The calculation of electro-dipping force, acting on a dielectric particle, attached to the boundary between water and nonpolar fluid, is important for the characterization of the surface charge density of micron-size objects and their three-phase contact angles . The problem was solved semi-analytically, using the Mahler–Fox transformation in the simplified case of one phase with infinite dielectric permittivity . We generalize this approach, taking into consideration the finite dielectric permittivity of the polar phase. We propose a numerical method for calculating the distribution of the electrostatic potential in all phases and the respective values of the dimensionless electro-dipping force. The expression for the weak singularity parameter at the three-phase contact line is analytically derived. In all studied cases, it is weaker than that in the model case . The obtained results show that: (i) the electrostatic potential distribution is close to that in the model case for micron-size particles, large values of the ionic strength and dielectric constant of the polar phase; (ii) the force, arising from the electrostatic field in the polar phase, cannot be neglected for small (nano-size) particles and low ionic strengths.
Electrostatic potential distribution Laplace equations Complex numerical domains and boundary conditions Toroidal coordinates
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