On thermophoresis modeling in inert nanofluids

• Similarities and differences between thermophoresis and thermodiffusion are elucidated.
• Two model expressions are introduced for the estimation of thermophoresis coefficient.
• One model based on the hydrodynamics theory is introduced and evaluated.
• A second model based on the nonequilibrium thermodynamics is developed and evaluated.

Thermophoresis plays an important role in forced and natural convection in channels and enclosures when nanofluids are used instead of pure fluids. One objective of this work, therefore, is to investigate whether reliable expressions exist for the estimation of thermophoresis data. As the second objective of this work we will show similarities between thermophoresis of nanoparticles and macromolecule dispersed in a base fluid with thermodiffusion of species in binary mixtures. To this end, a nonequilibrium thermodynamics-based expression primarily developed for the estimation of thermodiffusion factor in binary mixtures is extended and applied to thermophoresis in nanofluids. A hydrodynamics-based expression and the nonequilibrium thermodynamic-based expression developed here, are used to estimate the thermophoretic velocity in nanofluids. Validation results suggest that the general form of the hydrodynamics-based equation is valid for thermophoresis of nano-sized and even sub-nanometer particles in liquids; however, the correct prediction of the matching parameter is still unresolved. Also, the nonequilibrium thermodynamics combined with the concept of activation energy of viscous is somewhat capable of estimating thermophoresis coefficient of inert particles and macromolecules of about 1 nm or smaller. The agreement, however, is qualitative.