Thermophoretic capture of submicron particles by a droplet

Thermophoresis is an important mechanism for submicron particle capture by droplets. The thermophoretic deposition efficiencies under varying Reynolds (Re) numbers and temperature differences are obtained from the direct numerical simulation of the submicron particle flowing around the droplet. Comparison of the results calculated under the same conditions through the classical thermophoretic deposition efficiency formula and by numerical simulation shows that the Davenport formula always returns greater values than the numerical simulation, by a relative deviation of 19.8%-63.8%. The relative deviation decreased first and then increased with increasing difference in temperature, and increased gradually with increasing Re. The deviation resulted from the assumption that the particle concentration on the droplet surface is equal to that of the incoming flow in the formula deduction process. The convection of the gas and the thermophoresis of the particles together determined the migration of the particles in the boundary layer, and so determined the particle concentration distribution on the surface of droplets. Thus, the particle concentrations on the surface of droplets are actually lower than those of the incoming flow and are distributed bimodally on the surface. The dimensionless particle concentration on the surface of droplets decreased with increasing Re, and increased first then decreased later with increasing difference in temperature. The dimensionless thermophoretic driving velocity and Re were adopted to correct the formula. The results calculated by the corrected formula were consistent with the numerical simulation employed in this paper, such that the maximum relative deviation was reduced from the original 66.8% to less than 8%.