Electrophoresis of a slightly deformed spherical charged biocolloid in a gel-like medium

We investigate the electrophoretic migration of a slightly deformed spherical charged colloidal biocolloid that represents either a liposomal biocolloid or any biocolloid embedded in a charged Brinkman medium, which typifies any ion exchange membrane, agarose-type hydrogel for biocolloid separation or any tissue region selected for targeted drug delivery. The slightly deformed geometry allows us to consider a non-uniform surface charge density for the biocolloid. Under the weak electric field assumption, the fundamental electrokinetic model, together with the fluid momentum equation for the Brinkman medium, is analysed. Electrophoresis can selectively separate these charged biocolloids based on their shape and size by exploiting differences in medium permeability and fixed charge density. This study shows that a slightly deformed spherical charged biocolloid exhibits higher electrophoretic mobility than a perfectly spherical one. However, the orientation of the biocolloid in an applied electric field is crucial, as its shape influences the distribution of electrostatic potential and the flow pattern near its surface. Evidently, this shape-dependent mobility enables precise drug targeting, allowing them to be directed to specific areas within a biological tissue. This study suggests that optimal targeting occurs when the electrophoretic mobility of a slightly deformed spherical shape is finely adjusted to match the electrostatic and hydrodynamic characteristics of the biological target.