systems are agitated for example by mechanical mixing, a regular emulsion (macroemulsion) is developed where one phase is a microemulsion and the other phase(s) are the aqueous and organic excess phases. In contrast to microemulsions and other thermodynamically stable liquid phases, a macroemulsion is only kinetically stabilized by continuous energy input or the presence of surface-active agents which slow the coalescence process. Microemulsions are widely used in pharmaceuticals, cleaners, cosmetics or personal care products [140]. Since some microemulsions only inherit a limited thermal stability, they are considered less suitable for products in daily life but can be used as intermediates in emulsion production [126] or to improve processes such as the extraction of metals [15, 25], dyes [26] and pollutants [81]. This work focuses on the application of microemulsion systems as reaction media and seeks to understand the influencing factors on dispersion and phase separation of macroemulsions formed by agitation of microemulsion systems. Details on the exact nature of the respective excess and microemulsion phases will be provided in section 3.1.
1.2
Application of microemulsion systems as reaction media
Within the last years, microemulsion systems were applied as reaction media for the hydroformylation of the long-chained olefin 1-dodecene in lab scale batch experiments and in a continuous miniplant [42, 94, 112]. The initial turn-over-frequency (TOF) at constant composition under 3Φ process conditions is a function of aeration stirrer speed as illustrated in Figure 5 [42]. Therefore, a significant influence of the droplet size distributions, respectively the liquid/liquid interfacial area and/or the synthesis gas bubble size distribution and the gas/liquid interfacial area on mass transfer exists. In miniplant scale, the hydroformylation of long-chained olefins was performed in a continuous stirred tank (CSTR) with subsequent phase separation in a decanter [94]. Since the catalyst is mainly located in the aqueous phase in 2
̄Φ and 2̄Φ systems and in the microemulsion phase under 3Φ conditions, it can be separated from the unpolar organic educt/product phase. The loss of catalyst is strongly
Temp era utre T [ °C] Amount of surfactant γ [-] 3φ 2φ 2φ 1φ Tmin Tmax γmin γmax
0 200 400 600 800 1000 1200 0 500 1000 1500 2000 Turn -ove r-freq ue ncy TOF [1/h] Stirrer speed n [rpm]
Fig. 5: Initial turn-over-frequency as a function of stirrer speed in a batch reactor during hydroformylation. Water,
1-dodecene, Marlipal 24/70, Rh(acac)(CO)2 + SulfoXantPhos (α = 0.5, γ = 0.08, T = 85◦C) (according to [42])
influenced by its solubility in the respective phases and the quality of the phase separation process. The phase separation in microemulsion systems is fastest within the 3Φ conditions as indicated in Figure 6 [60, 94]. In 2
̄Φ and 2̄Φ systems comparatively high separation times up to several hours, days or even months occur [64]. The main reason for this separation behavior according to previous studies [3, 125] is the influence of temperature and surfactant solubility on the liquid/liquid interface rigidity, which strongly impacts the drop/drop and drop/interface coalescence. However, numerous other aspects such as density, viscosity, interfacial tensions, surfactant type, additives and especially the initial dispersion conditions and droplet size distributions also influence the phase separation process.
A fundamental understanding of these mechanisms is crucial for process optimization and control. Therefore, a detailed investigation of dispersion and phase separation in microemulsion systems was performed while focusing on the impact of the third liquid phase on the developed drop size distributions and the phase separation behavior. 0 100 200 300 400 500 60 70 80 90 100 Se pa ratio n time t se p [min] Temperature T [° ] 3φ 2φ 2φ
Fig. 6: Phase separation time in a constant geometrical setup as a function of phase conditions and temperature for a
2
Scope and outline of the thesis
Aim of this thesis is the analysis and prediction of dispersion and phase separation processes in microemulsion systems especially under 3Φ conditions. This section briefly summarizes the general structure of the thesis and provides an overview of the relevant own publications.
2.1
General structure of the thesis
The structure of the thesis is depicted in Figure 7. The first step is a basic characterization of the phase behavior in combination with a determination of the physical properties such as rheology, density and interfacial tension of the systems. These examinations, which are the basis for all subsequent steps, were performed for different non-ionic surfactants with and without additives which are relevant for the hydroformylation process. For system characterization and process control it is crucial to know which type of dispersion occurs in agitated systems. Therefore, a methodology to identify the respective phases in agitated 3Φ systems using an in-situ endoscope measurement technique was developed. Additionally, the aspect of emulsion rheology was investigated since it significantly influences the flow conditions of the systems.
