  The work discusses the problem of measurement of the zeta-potential for
electrolyte-based suspensions of nanoparticle. A theory is presented for the
effect of the diffuse electric double layer, including the interphase
(stagnant) layer, on the effective conductivity of such suspensions. The theory
is based on the method of compact groups of inhomogeneities applied to a model
system of hard-core-penetrable-shell particles embedded together with the base
liquid in a uniform host of the conductivity. The cores represent the
particles. The shells are electrically inhomogeneous in the radial direction,
their conductivity profile being a continuous function. This model is possible
to analyze rigorously in the static limit. The desired conductivity is found
from the integral relation which allows us to express the electrical
conductivity in the terms of the zeta-potential, thickness of the stagnant
layer, matrix molarity, etc. The theory reveals the existence of different
scenarios of behavior of the conductivity depending on the geometrical and
electrical parameters of the stagnant layer. It is shown that the functional
dependence between the thickness and zeta-potential can be obtained from the
rate of change of the conductivity with concentration for diluted suspensions;
this rate can be measured experimentally. It is pointed out that the
hydrodynamic radius of a nanoparticle can be obtained from the
Smoluchowski-Einstein diffusion coefficient, which can be measured by the
method of laser correlation spectroscopy. In order to find the zeta-potential,
it is necessary to simultaneously do a series of independent measurements: find
the slope of the conductivity and estimate the thickness of the stagnant layer.
