Numerical Investigation on the Effects of a Precursor Wetting Film on the Displacement of Two Immiscible Phases Along a Channel

Abstract

A set of numerical experiments has been conducted to study the effect of a precursor fluid layer on the motion of two phase system in a channel. This system is characterized by coupled CahnHillard and Navier-Stokes system together with slip boundary conditions. The solution of the governing equation involves first the solution of Cahn-Hillard equation with semi-implicit and Mixed finite element discritization with a convex splitting scheme. The Navier-Stokes equations are then solved with a P2-P0 mixed finite element method. Three cases have been investigated; in the first the effect of different wettability scenarios with no precursor layer has been investigated. In the second scenario, the effect of the precursor layer for different wettability conditions is investigated. In the third case, the effect of the thickness of the precursor layer is investigated. It is found that, wettability conditions have considerable effect on the flow of the considered two-phase system. Furthermore the existence of the precursor layer has additional influence on the breakthrough of the phases.

Flow split characterization of two immiscible phases with different wettability scenarios: A numerical investigation using a coupled Cahn–Hilliard and Navier–Stokes system

“…Since we solve . The used framework is well documented and several verification examples can be found in Gao and Wang [21] and in Bao et al [26,27]. These include: 1) two phase Couette flow in a channel, 2) coalescence of two droplets, 3) evolution of contact line over curved surface, and 4) droplet displacement under shear flow, which provides confidence in the modeling approach.…”

“…The numerical solution of the governing equations describing the flow of multiphase systems has been the topic for extensive research because of its practical importance [e.g., [22][23][24][25]. More details about the current modeling approach can be found in Bao et al [26,27]. For the sake of completion, however, we highlight the essence of the numerical scheme used in this work.…”

A Unified, One Fluid Model for the Drag of Fluid and Solid Dispersals by Permeate Flux towards a Membrane Surface

“…The problem will even be more complicated should the object be another fluid immiscible with the surrounding fluid. The governing equations that are applicable to all phases represent conservation laws of mass and momentum [ 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. As mentioned, these equations can apply to all fluid regions augmented with equations at the interface between phases.…”

“…In the context of this work, we adopt the assumption of no jump in the shear stress on the interface. Our motive in this stems from the sharp interface limit in which the interface represents a surface of discontinuity deprived from any physical properties [ 26 , 27 ]. Such an assumption, together with the sharp interface limit argument, implies the following two points—namely, (1) no jump in the velocity at the interface, (2) no jump in the shear stress along the interface as long as there is no gradient in the interfacial tension.…”

A multicontinuum approach for the problem of filtration of oily‐water systems across thin flat membranes: II. Validation and examples

“…The generated shear stresses at the membrane surface, due to the crossflow velocity, CFV, tend to sweep off accumulated oil droplets. Several modeling approaches have been proposed to investigate the permeation mechanisms across the membrane . More details about these models can be found in the first part of this work .…”