Force Balance at the Transition from Selective Withdrawal to Viscous Entrainment

Abstract

We simulate the evolution of the steady-state interface in the selective withdrawal regime. Selective withdrawal ends when the upward pull exerted by the viscous flow in the withdrawing liquid layer overcomes the downward force due to surface tension. The lower-layer dynamics are unimportant. The dominant contribution to the surface-tension force comes from the large area where the interface is weakly deflected, instead of the small area where the surface is most distorted. A scaling estimate based on this idea yields results that agree quantitatively with both simulations and previous experiments.

Selective withdrawal of polymer solutions: Experiments

“…In all cases, there is a critical condition, reached by increasing Q or decreasing h, where the tip ruptures into a jet. This scenario was later confirmed by the numerical computations of Blanchette et al [22]. The existence of a critical condition is consistent with the computational result of Lister [4] for equal-viscosity fluids.…”

“…To reconcile this with the liquid-liquid results [1,5,22], we speculate that when the viscosity ratio becomes sufficiently small, the critical flow rate will increase without bound. The critical condition in selective withdrawal can also be likened to the burst of a drop or bubble in extensional flow [23].…”

Local interfacial stability near a zero vorticity point

“…Cohen & Nagel (2002), Blanchette & Zhang (2009). Yet another instance occurs when a liquid jet enters a coaxially and more rapidly flowing immiscible liquid.…”

Porous polymer particles—A comprehensive guide to synthesis, characterization, functionalization and applications

“…Another technique waiting to be used for porous particle production is called selective withdrawal [251][252][253][254][255]. Reported initially by Nagel et al [251], the bottom liquid, which is going to be the dispersed phase, is withdrawn just from the interface by a tube where the continuous phase liquid is on top (Fig.…”