Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Abstract

This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volumeof-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier-Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

“…The first two tasks, collectively denoted multi-phase flow methods, have been studied computationally in a remarkable volume of work, as summarized in a recent review by Wörner [68]. Prominent surveys for each of the main families of methods are (Level-set methods) Sethian & Smereka [55], (Front-tracking) Tryggvason et al [66], (Volume fraction methods) Scardovelli & Zaleski [54] and (Phase field methods) Anderson et al [2].…”

Spurious Current Suppression in VOF-CSF Simulation of Slug Flow through Small Channels

“…Liquid-gas slug flow in small capillary tubes and microchannels is important in heat transfer applications [1][2][3][4], micro-reaction systems [5,6], and microfluidic control [7,8]. Bretherton [9] pioneered theoretical analysis of single bubble motion in a rigid round channel under a lubrication assumption that at low Capillary numbers, viscous forces only affect the static interface profile near the wall.…”

“…Recently, Magnini et al [23,24] investigated microchannel flow boiling in this regime, and found evaporation from the liquid film to be the dominant mechanism of heat transfer. More detailed accounts of the development of theoretical and numerical models can be found in recent review articles on the subject [8,25,26]. Most prior numerical studies, as summarized by Talimi et al [26], were limited to Ca > ~0.005, although flow behavior at smaller…”

“…The continuum surface force (CSF) model [27] is one of the most popular methods for numerical treatment of surface tension forces, and is implemented in commercial computational fluid dynamics software packages [8,25,26]; however, it also induces unphysical spurious currents that hinder numerical investigation under small Capillary number conditions [28]. A large body of research has focused on developing methods to reduce these spurious currents (see review by Wörner [8]).…”

“…A large body of research has focused on developing methods to reduce these spurious currents (see review by Wörner [8]). Spurious currents are particularly limiting in the simulation of slug flow at small Capillary numbers.…”