7.3 Results and discussion
7.3.2 Effect of surface wettability on droplet dynamics
The droplet flow past a solid obstruction includes a direct contact of obstruction surface and droplet fluid. Therefore, the surface characteristics of the obstruction largely affect the dynamics of droplet when it crosses past the obstruction. Thus, to investigate the droplet dynamics, various wetting conditions of the solid walls of the channel and the surface of the solid obstruction have been considered in the present section. Basically, wetting or wettability is the property of the surface which defines the ability of fluid to spread over the solid surface. In nature, different types of wetting patterns are found, uniformly hydrophobic (non-wetting) and hydrophilic (wetting) are two of them. In the case of uniformly hydrophobic surface, the surface tries to repel the mass of fluid and in the case of hydrophilic wettability, the surface tries to attract and makes bond with the mass of fluid. However, it is reported in
132
Analysis of Deformation and Breakup of a Three-dimensional Droplet Past a Solid Spherical Obstruction
Time=3.5 Time=4 Time=4.5 Time=5
Time=6 Time=6.5 Time=7 Time=7.5
Figure 7.9: The y−z sliced view (at mid plane of x) of the time evolution of the droplet past a spherical obstruction at Ca=0.407, M=1 andθ = 60◦
Time=4.5 Time=5.5 Time=6 Time=6.5
Figure 7.10: The isosurface plots of the time evolution of the droplet past a spherical obstruction at Ca=0.407, M=1 and θ= 90◦
7.3 Results and discussion 133 Time=5 Time=5.5 Time=6 Time=6.5 Time=7
Figure 7.11: The y−z sliced view (at mid plane of x) of the time evolution of the droplet past a spherical obstruction at Ca=0.407, M=1 and θ = 90◦
literature that the dynamics of wetting surfaces are more complicated compared to non-wetting surfaces.
g2w
Vf
-0.08 -0.04 0 0.04 0.08 0.12 0
0.2 0.4 0.6 0.8 1
Figure 7.12: Effect of surface wettability on fraction of deposited volume on the upper surface of obstruction at Ca=0.407 and obstruction radius, r=40 lu
The dynamics of the droplet in hydrophobic surface of obstruction are well ex- plained in the section 7.3.1; results shown in Figs. 7.3-7.4. The discussions are herein focused on the hydrophilic surface of the solid obstruction. As illustrated in Figs. 7.8-7.9, when there is head to head impact of the droplet with the obstruction, the surface attracts most of the fluid to adhere on it owing to its high adhesive prop- erty. During this process, a continuous phase fluid is entrapped when the droplet
134
Analysis of Deformation and Breakup of a Three-dimensional Droplet Past a Solid Spherical Obstruction
Time=4 Time=4.5 Time=5 Time=5.5 Time=6.5 Time=7.5
(a)
Time=5 Time=6 Time=7 Time=10 Time=12 Time=13
(b)
Figure 7.13: The isosurface plots of the time evolution of the droplet past a spherical obstruction at Ca=0.407, M=1 and θ = 60◦ for spherical obstruction radius, (a) r=30 lu, (b) r=50 lu
makes an envelope over the obstruction. However, the combined effect of adhesion and gravity tries to make the droplet layer thinner and hence, the droplet fluid layer breaks at the top surface of the obstruction. It is observed that the high philicity of the surface creates difficulty for the droplet to flow down on the surface and hence, it completely wets the surface of the obstruction. When the droplet fluid moves down the obstruction surface, it assumes a bullet like shape and then the fluid, owing to gravity, elongates further whereas adhesion tries to get the fluid attached on the surface. The investigation also shows that the deposition of the droplet fluid, in the case of a hydrophobic wetting surface, is brought about on the upper surface of
7.3 Results and discussion 135 Time=4 Time=4.5 Time=5 Time=5.5 Time=6.5 Time=7.5
(a)
Time=5 Time=6 Time=7 Time=10 Time=12 Time=13
(b)
Figure 7.14: The y−z sliced view (at mid plane of x) of the time evolution of the droplet past a spherical obstruction at Ca=0.407, M=1 and θ = 60◦ for spherical obstruction radius, (a) r=30 lu, (b) r=50 lu
surface and more on the downward side of the obstruction. In the case of the neutral wetting surface (Figs. 7.10-7.11), it is found that the deposition of the droplet is only on the downward side of the obstruction. We further conducted simulations over a wide range of the contact angles and found that the location of deposition is changed from the upward to downward along the cylinder surface with the decrease in contact angle. This happens as the wetting droplet tends to get attached to the surface tightly, and the thin layer of liquid deposition is dragged away by the gravity force. The effect of surface wettability on the fraction of the deposited volume of droplet fluid on the upper surface of the obstruction has been illustrated in Fig.
7.12. The results are shown at Ca=0.407 and r=40 lu for various surface wettabil-
136
Analysis of Deformation and Breakup of a Three-dimensional Droplet Past a Solid Spherical Obstruction
r
Vf
25 30 35 40 45 50 55 60 65 0
1 2 3 4 5
Figure 7.15: Effect of obstruction size (i.e., radius, r) on fraction of deposited volume on the upper surface of obstruction at Ca=0.407 and θ= 60◦
ities. The study shows that the fraction of deposited volume of droplet fluid first decreases (in the case of hydrophilic wettability) and then increases (in the case of hydrophilic wettability) with the increasing value of θ. It is interesting to see that the deposition of droplet fluid on the upper surface of the obstruction is found to be zero in the case of neutral wetting (θ= 0◦).