Magnetohydrodynamic motion of a colloidal sphere with self-electrochemical surface reactions in a spherical cavity

An analytical study is presented for the magnetic-field-induced motion of a colloidal sphere with spontaneous electrochemical reactions on its surface situated at the center of a spherical cavity filled with an electrolyte solution at the quasi-steady state. The zeta potential associated with the particle surface may have an arbitrary distribution, whereas the electric double layers adjoining the particle and cavity surfaces are taken to be thin relative to the particle size and the spacing between the solid surfaces. The electric current and magnetic flux density distributions are solved for the particle and fluid phases of arbitrary electric conductivities and magnetic permeabilities. Applying a generalized reciprocal theorem to the Stokes equations with a Lorentz force term resulting from these density distributions for the fluid motion, we obtain explicit formulas for the translational and angular velocities of the colloidal sphere valid for all values of the particle-to-cavity size ratio. The particle velocities decrease monotonically with an increase in this size ratio. For the limiting case of an infinitely large cavity, our result reduces to the relevant solution for an unconfined spherical particle. The boundary effect on the movement of the particle with interfacial self-electrochemical reactions induced by the magnetohydrodynamic force is equivalent to that in sedimentation and much stronger than that in general phoretic motions.