Linear odd electrophoresis of a sphere in a charged chiral active fluid

The electrophoresis of charged colloidal particles in fluids exhibiting odd viscosity represents a fundamental challenge in understanding transport phenomena within charge-stabilized chiral active suspensions. Here, we provide the first concept of a charged chiral active fluid, where electrokinetics is coupled to odd Stokes flow, to explore how classical results from electrophoresis in Newtonian fluids generalize in the presence of odd viscosity. In particular, we derive a general expression for the electrophoretic mobility for particles of any shape under weak external electric fields using the Lorentz reciprocal theorem for odd fluids. By applying this result to a conducting charged sphere at low zeta potentials, we obtain an exact, closed-form analytical expression for the electrophoretic mobility, valid for arbitrary values of the Debye screening length and the odd-viscosity coefficient. Similar to Newtonian fluids, we find that the electrophoretic mobility is proportional to the translational mobility of an uncharged sphere, modulated by the Henry function. However, unlike in Newtonian fluids, odd viscosity leads to directional asymmetries in the electrophoretic mobility tensor that persist even for thin electric double layers. This case contrasts significantly with a charged anisotropic particle suspended in an isotropic Newtonian fluid, where anisotropic effects would vanish under the same electrostatic-screening conditions.