P. Tandon et De. Rosner, TRANSLATIONAL BROWNIAN DIFFUSION-COEFFICIENT OF LARGE (MULTIPARTICLE)SUSPENDED AGGREGATES, Industrial & engineering chemistry research, 34(10), 1995, pp. 3265-3277
Aggregates (composed of large numbers of ''primary'' particles) are pr
oduced in many engineering environments. One convenient characterizati
on is the fractal dimension D-f, the exponent describing how the numbe
r of primary particles in each aggregate scales with radial distance f
rom its center of mass. By viewing each ensemble of aggregates of fixe
d size N as a radially nonuniform but spherically symmetric ''porous s
olid'' body, we describe a finite-analytic, pseudocontinuum prediction
of the drag, and corresponding translational Brownian diffusivity, fo
r a fractal aggregate containing N (>>1) primary particles in the near
-continuum (Kn << 1) regime. While Stokes' equation is used to define
the creeping Newtonian flow outside the aggregate, Brinkman's equation
is used inside, with suitable matching conditions imposed at R(max) =
[(D-f + 2)/D-f](1/2)R(gyr), where R(gyr) is the familiar gyration rad
ius. A rational/accurate correlation technique is developed to rapidly
estimate drag for an aggregate with any self-consistent combination o
f N, D-f, and Kn(2R1). Our numerical results/rational correlations all
ow prediction of aggregate deposition rates via the mechanisms of Brow
nian diffusion and/or inertial impaction, modeling sol reaction engine
ering systems involving aggregate Brownian coagulation and in interpre
ting dynamic light scattering measurements on aggregate populations.