Inertial impedance of coalescence during collision of liquid drops

Abstract

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories.

Effects of surfactant adsorption on the formation of compound droplets in microfluidic devices

“…10(c) ). 47 From Fig. 9(b) , it is clearly seen that the structures of collected W1/O compound droplets from 2.0% PVA are the same and they are stable, since each compound droplet contains only one W1 droplet inside and there are more surfactants at the O/W2 interface.…”

“…8(b) ). 47 Therefore, both coalescence and rupture can happen in the O phase. For the W2 phases with 0.1% PVA, 0.5% PVA and 2.0% PVA, W1/O compound droplets are formed stably and W1 droplets does not accumulate in the O phase.…”

Surfing of drops on moving liquid–liquid interfaces

“…During the drop impact and rebound, Re might be close to 1 because the film is thick and the inertia of the film fluid should not be ignored. However, according to Sambath et al (2019), the inertia of the film liquids has low effect on the impact dynamics compared to the liquid in the drop. The corresponding 2 dimensional momentum equation for the lubrication film can be reduced to:…”

Local dynamics during thinning and rupture of liquid sheets of power-law fluids

“…2007; Sambath et al. 2019; Anthony, Harris & Basaran 2020), as well as in applications involving bubbles bursting at interfaces (Stewart et al. 2015).…”

“…as liquid sheets or free liquid films, plays a critical role in foam evolution (Cohen-Addad, Höhler & Pitois 2013), drop coalescence and emulsion stability (Loewenberg & Hinch 1996;Yoon et al 2007;Sambath et al 2019;Anthony, Harris & Basaran 2020), as well as in applications involving bubbles bursting at interfaces (Stewart et al 2015). Similarly, the thinning dynamics of films supported by a solid substrate, with one free surface, is crucial in applications as diverse as coating flows (Christodoulou & Scriven 1989;Weinstein & Ruschak 2004), tear film substitutes (Braun 2012), heat transfer (Lohse & Villermaux 2020) and pattern formation (Mukherjee & Sharma 2015).…”