Effects of thermoosmosis and thermophoresis of finite-sized ions along with a pressure-driven flow on the thermoelectric field in a conical hydrophobic nanopore

Abstract

Thermoelectric transport driven by an imposed temperature gradient of an ionized liquid through a charged hydrophobic conical nanopore in a membrane separating two reservoirs is studied in the context of conversion of waste heat to electricity and to generate a liquid flow through the pore. We have also considered the impact of an imposed pressure gradient to enhance the thermoelectric transport. The thermoelectric field arises due to the interplay between the thermophoresis created by the Soret effect, thermoosmosis of ions and the induced electric field governed electrophoretic transport of ions along with the EOF. In addition, the geometric asymmetry of the conical pore also generates an ionic concentration gradient. We consider a modified model for the electrokinetics which incorporates the hydrodynamic steric interactions of finite-sized ions and the viscosity of the suspension medium is considered to vary with the local ionic volume fraction. This modification extends the present model to become valid for a larger range of surface charge density for which the ionic volume fraction can become $\sim O(0.1)$. While the counterion saturation created by the steric effect attenuates the surface charge screening, an enhanced viscosity near the charged surface creates a larger hydrodynamic friction and reduced ionic flux. Based on the modified model we have analyzed the impact of surface charge density and slip length of the membrane on the thermoelectric field by considering the temperature dependent viscosity, dielectric permittivity and ionic diffusivity for a wide range of the bulk ionic concentration. The occurrence of the ion concentration polarization in the conical pore and its impact on the thermoelectric field is analyzed.