Research Projects

Electrophoresis, characterized as the migration of a charged particle under the influence of an externally imposed electric field, has important applications in biochemical analysis and medical diagnostics. Many of these applications often use non-uniformly charged particles in buffer solutions with complex rheology, a paradigm that remains hugely under-explored and yet is rich in mathematical rigor. In the present project, we thus aim to formulate a general analytical framework using a combination of regular and matched (singular) asymptotic techniques, along with the generalized reciprocal theorem, to probe the electrophoretic motion of a non-uniformly charged particle in viscoelastic media. The particle trajectories as well as the possible influence of depletion layers around the particle surface will also be explored in this project. The asymptotic solutions will subsequently be validated and expanded upon using numerical simulations of the complete set of the governing equations that combine electromechanics with complex fluidic rheology.