A multiphase electrokinetic flow model for electrolytes with liquid/liquid interfaces
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 . 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 and permittivity ; suspended in a non-conducting medium of uniform viscosity and permittivity 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.