A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

The flow and heat transfer past a heated cylinder of square cross section mounted horizontally above a plane wall and subjected to a uniform shear flow is considered. The flow field is considered for a moderate range of Reynolds number (based on the incident stream at the cylinder upstream face and the height of the cylinder) and Grashof number at cylinder-to-wall gap height 0.5 times the cylinder height. The flow field and heat transfer are computed through a pressure-correction-based iterative algorithm with the QUICK scheme in convective terms. The code is tested for accuracy by comparing with published results for certain values of the flow parameters. We examine the combined effects of buoyancy and shear flow on the vortex shedding behind the cylinder in close proximity to a plane wall. A boundary layer develops along the wall, and this interacts with the shear layer formed along the two sides of the cylinder. The role of the thermally induced baroclinic vorticity production term on the vortex shedding is examined. Our results show that the breakdown of vortex shedding takes place beyond certain values of Richardson number (which depends on the Reynolds number). The dependence of the average rate of heat transfer from the surface of the cylinder on Reynolds number and Grashof number is also investigated.

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.