Elsevier

Journal of Computational Physics

Volume 251, 15 October 2013, Pages 209-222
Journal of Computational Physics

A multiphase electrokinetic flow model for electrolytes with liquid/liquid interfaces

https://doi.org/10.1016/j.jcp.2013.05.026Get rights and content

Abstract

A numerical model for electrokinetic flow of multiphase systems with deformable interfaces is presented, based on a combined level set-volume of fluid technique. A new feature is a multiphase formulation of the Nernst–Planck transport equation for advection, diffusion and conduction of individual charge carrier species that ensures their conservation in each fluid phase. The numerical model is validated against the analytical results of Zholkovskij et al. (2002) [1], and results for the problem of two drops coalescing in the presence of mobile charge carriers are presented. The time taken for two drops containing ions to coalesce decreases with increasing ion concentration.

Section snippets

Background

Multiphase electrohydrodynamic flow is present in many engineering systems, including ink-jet printing and electrospraying [2], [3]. These flows are particularly relevant to microfluidic systems. The presence of electric forces in these systems can be utilised to form, sort and merge drops on demand [4], [5], [6], [7]; and can be used in devices for micromixing, DNA extraction and sample analysis [8], [9], [10].

Early analytical descriptions of the deformation of a drop subjected to an external

Formulation

The flow of two immiscible, Newtonian electrolytic fluids is considered. For notational simplicity we denote one phase as the disperse phase, and the other as the continuous phase. For the physical systems considered here, only the disperse phase alone, or the continuous phase alone, contains mobile charge carriers. This assumption is valid for common conducting/non-conducting fluids such as oil-in-water or water-in-oil flows, and is representative of most microfluidic multiphase flows. The

Numerical implementation

Eqs. (1), (2), (3), (10) and (12) are solved using a combined volume of fluid and level set (CLSVOF) algorithm [46] on a staggered, uniform mesh of cell-size Δr=Δz=α. Fluid pressures, ion concentrations and electric potentials are located at cell centres, and the velocity components at cell faces.

The disperse-phase volume fraction ϕ is located at the cell centres of a mesh (termed the “fine” mesh) that is twice as fine as the mesh (termed the “coarse” mesh) used for all other variables (Fig. 1

Conducting drop in a non-conducting medium

To test the algorithm presented in the previous section, the deformation of a conducting drop of radius R, uniform viscosity μd and permittivity εd; suspended in a non-conducting medium of uniform viscosity μc and permittivity εc is considered (Fig. 2). This type of flow is representative of most water-in-oil systems. An electric field is applied in the z-direction, uniform at large distances from the drop. Because the surrounding medium is non-conducting, the dimensionless continuous inverse

Conclusions

A combined level set and volume of fluid (CLSVOF) formulation has been presented that is capable of modelling multiphase, electrokinetic phenomena. In particular, any one of the fluid phases is considered to possess mobile charge carriers, where the local concentration of each ion species is a function of both space and time. The ion concentrations are transported in combination with the disperse volume-fraction, ensuring conservation of ions, and hence charge, within each phase. The presence

Acknowledgements

This research was supported by the Australian Research Council Grants Scheme and by computational resources on the National Computational Infrastructure Facility through the National Computational Merit Allocation Scheme.

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    Present address: CSIRO Mathematics, Informatics and Statistics, Clayton, Victoria 3169, Australia.

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