Spout States in the Selective Withdrawal of Immiscible Fluids through a Nozzle Suspended above a Two-Fluid Interface

Abstract

In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities nu(upper) and nu(lower) = lambda nu(upper). At low withdrawal rates, the interface gently deforms into a hump. At a transition withdrawal rate, a spout of the lower fluid becomes entrained with the flow of the upper one into the nozzle. When lambda=0.005, the spouts at the transition are very thin with features that are over an order of magnitude smaller than any observed in the humps. When lambda=20, there is an intricate pattern of hysteresis and a spout appears which is qualitatively different from those seen at lower lambda. No corresponding qualitative difference is seen in the hump shapes.

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 Reported initially by Nagel et al [251], the bottom liquid, which is going to be the dispersed phase, is withdrawn just from the interface by a tube where the continuous phase liquid is on top (Fig.…”

Viscous Withdrawal of Miscible Liquid Layers

“…Analogous steady-state entrained structures arise in drainage flows [2,3], oil extraction [4], as well as viscous withdrawal of immiscible liquid layers, which occur in microfluidics [5], fiber coating [6] and encapsulation of biological cells [7]. Recent works exploring the connections between thermodynamic phase transitions and the topology transition that takes place at the onset of entrainment have noted that, in order for the entrained structure to be completely isolated from the large-scale flow dynamics, the shape of its base must be a power-law cusp [2,8,9,10]. Intriguingly, experiments [11,12] on miscible entrainment also seem to show a robust cusp-like shape at the base of long-lived tendrils (see Fig.…”

“…We solve for z s , α and B analytically as follows. Since z s should be be near the base of the tendril, we approximate R(z) by the upstream shape R s (8) and find that z s ≈ 0.609 ℓ z , α ≈ 0.052, and B ≈ 1.18 S. We can solve for the appropriate tendril solution numerically by varying the dimensionless entrainment coefficient c 0 so that R(z) and its derivative merge smoothly onto R I (z). Fig.…”

“…The logarithmic dependence ultimately results from the decaying exponential shape of the tendril at z ∼ ℓ z (8). How this emerges is complicated because c 0 is essentially determined by demanding R ∞ (z) merge onto R s (z) through a region where all the terms in the governing equation (5) are equally important.…”

“…However, recent particle-image-velocimetry (PIV) measurements within the base of an anchored tendril reveal a stagnation-point velocity field, one more appropriately described by a characteristic strain rate E (s −1 ) instead of a characteristic velocity scale [15]. Viscous withdrawal experiments on immiscible layers suggest how an interior stagnation point can arise [8]. When the effect of The dark vertical line on the left is a thermocouple [13].…”