The lift force on a charged sphere that translates and rotates in an electrolyte

The distortion of the charge cloud around a uniformly charged, dielectric, rigid sphere that translates and rotates in an unbounded binary, symmetric electrolyte at zero Reynolds number is examined. The zeta potential of the particle ζ is assumed small relative to the thermal voltage scale. It is assumed that the equilibrium structure of the cloud is slightly distorted, which requires that the Péclet numbers characterizing distortion due to particle translation, $$ , and rotation, $$ , are small compared to unity. Here, a is radius of the particle; D is the ionic diffusion coefficient; $$ and $$ , where U and Ω are the rectilinear and angular velocities of the particle, respectively. Perturbation expansions for small $$ and $$ are employed to calculate the nonequilibrium structure of the cloud, whence the force and torque on the particle are determined. In particular, we predict that the sphere experiences a force orthogonal to its directions of translation and rotation. This "lift" force arises from the nonlinear distortion of the cloud under the combined actions of particle translation and rotation. The lift force is given by $$ . Here, ε is the permittivity of the electrolyte; $$ is the Debye length; and $$ is a negative function that decreases in magnitude with increasing $$ . The lift force implies that an unconstrained particle would follow a curved path; an electrokinetic analog of the inertial Magnus effect. Finally, the implication of the lift force on cross-streamline migration of an electrophoretic particle in shear flow is discussed.