Numerical simulation of two-fluid flow of electrolyte solution with charged deforming interfaces

Simulation of a Perfect Dielectric Drop in Electro-Osmotic Flow of an Electrolyte Through a Microchannel

“…The electrokinetic flow model for multiphase flow extended to account for interfacial charges presented by Berry and co-workers (Berry et al, 2013) and Davidson and co-workers (Davidson et al, 2014) allows for a better prediction of drop mobility and deformation as well as a comprehensive study of the electrokinetic forces acting on the surface of the drop. This model has recently been validated using analytical solutions and experimental results from published literature (Davidson et al, 2015) and were shown to have accurate predictions. The advances presented by the authors in electrokinetic numerical modelling of microfluidic systems represent an important step towards understanding liquid droplet behaviours in microchannels, which is crucial to successful design and operation of numerous applications.…”

“…The LS-VOF-based numerical method uses the following equations to describe fluid behaviour in the microchannel (Davidson et al, 2015):…”

“…The ion transport is described by Equation 9, which incorporates advection, diffusion and conduction of ions. n+ and n-are the cations and anions concentrations in the electrolyte solution, respectively (Davidson et al, 2015).…”

“…A modification on the Nernst-Planck equation for ion transport was made to implement an ion-impenetrable boundary condition and ensure that there would be no ion flux across the interface. The calculation is performed in a two-dimensional axisymmetric staggered grid and the algorithm is an explicit time stepping method with time steps defined dynamically to satisfy stability limits (Davidson et al, 2015).…”

“…The electric field is solved in the Poisson equation (Equation 8) with a representation of the surface charge Sq. Detailed expressions for the method can be seen in (Davidson et al, 2014), (Liu et al, 2000) and (Davidson et al, 2015).…”