Effect of pH on the electrophoretic mobility of a particle with a charge-regulated membrane in a general electrolyte solution

The electrophoretic motion of an entity comprised of a rigid, uncharged core covered by a charge-regulated membrane which simulates a biological cell, in a general a:b electrolyte solution is analyzed. The membrane carries a fixed charge which arises from the dissociation of the acidic functional group HA. We show that the higher the concentration of cations in the bulk liquid phase, the lower the absolute Donnan potential, _D, and the lower the concentration of functional group, N₀, the lower the _D. Also, the higher the pH, the higher the absolute electrical potential, and the greater the N₀, the lower the pH. The absolute mobility of a cell, μ, increases with pH, but decreases with the increase in the friction coefficient of the membrane phase, γ. For a fixed total number of HA, if γ is large, μ/μ_s is less than unity, μ_s being the mobility of the corresponding rigid particle, and it decreases with the thickness of membrane d, and the inverse is true if γ is small. For a medium γ, the variation of μ/μ_s as a function of d has a local maximum, and depending upon d, it can be either greater or less than unity.