Numerical simulations of self-propelled jumping upon drop coalescence on non-wetting surfaces

Abstract

Coalescing drops spontaneously jump out of plane on a variety of biological and synthetic superhydrophobic surfaces, with potential applications ranging from self-cleaning materials to self-sustained condensers. To investigate the mechanism of self-propelled jumping, we report three-dimensional phase-field simulations of two identical spherical drops coalescing on a flat surface with a contact angle of 180 • . The numerical simulations capture the spontaneous jumping process, which follows the capillary-inertial scaling. The out-of-plane directionality is shown to result from the counter-action of the substrate to the impingement of the liquid bridge between the coalescing drops. A viscous cutoff to the capillary-inertial velocity scaling is identified when the Ohnesorge number of the initial drops is around 0.1, but the corresponding viscous cutoff radius is too small to be tested experimentally. Compared to experiments on both superhydrophobic and Leidenfrost surfaces, our simulations accurately predict the nearly constant jumping velocity of around 0.2 when scaled by the capillary-inertial velocity. By comparing the simulated drop coalescence processes with and without the substrate, we attribute this low non-dimensional velocity to the substrate intercepting only a small fraction of the expanding liquid bridge.

Dropwise condensation heat transfer process optimisation on superhydrophobic surfaces using a multi-disciplinary approach

“…The validation mainly focuses on the evaluation on the maximum velocity of merged droplet upon the coalescence of two symmetrical droplets with initial radius r = 75 m and static contact angle s = 180 . This was the only contact angle considered in [12].The resulting process of the 3D coalescence is depicted in Figure 4 and is in agreement with that one of Liu et al [12]. After the coalescence is originated by the overlapping interfaces, a liquid bridge develops upon coalescence with an expanding bridge reaching the surface at around 0.00007s, at which point the merged droplet experiences an upward motion.…”

“…Coalescence-induced jumping phenomena occur on superhydrophobic surfaces but within a small range of initial droplet radii. Recent interest in these phenomena has led to the influence of the droplets radii on the resulting jumping velocity to be explored [3,[8][9][10][11][12]. However, previous analysis on coalescence-induced jumping droplets focused only a limited range of contact angles and droplet radius [10][11][12].…”

“…However, previous analysis on coalescence-induced jumping droplets focused only a limited range of contact angles and droplet radius [10][11][12]. While Liu et al [12] assumed only the contact angle of 180 o ; Cheng et al [13] proposed a wider range in their numerical investigations. In this study we investigate such jumping phenomena both experimentally and numerically.…”

“…= 0 for gas, = 1 for liquid. Accordingly, gradients of the phase fraction are encountered only in the region of the interface as represented in Fig Two immiscible fluids are considered as one effective fluid throughout the domain, the physical properties of which are calculated as weighted averages based on the distribution of the liquid volume fraction,:where l and g are the liquid and gas densities, whereas µ l and µ g are the liquid and gas viscosities respectively.In the present study a modified approach similar to the one proposed in [ The VτF domain consists of the [0, 2600 m] 3 block discretised with around 1.3M cuboid elements as indicated in Figure 3 with: (i) no-slip imposed on the bottom, left and right walls for velocity, (ii) zero dynamic pressure and (iii) zero gradient on left and right walls with constant static angle equals to s on the bottom wall for phase fraction.The VOF numerical methodology is validated and tested against the results published by Liu et al [12]. The validation mainly focuses on the evaluation on the maximum velocity of merged droplet upon the coalescence of two symmetrical droplets with initial radius r = 75 m and static contact angle s = 180 .…”

“…As identified by Liu Et al. [12] and based on these figures, the jumping process upon coalescence can be approximately divided into four stages: (I) expansion of the liquid bridge between the coalescing droplets, till approximately 0.00007s; (II) acceleration of the merged droplet on the surface, eventually reaching a maximum velocity at 0.00023s; (III) detachment of the merged droplet from the surface, till a complete departure at 0.000255s; and (IV) deceleration of the departed drop in air, where the oscillating drop relaxes towards the ultimate equilibrium shape of a sphere.The jumping velocity j is extracted from the curve and is found to be 0.210 m/s and is in very good agreement with the value 0.211 m/s found Liu Et al. [12].…”