Physical properties Phase behavior Phase identification Emulsion rheology Phase separation Drop size distributions
Fig. 7: Schematic structure of the thesis
The main part of the thesis is the analysis and description of drop size distributions and phase separation processes under different process conditions. These two topics are closely interconnected since the dispersion characteristics define the initial conditions for phase separation. The complete data sets were used to discuss different approaches towards modeling of the droplet sizes and phase separation behaviour especially under 3Φ conditions. In summary this thesis seeks to provide an answer to the question: How and why does the third liquid phase of microemulsion systems influence drop size distributions and phase separation?
2.2
Journal articles used for this thesis
An overview of the papers used for this thesis including their main topic is illustrated in Figure 8. The publications I and II are proof-of-concept studies for the application of the endoscope measurement technique in microemulsion systems and their complete characterization. The effect of initial dispersion conditions on the phase separation in 3Φ systems is analyzed in publication III. The results for both dispersion and coalescence are summarized and extended in publication IV which discusses the impact of complex droplets such as multiple emulsions under 3Φ conditions. The paper V focuses on the modeling of drop size distributions while discussing relevant obstacles that can occur under 3Φ conditions. The detailed references can be found in the following list of own publications, which are referred to by their roman numerals in all sections of the thesis.
(I) Hohl, L.; Paul, N.; Kraume, M. (2016): Dispersion conditions and drop size distributions in stirred micellar multiphase systems. Chem. Eng. Process., 99, 149-154, DOI: 10.1016/j.cep.2015.08.011
(II) Hohl, L.; Schulz, J.; Paul, N.; Kraume, M. (2016): Analysis of physical properties, dispersion conditions and drop size distributions in complex liquid/liquid systems. Chem. Eng. Res. Des., 108, 210-216, DOI: 10.1016/j.cherd.2016.01.010
(III) Hohl, L.; Knossalla, M.; Kraume, M. (2017): Influence of dispersion conditions on phase separation pro-cesses in liquid multiphase systems. Chem. Eng. Sci. (2017), 171, 76-87, DOI: 10.1016/j.ces.2017.05.005 (IV) Hohl, L.; Kraume, M. (2018): The formation of complex droplets in liquid three phase systems and
their influence on dispersion and coalescence. Chem. Eng. Res. Des. (2018), 129, 89-101, DOI: 10.1016/j.cherd.2017.10.027
(V) Hohl, L.; Schulz, J.; Kraume, M.: Towards drop size modeling in three phase microemulsion systems. J. Chem. Eng. Jpn. (2018), 51, 383-388, DOI: 10.1252/jcej.17we291
II
Analysis of physical properties, dispersion conditions and drop size distributions in complex
liquid/liquid systems Proof of concept: Complete charaterization (3φ)
IV
Formation of complex droplets in liquid three phase systems and their influence on dispersion
and coalescence How and why the third phase can influence dispersion and
phase separation
V
Towards drop size modeling in three phase microemulsion
systems
Simplification of 3φ systems Fit parameter discussion
Dispersion
Phase separation
I
Dispersion conditions and drop size distributions in stirred micellar multiphase systems
Proof of concept: Drop size measurements (3φ)
III
Influence of dispersion conditions on phase separation
in liquid multiphase systems Separation in 2φ and 3φ
systems
3
State of the Art
This section provides an overview of the present state of the art concerning phase behavior in presence of surfac-tants, physical properties of the phases and relevant parameters for the dispersion and separation of multiphase systems. The basis for the formation of microemulsion system is the presence of amphiphilic molecules such as surfactants, which possess both hydrophilic and lipophilic properties. In case of surfactants these properties are defined by a hydrophilic head group and a lipophilic hydrocarbon chain. A classification can be performed by the charge of the head group which is either anionic, cationic, zwitter-ionic or non-ionic. In this thesis, only non-ionic surfactants were investigated since the presence of ions at the liquid/liquid interface would further increase the complexity of relevant effects such as the drop/drop coalescence. The hydrocarbon chain can be linear, branched or aromatic or a combination of these structures. Another option is to use the HLB value (hydrophilic-lipophilic balance) that describes the physicochemical nature of the surfactants by relating the hy-drophilic with the lipophilic parts of the molecule [39, 40, 101]. For HLB = 0 - 10 the surfactant is more soluble in lipophilic substances and for HLB = 11 - 20 in hydrophilic media, although the solubilities are also sensitive to temperature as will be discussed in the following subsection. The HLB provides a simple way for surfactant comparison, with the disadvantage that molecules with different sizes can have the same HLB value as long as they possess equivalent mass ratios. Due to their amphiphilic nature, surfactants tend to adsorb at the phase interfaces in multiphase systems. In case of water/oil systems, the hydrophobic tail is located in the unpolar organic phase and the hydrophilic head in the polar aqueous phase. Solubility effects and the corresponding phase behavior as well as the influence of surfactants on rheology and interfacial tension are discussed in the subsequent section.
