For particle populations in a non-isothermal carrier gas, size-dependent particle thermophoresis provides an often-overlooked coagulation mechanism But strong temperature gradients can either induce the coagulation of non-Brownian particles, or, more generally, alter the collision/coagulation frequency for Brownian particles. Here we consider a rapidly coalescing aerosol of uniform composition, Brownian spherical particles evolving under the combined influence of both mechanisms: ie., well-known Brownian coagulation (Smoluchowski, Friedlander, et.al.) and thermophoresis-induced coagulation (Rosner and Arias-Zugasti [2, 3]).
We first derive a combined coagulation frequency based on a thermophoresis-modified continuum-limit coagulation frequency. The Brownian + thermophoresis combined coagulation frequency is modeled in a way similar to the Brownian + sedimentation coagulation frequency  (with the gravitational sedimentation velocity replaced by the size-dependent near-continuum thermophoretic velocity).
The relative intensity of each coagulation mechanism can be characterized by a dimensionless Peclet number, defined by the corresponding ratio of characteristic coagulation frequencies. Introducing the combined coagulation frequency as a kernel into a Smoluchowski-type population-balance integro-PDE, we perform a systematic parametric study of the time evolution of a coagulation-aged, initially log-normal population, as a function of the aforementioned Peclet number (Pe) and particle/gas Fourier thermal conductivity ratio, kp/kg. We have also investigated the errors associated with the frequently made “additive kernel” approximation.
Our numerical results show that in the long-time limit quasi-self-preserving populations (QSPPs) are reached. When the reference Pe is much smaller than, say, 0.1, previously well-studied Brownian self-preserving population results are recovered. For Pe-values larger than about 10 our QSPP become indistinguishable from our recently reported TP-“dominated” results . However, for intermediate Pe-values characteristic distortions set in, corresponding to increased population spread and skewness, and slightly smaller departures from log-normality.
Extensions of this research of current interest  include accounting for a) unequal “particle” thermal conductivities, b) thermo-capillary fluid motion, c) non-ideal carrier vapor effects at higher pressures, and d) finite-rate particle “coalescence” rates.
a. For presentation at AIChE 2011Mtg (October), Minneapolis MN
b. Chemical & Environmental Engineering Dept., Yale University, New Haven, CT 06520-8286, USA
.c. Dept. de Física Matemática y de Fluidos, UNED, Apdo: 60141, 28080 Madrid, Spain
Supported by NSF under Grant: CBET-1037733 at Yale University and Ministerio de Ciencia e Innovación (#ENE2008-06515-C04-03) and Comunidad de Madrid (#S2009/ENE-1597) at UNED.
 Rosner DE and Arias-Zugasti M (2011) Phys. Rev. Lett. 106 015502 (January 7, 2011)
 Arias-Zugasti M and Rosner DE (2011) Phys. Rev. E (submitted)
 Rosner DE and Arias-Zugasti M (2011) Industrial & Engineering Chemistry Research [submitted (for Churchill 90 issue)]
 Simons S, Williams MMR, and Cassell JS (1986) Journal of Aerosol Science 17 789