Dynamic electrophoresis is the foundation for electroacoustical
measurements, in which the electroacoustical signals may be used to
analyze the size and electrostatic charge of colloidal entities by
means of the results for dynamic electrophoretic mobility. Thus, the
electrophoresis under an alternating electric field is the key foundation
for electroacoustic theory. In this article, we develop a tractable
analytical theory for the dynamic electrophoresis of hydrophobic and
dielectric fluid droplets possessing uniform surface charge density.
The tiny fluid droplets possess charged mobile surfaces and have found
widespread applications in our day-to-day life. For dielectric fluid
droplets (e.g., oil–water emulsions), the tangential electric
stress at the interface is nonzero, which significantly affects its
electrohydrodynamics under an oscillatory electric field, which has,
however, a negligible impact on the electrophoretic motion of conducting
droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid
droplets often show hydrophobicity when they are immersed in an aqueous
medium, and the impact of the electric field on hydrophobic surfaces
remains a research frontier in the chemical discipline. Whereas a
number of approximate expressions for electrophoretic mobility have
been derived for the conducting droplet, none of them are applicable
to such generic hydrophobic fluid droplets with dielectric permittivity
that is significantly lower than or comparable to that of an aqueous
medium. In this work, within the Debye–Hückel electrostatic
framework, we elaborate an original analytical expression of dynamic
electrophoretic mobility for this generic dielectric fluid droplet
with a hydrophobic surface considering that the droplet retains its
spherical shape during its oscillatory motion. We further derived
a set of simplified expressions for dynamic electrophoretic mobility
deduced under several limiting cases. The results are further illustrated,
indicating the impact of pertinent parameters.