3.1
Phase behavior and physical properties
The three binary mixtures of the components water, oil and non-ionic surfactant possess a lower miscibility gap located at temperatures below T ≈ 25◦C for the binary water/surfactant and oil/surfactant systems (Fig. 9) [60].
water oil
surfactant
Fig. 9: Schematic phase prism of the ternary mixture of water, oil and non-ionic surfactant at constant atmospheric
pressure. The unfolded sides represent the respective binary mixtures and their miscibility gaps. The temperatures only serve as an orientation and can vary depending on the components (according to [60])
Water and long-chained olefins are practically insoluble in each other, although the solubility rises with temper-ature. An upper miscibility gap between water and surfactant occurs at temperatures around T ≈ 100◦C [60]. The effect of pressure on the solubility is small in comparison to temperature and will be completely neglected in this thesis [60, 61]. The phase behavior of the ternary systems is mainly determined by the interaction of the lower miscibility gap between oil and surfactant with the upper miscibility gap between water and surfactant [60]. The schematic Gibbs triangle diagrams of such a ternary system are presented in Figure 10 (left) for rising temperatures. At low temperatures the non-ionic surfactant is more soluble in water than in oil as indicated by the schematic slope of the tie lines. The tips of the tie lines depict the composition of the corresponding phases. With increasing surfactant concentration the tie lines shorten while approaching the critical point cp, towards
which the compositions of the respective phases converge until they merge into one phase. With increasing temperatures, the solubility of the non-ionic surfactant in oil increases which leads to differently oriented tie lines. The volume fraction of the aqueous phase decreases with higher temperature as the solubility of the
cpα cpβ T1 T2> T1 T3> T2 T4 > T3 T5> T4 T6> T5 T emp era utre T [ °C] Amount of surfactant γ [-] (α = const.) 3φ Winsor III 2φ Winsor I 2φ Winsor II 1φ Winsor IV Tmax Tmin γmin γmax γ
T
tricritical point water oil surfactantFig. 10: Phase triangles, phase prism and T-γ diagram at constant atmospheric pressure (acc. to [58, 125, 152])
mi T emp era utre T [ °C ] Amount of surfactant γ [-] 3φ 2φ 2φ 1φ org aq microemulsion microemulsion microemulsion bicontinuos microemulsion Tma Tmin γmin γma
Fig. 11: Phase behavior of microemulsion systems at constant oil/water ratio α: aqueous phase (aq) = blue, organic
phase (org) = yellow, bicontinuous microemulsion (mi) = gray (acc. to [58, 125])
surfactant in the organic phase rises. Correspondingly, the volume of the organic phase rises due to the larger solubilisation of water and higher amounts of surfactant within the organic phase. In systems which develop a 3Φ system, the critical line in the temperature over phase volume graph inherits a slope of zero at the tricritical point, leading to two critical end points. Therefore, the surfactant is not simply transferred from the aqueous to the organic phase with rising temperatures. Due to the colliding miscibility gaps with differently oriented tie lines, the aqueous phase decomposes into two phases - an aqueous excess phase and a microemulsion phase [58], as indicated by the gray areas in Figure 10. A phase prism diagram is obtained from the Gibbs triangles of the ternary system with the temperature T as the ordinate (Fig. 10, middle). A cut through this prism at a constant oil/water ratio α results in the T-γ section, the so-called Kahlweit "fish" diagram [60] (Fig. 10, right). The one-phase, two-phase, and three-phase systems can either be described using the nomenclature proposed by Winsor (Winsor I, II, III, IV systems) [152] or by Knickerbocker (1Φ, 2
̄Φ, 2̄Φ, 3Φ) [67]. All of the resulting conditions are microemulsion systems. The term "microemulsion" is a misnomer that easily leads to confusion because microemulsions are not a special case of regular emulsions. They are no dispersions, but thermodynam-ically stable mixtures of oil, water and surfactant [125]. To clarify the nomenclature also used in this thesis, a detailed version of the fish diagram is shown in Figure 11. The inner structure of the microemulsion phase either consists of oil-swollen micelles in a water continuum in equilibrium with an organic excess phase (2
̄Φ) or of water-swollen micelles in an oil continuum in equilibrium with an aqueous excess phase (2̄Φ).
