Comments on the conditions for similitude in electroosmotic flows

Microfluidic converging/diverging channels optimised for homogeneous extensional deformation

In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field.

Effect of direct current dielectrophoresis on the trajectory of a non-conducting colloidal sphere in a bent pore

Dielectrophoresis has shown a wide range of applications in microfluidic devices. Force approximations utilizing the point-dipole method in dielectrophoresis have provided convenient predictions for particle motion by neglecting interactions between the particle and its surrounding electric and flow fields. The validity of this approach, however, is unclear when the particle size is comparable to the characteristic length of the channel and when the particle is in close proximity to the channel wall. To address this issue, we apply an accurate numerical approach based on the boundary-element method (BEM) to solve the coupled electric field, flow, and particle motion. This method can handle much closer particle-wall distances than the other numerical approaches such as the finite-element method. Using the BEM and integrating the Maxwell stress tensor, we simulate an electrokinetic, spherical particle moving within a bent cylindrical pore to investigate how the dielectrophoretic force affects the particle's trajectory. In the simulation, both the particle and the channel wall are non-conducting, and the electric double layers adjacent to the solid surfaces are assumed to be thin with respect to the particle radius and particle-wall gap. The results show that as the particle comes close to the wall, its finite size has an increasingly important effect on its own transient motion and the point-dipole approximation may lead to significant error.