A theoretical and numerical investigation of travelling wave induction microfluidic pumping in a temperature gradient

The phenomenon of induction electrohydrodynamics (EHD) has recently received great attention as a promising driving mechanism for microfluidic pumping due to its miniaturization capability. To obtain a high working efficiency of induction micropumps, a vertical temperature gradient can be imposed along the depth of a pump channel. A travelling wave (TW) potential signal propagating along an electrode array at the channel substrate interacts with this conductive heat flux, resulting in a local free charge distribution inside the bulk fluid. The induced charge wave lags behind the voltage wave in the spatial phase, and this out-of-phase polarization based pumping effect exhibits a single structural dispersion at charge relaxation frequency of the dielectric system. The classical model of electrothermal flow has always been used to numerically obtain the flow field of TW pumps, but the effect of its small temperature gradient approximation has rarely been investigated. In this study, an enhanced treatment for induction EHD modelling is developed, in which the deflection of potential contour lines caused by large temperature gradients is successfully characterized by an advection-diffusion equation, and a more accurate expression of electrothermal body force is derived and introduced to fluid dynamics as a source term of electrical origin. For the calculation of a repulsion-type induction micropump, although both models present similar results in a small thermal gradient, the enhanced one can provide more exact frequency-dependence of the pump performance and spatial distribution of electrostatic force as well as the resulting velocity profile in an excessive heat flux. Furthermore, a model extension for Joule heating induced TW pumping is also presented, and surprisingly matches the unexpected nonlinear fluid flow behaviour at higher conductivities as reported in a pioneering literature. These results can provide valuable insights into induction pumping of lab-on-chip microfluidic samples.