These micelles are sometimes even referred to as "droplets" in literature or the respective microemulsion phases as "droplet-type" microemulsions which can lead to confusion with the droplets generated by mechanical mixing and the development of regular emulsions (macroemulsions). At high surfactant concentrations above γmaxthe
anisotropic single phase system (1Φ) is developed, where cylindrical, hexagonal, cubic or lamellar surfactant agglomerates are formed that can lead to liquid crystalline structures which increase the dynamic viscosity of the microemulsion [77]. The inner structure of microemulsions in 3Φ and 1Φ systems usually is called a bicontinuous type and described as inter-twinned continuous water and oil phases with a large amount of surfactant [20] or as accumulated swollen micelles so numerous that they touch one another [125]. The application of microemulsion systems as reaction media necessitates the development of a 3Φ condition for phase separation and catalyst recycling. Therefore, the phase behavior needs to be determined experimentally or be predicted with adequate precision, as discussed in the next subsection.
3.1.1 Prediction and determination of phase behavior
The phase behavior in microemulsion systems can partly be predicted using the semi-empirical HLD (Hydrophilic-Lipophilic Deviation) model [4, 122, 124, 125]. It can be interpreted as a set of molecular interactions and describes the deviation from an optimum formulation. The HLD value for systems with non-ionic surfactants includes the impact of the molecular structure of oil, non-ionic surfactant and co-surfactants, of electrolytes and of temperature on the phase behavior. It is defined as:
HLDnonionic= B(S) − kdi((E)ACN ) + Cc − j(A) + ct(∆T ). (4)
The salinity of the systems B(S) with S as the concentration of electrolyte in g/100 ml induces a charge shielding effect due to the contraction of the electric double layer [5, 122, 125]. The molecular structure of the oil is defined by kdi((E)ACN), where ACN is the alkane carbon number and equal to the number of carbon atoms
per alkane molecule. For non-alkane oils, the equivalent alkane carbon number EACN is employed, which can be detemined experimentally or calculated with quantum chemistry based thermodynamic equilibrium methods [82]. The value kdi describes the molecular interactions between the surfactant and the oil phase [5]. The
molecular structure of the non-ionic surfactant is represented by Cc, which is calculated using the molecular structure of the hydrophobic tail of the surfactant and the number of ethoxylene groups in the polar part of the surfactant molecule. The value j(A) depends on the co-surfactants in the systems or is a function of the alcohol type and concentration, which modify the interfacial layer by adsorbing at the interface and becoming part of the amphiphilic mixture. Short-chained alcohols such as methanol increase the hydrophobicity, whereas higher alcohols tend to increase the lipophilicity [16]. The value j(A) is zero if no co-surfactants or alcohols are present [5]. The impact of temperature ct ∆T is related to the weakening of the hydrogen bonds between the
molecules of water and the oxygen in the ethylene groups of the surfactant with rising temperature in relation to a reference of T = 25◦C [5, 122, 125]. Under the condition that all of these parameters are known with an adequate accuracy for a specific solvent system, the position of the so-called optimum formulation (HLD = 0) as indicated by Figure 12 (left) can be predicted. At HLD = 0, which is in the middle of the respective 3Φ temperature interval, the solubility of the surfactant in oil and water is almost equal and the bicontinuous microemulsion phase consists of equal parts water and oil [125]. The smallest interface rigidity and the highest tendency of systems to coalesce is at the optimum formulation in the middle of the 3Φ area, which leads to a fast phase separation. If the systems are supposed to be more stable towards coalescence, the HLD should be shifted away from HLD = 0. If salt is added to the non-ionic system, the HLD value rises. To reach HLD = 0 again another parameter needs to be adjusted, for example by reducing the temperature. If the oil chain length ((E)ACN) is increased, the HLD declines and the temperature needs to be enhanced to reach HLD = 0 again. The HLD model can also be used to predict the morphology and viscosity of the microemulsion phase, that strongly depend on phase behavior [66] and to estimate the middle of the 3Φ area where the fastest coalescence is expected. However, a prediction of the width of the 3Φ temperature interval, the detailed influence of process parameters on the specific separation times which occur or the type of dispersion also need to be known. Furthermore, impurities in technical grade chemicals can not be described easily which might necessitate to determine all parameters of the HLD equation for uncommon or technical grade solvent systems. Another option to identify the position of the 3Φ area is to use electrical conductivity measurements in stirred systems while varying the temperature. The electric conductivity κ of common liquids is determined by the amount of ions carrying the electrical charge. For most materials with constant composition, the conductivity can
Tem perat ur e T [° C] Surfactant concentration γ [-] k(E)ACN, j(A) B(S), Cc T min Tmax
