Flow of two immiscible fluids in a periodically constricted tube: Transitions to stratified, segmented, churn, spray, or segregated flow

Droplet microfluidics provides a versatile tool for measuring interfacial tensions between two immiscible fluids owing to its abilities of fast response, enhanced throughput, portability and easy manipulations of fluid compositions, comparing to conventional techniques. Purely homogeneous extension in the microfluidic device is desirable to measure the interfacial tension because the flow field enables symmetric droplet deformation along the outflow direction. To do so, we designed a microfluidic device consisting of a droplet production region to first generate emulsion droplets at a flow-focusing area. The droplets are then trapped at a stagnation point in the cross junction area, subsequently being stretched along the outflow direction under the extensional flow. These droplets in the device are either confined or unconfined in the channel walls depending on the channel height, which yields different droplet deformations. To calculate the interfacial tension for confined and unconfined droplet cases, quasi-static 2D Darcy approximation model and quasi-static 3D small deformation model are used. For the confined droplet case under the extensional flow, an effective viscosity of the two immiscible fluids, accounting for the viscosity ratio of continuous and dispersed phases, captures the droplet deformation well. However, the 2D model is limited to the case where the droplet is confined in the channel walls and deforms two-dimensionally. For the unconfined droplet case, the 3D model provides more robust estimates than the 2D model. We demonstrate that both 2D and 3D models provide good interfacial tension measurements under quasi-static extensional flows in comparison with the conventional pendant drop method.

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Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽

10.1515/anly-2019-0049 ◽

2020 ◽

Vol 40 (3) ◽

pp. 127-150

Author(s):

Tania Biswas ◽

Sheetal Dharmatti ◽

Manil T. Mohan

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Stokes Equations ◽

Minimum Principle ◽

Immiscible Fluids ◽

Second Order ◽

Navier Stokes ◽

Distributed Optimal Control ◽

Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

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Radial flow of two immiscible fluids: analytical solutions and bifurcations

Journal of Fluid Mechanics ◽

10.1017/s0022112002003129 ◽

2003 ◽

Vol 477 ◽

Cited By ~ 2

Author(s):

VAKHTANG PUTKARADZE

Keyword(s):

Analytical Solutions ◽

Radial Flow ◽

Immiscible Fluids

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Comparison principles for free-surface flows with gravity

Journal of Fluid Mechanics ◽

10.1017/s0022112091000770 ◽

1991 ◽

Vol 230 ◽

pp. 231-243 ◽

Cited By ~ 3

Author(s):

Walter Craig ◽

Peter Sternberg

Keyword(s):

Solitary Waves ◽

Finite Depth ◽

Free Surface Flows ◽

Immiscible Fluids ◽

Steady Flows ◽

Two Dimensional ◽

Surface Flows ◽

Ship Hulls ◽

Geometrical Information ◽

Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

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