Effect of thermophoresis and its mathematical models on the transport and deposition of aerosol particles in natural convective flow on vertical and horizontal plates

• Deposition of nano- to micro-sized particles due to natural convection is computed.
• Deposition on both vertical and horizontal surfaces is considered.
• The role of thermophoresis and its various mathematical expressions is examined.
• The two thermophoretic models (Talbot et. al.; Beresnev and Chernyak) may differ significantly under certain circumstances.

An analysis is performed to study aerosol particle transport and deposition onto an isothermal horizontal or vertical plate due to the combined effects of laminar natural convection, Brownian diffusion and thermophoresis. Four configurations are considered: flow above a heated horizontal plate, flow beneath a cold horizontal plate, flow due to a heated vertical plate and that due to a cold vertical plate. Nano- to micro-sized particles (particle diameter in the range 1 nm to 5 μm) in air are considered. It is found that the deposition velocity decreases with an increase in particle diameter dpdp (i.e. an increase in particle Schmidt number ScSc), and increases with a decrease in the value of non-dimensional temperature difference ΔT^ (from positive to negative values). For a downward-facing cold horizontal plate or cooled vertical plate, the thermal drift of particles assists Brownian diffusion which enhances deposition velocity. For an upward facing heated horizontal plate or heated vertical plate, the thermal drift away from the surface decreases the overall deposition velocity which decreases drastically above a certain particle size. It is shown that the thermal drift may enhance the deposition rate by several orders of magnitude under certain circumstances. The profound role of using different expressions for the thermophoretic force coefficient (κκ) is assessed. It is found that the deposition velocity calculated using the expression for κκ suggested by Talbot et al. (1980) is always higher than the values predicted by employing the expression proposed by Beresnev and Chernyak (1995). The difference in the calculated deposition velocity for the two thermophoretic models is significant when the particle diameter dpdp is large and the fluid to particle thermal conductivity ratio λrλr is small. For example, at dpdp~1 μm, the Talbot et al. model may overpredict the deposition velocity by a factor 3, and at dpdp~5 μm, the Talbot et al. model may overpredict the deposition velocity by a factor 10. There is negligible difference between the two models when dpdp<100 nm.