o/w emulsion with high electrical conductivity w/o emulsion with low electrical conductivity
Tem per atur e T [° C] Surfactant concentration γ [-]
Fig. 12: Left: Schematic of the optimum formulation and the influence of parameter variation on the position of 3Φ area
in the T-γ graph, Right: Investigation of phase behavior with a cut through the fish diagram at γ (α = constant)
be approximated as a linear function of temperature [151]. At the transition from 2
̄Φ to 2̄Φ conditions, a phase inversion from an o/w emulsion to a w/o emulsion occurs which induces an abrupt decline in electrical conductivity due to the changing continuous phase from aqueous to organic (Fig. 12, right). Within the 3Φ systems, the conductivity depends on the current continuous phase, which can be either aqueous, organic or the bicontinuous microemulsion. These conductivity measurements can be combined with the commonly used optical method where the phase volume fractions in completely coalesced systems are investigated over temperature using samples with different compositions. A complete characterization of the phase behavior necessitates the preparation of numerous samples and a corresponding experimental effort, which can be reduced if an estimation of the HLD values is performed in advance.
Beside the position of the 3Φ area, the physical properties of the systems and its single phases are important characteristics of the microemulsion systems. The following subsections provide a short overview concerning interfacial phenomena and rheological behavior in microemulsion systems.
3.1.2 Interfacial phenomena
Molecules at the interface of a multiphase system inherit a different energy state than molecules in the bulk phase where the sum of all molecular interactions is neutralized. At the interface the molecules experience a force pulling them towards the bulk phase. The work needed to overcome this effect is defined as the interfacial tension, which depends on the type of molecules and molecular interactions such as van der Waals forces [29]. The free enthalpy of a system is directly proportional to its increase of interfacial area. Therefore, the system tends to minimize its interfacial area, preferring conditions with small surface to volume ratio, which is the reason that spherical droplets or bubbles are formed or a minimization of the interfacial area by complete coalescence of a dispersion occurs. The Gibbs isotherm
(︃ δσ δcs )︃ T = −RT Γ cs (5)
relates the interfacial tension σ to the concentration of surface-active component cs while taking into account
the universal gas constant R, temperature T and interface coverage Γ. As the surfactant concentration in the bulk phase increases, the interfacial tension declines due to the adsorption of surfactant molecules at the interface which disturb the molecular interactions. The slope of the interfacial tension is governed by the current interface coverage in relation to the maximum possible coverage. The number of molecules per interfacial area depends on the molecular structure of the surfactant and the area which is occupied by each molecule. At the critical micelle concentration (CMC) the interface of a is fully covered and the surfactant molecules start to form agglomerates in the bulk phase [29]. The CMC for a given gas/liquid system is a function of the surfactants’ molecular structure such as the number of ethoxylate groups, the hydrocarbon chain length and of temperature. A further increase of surfactant concentration does not reduce the interfacial tension any further, but influences other properties of the liquid phase such as their density and viscosity and the type of micellar agglomerates [53]. Although the CMC is defined for gas/liquid interfaces, a similar behavior occurs in liquid/liquid systems. The minimum amount of surfactant γmin needed to reach the 3Φ conditions is higher than the corresponding
concentration needed to achieve a constant interfacial tension against the oil phase. Therefore, the interfacial tensions above this concentration are not governed by the overall surfactant concentration in the system anymore, but by the temperature, changing solubilities and corresponding phase compositions. The schematic interfacial tensions in microemulsion systems as a function of temperature are depicted in Figure 13 [60, 61]. Within the 2
̄Φ conditions, the interfacial tension steadily declines. Under 3Φ conditions σaq/org undergoes a deep minimum at the optimum formulation, but still is the highest interfacial tension of the system in comparison to the other two interfacial tensions. Within the 2̄Φ conditions the interfacial tension rises with temperature. The interfacial tension σaq/mi has a value of zero at the transition temperature from 2
̄Φ to 3Φ conditions
Tmin, where the aqueous o/w microemulsion phase divides into an aqueous excess phase and the bicontinuous microemulsion phase. The interfacial tension σaq/mithen steadily rises with temperature within the 3Φ interval
as the solubility of the surfactant in water decreases. The inner composition of the microemulsion phase changes from high amounts of water to equal amounts of oil and water at the optimum formulation to high amounts of oil. At Tmax which marks the transition to the 2̄Φ condition, the interfacial tension σaq/mi reaches the same
value as σaq/org and the bicontinuous microemulsion phase vanishes. The interfacial tension σmi/org behaves
exactly contrary since the solubility of surfactant in oil steadily increases.
