Thermophoretically augmented mass-, momentum- and energy-transfer rates in high particle mass loaded laminar forced convection systems

Abstract

In previous treatments of thermophoretically modified aerosol particle transport, even those which allowed for variable host gas thermophysical properties, it has been assumed that the particle mass fraction is small enough to neglect the influence of the suspended particles on the hot gas momentum density and energy density fields. However, in high-intensity materials processing applications [e.g. optical waveguide (OWG) “preform” deposition from silica-mist-laden combustion products] particle mass loadings often exceed 1 3 , and the thermophoretically enhanced particle mass deposition flux itself modifies the local mixture velocity and temperature fields in the vicinity of the deposition surface. A self-consistent pseudo-single-phase mixture (“diffusion”) approximation, which exploits the fact that the volume fraction of suspended particles is negligible even when the particle mass fraction is quiet near the unity, is introduced here to calculate the fully coupled problem of mass, energy and momentum diffusion-convection for laminar boundary layer (LBL) flows of a combustion gas mixture containing submicron particles of appreciable thermophoretic diffusivity but negligible Brownian diffusivity. It is shown that high particle mass loading systematically increases the wall fluxes of momentum (shear stress), heat and particle mass, much like the effects associated with “massive suction” in the single-phase LBL theory. Indeed, a simple rational correlation approach is introduced to capture the essential interactions leading to higher transport coefficients in such high mass loaded aerosol systems. The transfer coefficients we obtain from our “exact” numerical integrations of the self-similar LBL equations can be used to estimate LBL development and associated particle mass fluxes to surfaces of “arbitrary” shape. Moreover, we illustrate how they can also be used to predict the mass transfer behaviour of systems governed by more complex (radiation-convection) boundary conditions. Under conditions relevant to OWG perform deposition, we demonstrate, a posteriori, that our tractable mathematical model, which neglects the mass transfer effects of particle inertia (momentum, thermal), infrared-radiation absorption, DuFour energy transfer, and particle-particle coagulation, is fully self-consistent. This approach to high particle mass loaded materials processing applications has also opened the door to rational predictions of the partitioning of dopants (e.g. Ge, B, P, …) between the vapor and particle phases and, hence, the rather complex connection between deposit (OWG perform) and process feed compositions.