  A systematic theoretical study of temperature-gradient-induced electrokinetic
flow and thermoelectric potential of electrolyte solutions in a
micro-/nanocapillary is presented. The study is based on a semi-analytical
model developed by simultaneously solving the energy equation and the
Poisson-Nernst-Planck/Navier-Stokes equations with the lubrication theory. The
semi-analytical model is shown to be mainly governed by eight parameters,
including two temperature-related parameters (temperature and its gradient),
two electrokinetic parameters ($\zeta$ potential and the ratio of capillary
radius to the Debye length $\kappa_0a$) and four physical properties of cation
and anion (i.e. Soret coefficient difference $\Delta S_T$, average Soret
coefficient $S_T$, normalized difference in diffusivities $\chi$ and intrinsic
Peclet number $\lambda$). It is found that the thermoelectric field is induced
by three effects, which are respectively due to (1) the difference in the Soret
coefficients of cation and anion; (2) the selective ion diffusion resulting
from the temperature-modified Boltzmann distribution of ions; (3) the advective
transport of ions caused by the fluid flow. The first thermoelectric effect
prevails for lower $\zeta$ potentials or large $\kappa_0a$, while the second is
dominant for higher $\zeta$ potentials with very small $\kappa_0a$. The first
two thermoelectric effects can cooperate or counteract depending on the sign of
$\zeta\Delta S_T$. Finally, the temperature-gradient-induced electrokinetic
flow is found to be a superposition of an electroosmotic flow component due to
the thermoelectric field and a thermoosmotic flow component due to the combined
effects of osmotic pressure and dielectric body force. These two flow
components may cooperate or counteract depending on values of $\zeta$ and
$\kappa_0a$.