Interfac ial tens ion σ [N/m] Temperature T [°C] σaq/org σaq/mi σmi/org Tmin Tma 3φ 2φ 2φ
Fig. 13: Schematic interfacial tensions of the respective phases (acc. to [60])
The two interfacial tensions σaq/mi and σmi/org intersect in the middle of the 3Φ area at the optimum
formula-tion. More information on the phase behavior, interfacial tensions and thermodynamics of these systems can be found for example in [60]. The high interfacial tensions to the microemulsion phase at the optimum formulation are one reason for the fast coalescence in the middle of the 3Φ area. However, the sum of interfacial tensions alone cannot explain the fast phase separation in 3Φ systems, because the interfacial tension under 2
̄Φ and 2
̄Φ conditions are higher. Other parameters such as the interface rigidity also play an important role. A rigid surfactant membrane such as cubic liquid crystals requires more energy to deform, which hinders coalescence [3]. The interface rigidity rises with the surfactant concentration at the interface, as was shown amongst others by Paul et al. [108] using oscillating spinning drop measurements. The rigidity was described by Helfrich [47] using the free energy for interfacial area extension dG/dA, the membranes’ elastic modulus KM, the Gaussian
modulus KG, the orthogonal curvature of the amphiphilic membrane a1and a2as well as the natural curvature of the interface a0 which is an equilibrium property:
dG dA = KM 2 (a1+ a2− 2a0) 2+ K Ga1a2. (6)
Acosta et al. [3] proposed a technique to estimate the interface rigidity on the basis of interfacial tension and solubilization using the interfacial tension σaq/mi or σmi/org, the interfacial rigidity Ri and the characteristic
length of the surfactant membrane in the microemulsion phase at optimum formulation ξopt
σaq/mior σmi/org= Ri
4πξ2 opt
. (7)
The value ξoptcan be calculated using the dispersed phase fractions of oil and water within the microemulsion
can be determined with the initial surfactant concentration in the aqueous solution, the initial volume of the aqueous solution in the system, the fraction of surfactant, cosurfactant and hydrophilic linkers in the microemul-sion phase with respect to the total surfactant concentration and the area per molecule of the surfactant [3]. In addition, the presence of additives such as salt or alcohols in these systems can have extensive influence on the interface rigidity. The addition of short-chained alcohols such as propanol to octanol reduces the rigidity of the interfacial membranes and prevents effects such as the development of liquid crystals or metastable gel-like macroemulsion phases, whereas different effects are obtained while using long-chained alcohols such as dode-canol [3]. These studies already indicate that the prediction of the interface rigidity is a challenging task since several not easily accessible system properties need to be known. The application of technical grade surfactants can further complicate the description of interface rigidity, if molecules with different chain length are present at the interface. This can impede tasks such as the measurement of the inner composition of the bicontinuous microemulsion phase. In addition to these interfacial properties of the microemulsion systems, other factors such as the viscosity of the single phases and the emulsion rheology are of importance for dispersion and phase separation.
