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.

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The phase-field method coupled with the Navier-Stokes equations is a rather new approach for scale-resolving numerical simulation of interfacial two-phase flows. The intention is to implement it as finite-volume method in the open source library for computational continuum mechanics OpenFOAM and make it freely available. An overview on the governing equations is given and the numerical method is shortly discussed. The focus is on application and validation of the code for some fundamental wetting phenomena, namely the capillary rise in a narrow channel and the spreading of a droplet on a flat surface, which is chemically homogeneous or regularly patterned. The numerical results on static meshes agree well with analytical solutions and experimental/numerical results from literature. Also, first 3D finite-volume simulations with adaptive mesh refinement near the interface are presented as a key element to achieve CPU-time efficient simulations.

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Results of direct numerical simulation (DNS) for Rayleigh–Bénard convection for the Prandtl number $\hbox{\it Pr}\,{=}\,0.025$ are used to show some peculiarities of turbulent natural convection for low-Prandtl-number fluids. Simulations for this flow at sufficiently large Rayleigh numbers became feasible only recently because this flow requires the resolution of very small velocity scales and the recording of long-wave structures for the slow changes in the convective temperature field. The results are used to analyse standard turbulent heat flux models. The analysis for a model based on the Reynolds analogy indicates strong deficiencies of such turbulent heat flux models for low-Prandtl-number fluids. Turbulence models for buoyant flows which are not based on the Reynolds analogy include also the transport equation for the temperature variance $\overline{\theta^2}$. Detailed analysis of this transport equation and of the transport equation for the temperature variance dissipation rate is performed using DNS data. The results show the relevance of the turbulent diffusion terms and strong quantitative and qualitative deficiencies of standard models for turbulent diffusion of the temperature variance $\overline{\theta^2}$ and for the turbulent diffusion of the temperature variance dissipation rate $\epsilon_\theta$. Using the two-point correlation technique, statistical turbulence models for the turbulent diffusion of the temperature variance and for the turbulent diffusion of the temperature variance dissipation rate are proposed. These new models explicitly consider the molecular fluid properties. The new models reproduce the DNS results for $\hbox{\it Pr}\,{=}\,0.025$ and $\hbox{\it Pr}\,{=}\,0.71$ sufficiently well.

Microfluidic devices often contain several phases. Their design can be supported by interface-resolving numerical simulations, requiring accurate methods and validated computer codes. Especially challenging are submillimetre air bubbles in water due to their large density contrast and dominance of surface tension. Here, we evaluate two numerical methods implemented in OpenFOAM ® , namely the standard solver interFoam with an algebraic volume-of-fluid method relying on a sharp interface representation and phaseFieldFoam relying on the phase-field method with diffuse interface representation. For a circular bubble in static equilibrium, we explore the impacts of uniform grid resolution and bubble size on bubble shape, mass conservation, pressure jump and spurious currents. While the standard interFoam solver exhibits excellent mass conservation with errors below 0.1% on fine grids, it lacks the accuracy to predict reasonable physics for a bubble in microfluidic systems. At higher resolution, large spurious currents significantly displace and deform the bubble, which is oscillating with resolution dependent mode and frequency. Furthermore, the pressure jump is consistently underestimated by more than 10%. The solver phaseFieldFoam suffers from much larger mass losses of up to 2%, which decrease as the ratio between interface thickness and bubble diameter decreases provided the diffuse interface region is adequately resolved. Spurious currents are very low and the bubble remains circular preserving its initial position with an error in pressure jump below 1%.