Generally, filtrations can be distinguished according to their applied flow direction between dead-end and crossflow process procedures, where dead-end filtration describes a method based on pressure differences between rough and pure medium and vertical flow directions to filter media. In contrast, crossflow filtration is characterized by an additional parallel movement of the rough media along the filter surface [11].
Regardless of place and flow direction of particle retention, filtrations can be described by Darcy’s law (see Equation 2-1), which is a basic application for the change in volume flow (𝑞) in dependence on filter area (𝐴), viscosity of the filtered medium (𝜂𝐿), filter resistance (𝑅ℎ) and pressure difference (∆𝑝) [12,13]. Because particle retention is influenced by different filtration operations, the mechanical effect of pore or capillary flow caused by driving forces must be considered to overcome a flow resistance for the fluid phase (see Equation 2-2) [14]. Depending on the location of particle retention an increase in filter resistance can be observed [12].
𝑞 =𝜕𝑉𝐹,𝐴
Thus, Equation 2-2 describes the dependence on filtered volume (𝑉𝐹,𝐴) over time (𝑡), filter surface (𝐴) and flow coefficient (𝑘𝐹𝐶). Flow coefficient is crucial for determining the liquid flow-through amount, which is dependent on layer thickness, type and structure of filter medium, flow properties of liquid and pressure difference (∆𝑝) [12].
Exponent 𝑛 assumes different values to specific retention mechanisms in operation or changes in the internal structure of the filtering layer. A distinction of the formulas can be determined with regard to process design on pressure or volume flow [15]. In the
food industry, filtration processes often operate at constant filtrate volume flow, in order to ensure production scheduling.
Due to occurring retention effects, various model concepts were developed illustrating these different filtration operations. A fundamental distinction is made between surface and depth filtration [16]. Furthermore, cake, sieve and crossflow filtration can be named as special cases and connections between surface and depth filtration [11,17].
Simplified mathematical model conceptions on filtration processes are shown in Figure 2-1, which have been developed to predict the effectiveness and process performance of applied practical filtrations [18].
2.1.1 Depth filtration
During depth filtration, most separation takes place inside the filter media. Particle removal from unfiltered media is effected by the flow of a suspension through a medium composed of granular or fibrous nature [19]. A substantial proportion of solid particles (𝑐, compare Figure 2-1) that might pass through because of their geometric size are retained in the filter media [17]. This deposition in the interior of the filter causes an accumulation of deposited particles within the medium, which results in continuous changes to the filter media structure and affects the rate and flow resistance of filtration [20]. Furthermore, surface blockages of filter material must be avoided to ensure the maintenance of the filtration process.
Particle retention is achieved by means of holding by adhesive forces influenced by various transport mechanisms inside the filter like sieving, interception, inertia, sedimentation, diffusion, charge interactions or hydrodynamic interactions [11].
Regarding equation 2-2, depth filtration can be described using an exponent 𝑛 between 0–2, where 1 describes an intermediate blocking and 3/2 a standard blocking procedure [12,15].
2.1.2 Surface filtration
In contrast, surface filtration is effected by mechanical particle separation on the surface of a filter media. Due to retained particle properties and flow direction three types can be distinguished [16].
Sieve or blockage filtration describes a process whereby solid particles are retained on the filter media surface because of their geometric size. This is influenced by an exponential pressure rise (𝑝, compare Figure 2-1) at a constant volume flow (𝑉̇).
Complete blocking can be described with equation 2-2 using an exponent of 2 [11].
Figure 2-1: Model conceptions on filtration operations, modified according to [11,17,16]. A general distinction can be made between surface and depth filtration. Depth filtration is marked by an increase in solid particles (𝒄) with rising volume (𝑽), due to an exhaustion of absorption capacity of the filter material. Sieve and cake filtration are distinguished via a characteristic pressure rise (𝒑) at a constant volume flow (𝑽̇). In the case of crossflow filtration, initially a reduction in volume flow (𝑽̇) due to an accumulation of solids on the filter material can be observed, followed by a stationary phase with nearly no change in filtered volume [17].
Cake filtration is a case of surface filtration where solids are retained on the filter media surface with the help of filter aids (compare Figure 2-1) [17]. The filtered volume is influenced by filter cake height, filter area, dynamic fluid viscosity and resulting dynamic filter resistance [11,17]. Retention at the beginning of filtration is determined by the filter media pore size. Over time finer solid particles can be removed from suspension because of sufficiently high loading of suspended particles and filter aids, followed by a “bridging” across the filter pores. Ideally, filter cake resistance increases
in proportion to its thickness, resulting in a constant flow rate (𝑽̇). The surface filtration with constant pressure rise could be described using the exponent 0 [11].
Crossflow filtration is a further feature of surface filtration, where a crossflow suppresses the formation of a filter cake on filter media (compare Figure 2-1). Total exemption of particles on filter media surface cannot be guaranteed, which is why a stationary particle layer is desired [16]. As a result of a pressure difference (transmembrane pressure) between the rough and pure side, permeate is removed from the filter and retentate is further circulated [16,17]. This mechanism leads to a concentration of retentate and can be performed as long as the liquid remains pumpable [11].
Surface and depth filtration provide process engineering basics for diatomaceous earth (DE) and membrane filtration, which are mostly applied in the brewing industry. These types of filtration are mainly distinguished by their filter plants as well as the usage of different filter media (see Figure 2-2). Besides filter equipment, process management as well as filterability of beer have a great impact on beer filtration. Because of this multiplicity of influencing factors, beer filtration will be considered in more detail in the next chapters.