3.1.3 Single phase and emulsion rheology
This subsection describes the impact of molecular interactions such as the formation of agglomerates on the rheology of the single phases in microemulsion systems. Additionally, influencing factors on emulsion rheology such as the dispersed phase fraction and droplet sizes are illustrated. Similar to the aforementioned interfacial phenomena, the surfactant concentration is one important factor influencing the rheological behavior. Surfactant concentrations below the CMC lead to completely dissociated and strongly hydrated surfactant molecules, which often result in Newtownian rheological behavior and a viscosity that is only slightly elevated in comparison to the pure bulk phase. A rising surfactant concentration towards the CMC induces self-organization of the surfactant molecules in three dimensional networks that can lead to an increase of elastic and viscous properties [29]. Around the CMC, spherical micelles are formed resulting in a decrease of the viscosity due to the depletion of the hydrat shells which reduce the overall hydrodynamically relevant volume of the molecules [29]. To describe the viscosity of spherical micelles in infinite dilution, the Einstein equation can be used [29, 30]. With rising surfactant concentrations, deviations from this equation occur due to effects such as polydispersity of the micelles, hydrodynamic interactions and electroviscous effects. Several models for the description of different micelle types can be found in literature, which often necessitate detailed knowledge of the micellar structures such as their radius, length or density [29]. Surfactant solutions inherit viscoelastic properties, as described amongst others by Rehage and Hoffmann [119]. At high surfactant concentrations in the range of forty weight percent or more, lyotropic liquid crystals can occur which induce high elasticity as well as high dynamic viscosities and normal forces. At the maximum concentration the surfactant solution viscosity can be several magnitudes higher than the viscosity of the pure bulk phase [29]. The rheological behavior of microemulsion phases often is Newtonian or slightly shear thinning at high shear rates [29]. For bicontinuous microemulsions, low viscosities were reported whereas the rheology of o/w and w/o microemulsions is comparable to those of solutions with hard spheres. Microemulsions show elastic properties at high frequencies around f = 103 - 106 Hz. The kinematic viscosity of the microemulsion has a minimum in the middle of the 3Φ area [59]. The emulsion rheology is affected by the droplet size distribution, the dispersed phase volume fraction φ (Fig.14), the viscosities of the single phases, interface characteristics and the effects of pH or charge on the droplet repulsion [12, 89, 99, 102, 141]. Emulsions typically possess shear thinning behavior due to the hydrodynamic stress stretching the droplet shape. The ratio of hydrodynamic to interfacial stress is defined by the capillary number NCa
NCa= ηċγr
σ (8)
with the continuous phase viscosity ηc, shear rate ̇γ, droplet radius r and interfacial tension σ. NCa« 1 occurs if
interfacial forces dominate viscous forces. Most emulsion rheology studies focus on dilute dispersions with φ → 0 and NCa « 1, while there is a lack on expressions to describe the viscous behavior of concentrated emulsions
with φ → 1, especially for NCa» 1 [103]. Dilute dispersions usually possess viscous rheological behavior since
the droplets are separated from each other (Fig. 14).
For very dilute dispersions (φ < 0.01) with unimodal spherical particles, dominating viscous effects and neglected particle interactions, the Einstein equation can again be used to estimate the ratio of effective dispersion viscosity
φ = 0 φcpf≈ 0.58 φcpf≈ 0.64 φ = 1
dilute, viscous concentrated, elastic
compressed
φcpf≈ 0.74 Dispersed phase fraction φ [-]
Fig. 14: Droplets in dilute and dense dispersions [89]
are summarized in Table 1. With increasing dispersed phase fraction, the hydrodynamic interaction between the droplets induced by overlapping flow patterns become more relevant. The rheology of emulsions is influenced by the interfacial rheology of the emulsifier film which surrounds the droplets. If shear is applied to the film, the molecules of the film as well as molecules of the oil and water phase in vicinity are displaced from their initial positions. The developing stress depends on the molecular rearrangement and affects both the interfacial viscosity and the bulk viscosity in case of large deformable droplets. The effect of φ on the viscosity of an emulsion with deformable droplets is more pronounced than in emulsions with non-deformable droplets. The smaller the droplets are, the less deformation is likely and interfacial rheology becomes less relevant [141]. Emulsions can furthermore form an elastic gel network due to interactions of the densely packed emulsion droplets or interactions between the single components. The elasticity results from the work done against the interfacial tension in order to create additional droplet surface area when the shear further deforms the already compressed droplets [141]. Taylor [143] extended Einsteins equation to the case of deformable droplets, assuming no slippage at the liquid/liquid interface and the transmission of tangential and normal stresses from the continuous on the dispersed phase which induces fluid circulation within the droplets [143, 141]. It is valid for φ → 0, NCa → 0. Based on the Taylor equation, Pal [103] provided a model for concentrated emulsions
