Flow Patterns

Drop impact onto a thin pre-existing liquid layer on the wall may lead to different flow patterns depending on the drop impacting velocity. An experimental study on the impact of a train of drops onto a solid surface conducted by Yarin and Weiss [135]

revealed two different outcomes. At lower impact velocities the drops deform into a thin lamella spreading over the wall with a rim formed at its edge, whereas if the impact velocities are higher and the surface is wetted the lamella deforms into an uprising crown-like thin liquid sheet with a rim at its top edge ejecting a number of secondary droplets. The crown formation is a consequence of the momentum jump in the region where the fast-moving liquid in the lamella meets the liquid in the stationary layer. It is referred to as splashing and this scenario is shown on the photograph in Fig. 1.1 from Cossali et al. [17], which clearly resolves the unstable

free rim where small finger-like jets are generated from bending perturbations of the rim before braking up by surface tension and enabling secondary droplets of different sizes to be detached from their tips. The free rim on the top of the crown propagates with the velocity determined by the surface tension, the liquid density and the thickness of the crown wall (Taylor [111]).

Figure 1.1: Drop splashing, from Cossali et al. [17]

Neglecting viscous losses at the instance of the impact Yarin and Weiss [135]

found an asymptotic solution to the flow in a thin liquid layer and derived an analytical model for the dimensionless crown radius in the following form

R_cr =β

√

(t−τ), (1.12)

applicable to single-drop impacts, whereβdepends on the impact velocity, the initial drop diameter and the thickness of the pre-existing liquid film andτ is the time shift.

The critical conditions at which splashing occurs is termed the splashing thresh-old. The threshold velocity for splashing is found by Yarin and Weiss [135] to be a function only of physical properties, indicating the fact that the crown ejection has its origin in the spreading lamella long after the actual time instance of the impact.

In single-drop impacts onto a thin liquid film an equivalent parameter characterizing the splashing threshold is the so-called K-parameter introduced by Cossali et al. [17]

K = We

Oh^0.4, (1.13)

which depends on the relative film thickness and on surface roughness for very thin liquid films. A higher roughness affects the flow in the thin region in the vicinity of the surface, triggering the splash at lower impact velocities and therefore the splashing threshold decreases with increasing surface roughness.

In the initial moments of the impact at higher velocities the formation of a small-scale radial jet in the region of the neck between the drop and the liquid layer may be observed. This jetting results from squeezing the liquid of the oncoming drop and pushing it outward with the speed that can be an order of magnitude higher than the drop impact velocity. Another phenomenon observed in the initial moments of impact is the air encapsulation, pertinent also to drop collisions with

the dry substrate or in binary drop collisions. An air lens may be entrapped between the oncoming drop and the impacting target which evolves into a toroidal shape and finally leads to formation of one or several small air bubbles.

In impacts onto a dry surface the possible flow patterns are much more diverse.

In experiments done by Rioboo et al. [91] several different outcomes were observed.

In Fig. 1.2 six horizontal lines represent time sequences of the flow regimes after drop impact termed as deposition, prompt splash, corona splash, receding break-up, partial rebound and complete rebound, respectively.

Figure 1.2: Drop impact onto a dry wall, from Rioboo et al. [91]

In the deposition regime the lamella stays spread over the surface. The spreading ratio is proportional to the square root of time in the initial phase, whereas the dependence on the liquid properties becomes pronounced only at later stages of the spreading. Prompt splash is characterized by higher impact velocities and increased surface roughness resulting in detachment of small-sized droplets from the edge of the spreading lamella. The lamella stays spread over the surface as in the previous case. If the surface tension is decreased, the lamella may detach from the wall and crown is formed similar to the drop impact onto a liquid layer. The resulting flow pattern is the corona splash and the formation of the crown is triggered by surface roughness.

An important issue in drop impact on a surface is the surface capillarity, repre-sented by the contact angle which develops between the impacting dry surface and

the drop surface. In many industrial processes, speed and uniformity of wetting must be controlled in such manner that overrunning and entrainment of the fluid, commonly gas, being displaced by the advancing liquid must be avoided. In impacts at higher velocities, after the lamella has reached the maximum spreading ratio it begins to recede driven mainly by the surface tension and the surface wettability.

According to the capability of a given surface to hold the drop, the surface is said to be hydrophilic (with a contact angle lower than 90^◦), or hydrophobic (with a contact angle higher than 90^◦). If the surface is hydrophobic with higher values of the contact angle, the receding break-up flow pattern develops. The value of the contact angle depends on numerous parameters, some of which are the capillary and Weber numbers, ratios of densities and viscosities of lighter and heavier fluids (gas and liquid), the speed of the contact line, the material and the state of the target surface (ˇSikalo et al. [107]). Moreover, the static contact angle is not single valued and depends on the history of the system. The value of the contact angle may differ according to whether the contact line was brought to rest by wetting or de-wetting, i.e. by advancing or receding of the liquid. This behavior is known as the contact angle hysteresis. Since even at very small distances from the contact line, the free surface may be sharply curved and measured contact angles depend on the length scales resolvable by experimental equipment, the measured contact angle is called the apparent contact angle.

During the spreading motion of the lamella, the initial kinetic energy of the impacting drop is partly dissipated due to viscosity and partly converted into the surface energy due to the increased free-surface area. The surface energy of the lamella at the beginning of the receding motion may be sufficiently large to produce the receding velocity of the lamella high enough to result in its collapse around the impact point and push the liquid upward in the form of a rising liquid column similar to the Worthington jet. The uprising jet may stay connected to the surface and eject one or more droplets, which is the partial rebound, or completely detach from the surface as in the complete rebound. Rioboo et al. [91] have found that the onset of the different flow regimes cannot be characterized solely with the dimensionless groups outlined in Section 1.2.1, indicating the importance of the wettability and surface roughness in drop impacts onto a dry wall.

In binary drop collisions the flow patterns are rather similar to those en-countered in drop impact onto a dry wall. The experimental study of Willis and Orme [130] performed with binary drop collisions in vacuum revealed two character-istic flow regimes occurring after the collision, the sequence of which is depicted in Fig. 1.3. Those were termed the oblate (the left column in Fig. 1.3) and the prolate flow regime (the right column in Fig. 1.3).

The deformation of the drops after the collision in the oblate regime is charac-terized by stretching and formation of an extremely thin liquid sheet bounded by a rim at its edge. Similar to the drop impact onto a dry wall the kinetic energy of the colliding drops is lost into heat by viscous actions and simultaneously converted into the surface energy. After reaching the maximum spreading, the receding prolate motion begins driven by surface tension, in which the liquid sheet collapses forming

Figure 1.3: Normal binary drop collision, from Willis and Orme [130]

an almost spherical shape followed by a prolate elongation. Depending on the im-pact parameters, the separation of the liquid may occur in either regimes, referred to as the shattering collision, if it occurs during the oblate regime and the reflexive separation, if occurred within the prolate regime. It is interesting to note that the normal axisymmetric collision of two drops may be represented as the impact of a single drop onto a plane of symmetry, which is similar to the initial phase of the impact onto a dry wall if the viscous effects near the wall can be neglected.