with the condition of NCa → 0, where K is the viscosity ratio K = ηd/ηc and φcpf is the close packing factor. Table 1: Exemplary emulsion rheology models
Model by Equation Einstein [30] ηef f ηc = 1 + k1φ Taylor [143] ηef f ηc = 1 + 2.5 ηd+0.4ηc ηd+ηc φ Pal [103] ηef f [︁2ηr+5K 2+5K ]︁1.5 = (︂ 1 −φφ cpf )︂−2.5φcpf Krieger + Doughtery [76] ηef f ηc = (︂ 1 −φφ cpf )︂−φcpfk1 Vand + Mooney [91, 145] ηef f ηc = e (︂ k1φ 1−φ/φcpf )︂
This factor is φcpf = 0.64 for spherical droplets [17]. If the droplets are compressed and start to deform,
the factor increases to φcpf = 0.74 [141] (Figure 14). Furthermore, it rises with the polydispersity of the
droplets. For high viscosity ratios, Pals equation simplifies to the power-law function attributed amongst others to Krieger and Doughtery [76], which can also be used to describe systems with high dispersed phase fractions assuming hard spheres. Equations where deformable droplets are assumed might not always be sufficient to describe surfactant systems where interfacial gradients and/or surface viscosity make the droplets appear as hard spheres and, therefore, act more like a solid/liquid suspension. An approach for concentrated suspensions that could also be used for microemulsion systems was performed by Vand [145] and Mooney [91]. In more elaborate emulsion rheology models, the whole drop size distribution is taken into account [89]. Recently, Baldyga et al. [12] developed a model to describe the influence of the drop size on rheology which can be used in combination with Population balance equations (PBE) and Computational Fluid Dynamics (CFD). Pal [102] showed that the polydispersity of emulsions can lead to a minimum of viscosity by mixing a fine emulsion (d ≈ 4 - 12 µm) with large viscosity and a coarse emulsion (d ≈ 25 - 30 µm) with low viscosity in different mass
ratios. Corresponding results were reported by Salager et al. [124] who concluded that the more polydisperse an emulsion is, the less viscous it becomes if all other parameters are constant. This effect might be relevant for 3Φ microemulsion systems if the two dispersed phases inherit different droplet size distributions.
3.2
Identification of the phases in agitated systems
In stirred macroemulsions of liquid 3Φ systems, two phases are dispersed and one phase is the continuous phase. For process understanding and control it is crucial to know the exact type of dispersion that occurs under specific operating conditions. Beside the aforementioned conductivity measurements which help to identify the contin-uous phase, the phase separation after agitation stop and the resulting direction of sedimentation, respectively ascension of the dispersed phases induced by their density differences to the continuous phase might be used to determine the initial dispersion conditions. The occurrence of a third liquid phase can lead to the formation of complex droplets, as was investigated in systems with simple fluids such as two immiscible oils and water by Guzowksi et al. [41]. Figure 15 shows a schematic stability diagram of systems with three different phases, where phase 1 is the ambient phase while the phases 2 and 3 are dispersed. The type of droplet interaction such as multiple emulsions or droplets partly attached to each other (Janus droplets) depends on the interfacial tensions and the corresponding Gibbs free energy of the systems. Conditions where the droplets are not in direct contact occur if the interfacial tension between the two dispersed phases is higher than the sum of inter-facial tensions of the dispersed phases to the continuous phase (σ2,3 > σ1,3 + σ1,2). Furthermore, a complete engulfing of one dispersed phase by the other dispersed phase can occur. In case of σ1,2 > σ1,3 + σ2,3, phase 2 forms the inner droplet of such a multiple emulsion, whereas phase 3 is the inner droplet for σ1,3 > σ1,2 + σ2,3. Partial engulfing occur if non of these conditions are fulfilled. It should be noted that these considerations only include the impact of the interfacial tensions on the dispersion in absence of external fields and mechanical influences.
1
1 2
3
Ratio of interfacial tensions σ1,3 / σ2,3
R at io of int erf ac ia lt ens ions σ1, 2 / σ 2, 3 non-engulfing complete engulfing partial engulfing complete
engulfing complete engulfing:σ1,3 > σ1,2 + σ2,3
phase 3 = inner droplet σ1,2 > σ1,3 + σ2,3
phase 2 = inner droplet non-engulfing: σ2,3 > σ1,3 + σ1,2
Fig. 15: Stability diagram and complex droplets in respect to the interfacial tensions in the absence of external fields
and at mechanical equilibrium (according to [41])
The interfacial tensions significantly affect the dispersion conditions and are an important factor influencing the drop breakage and coalescence phenomena and the resulting droplet size distributions in 2
̄Φ, 2̄Φ and 3Φ system, as is described in the following subsections.
