P. Tandon et De. Rosner, SINTERING KINETICS AND TRANSPORT PROPERTY EVOLUTION OF LARGE MULTIPARTICLE AGGREGATES, Chemical engineering communications, 151, 1996, pp. 147-168
Ultrafine (''nano''-) particles produced from highly supersaturated va
pors or liquids are usually aggregated, often containing thousands of
small 'primary' particles bound together in tenuous structures charact
erized by mass fractal dimensions less than 3. Such aggregates have la
rge initial surface area but are metastable with respect to more compa
ct configurations. Available restructuring mechanisms include surface
energy driven coalescence, which, in the case of viscous flow at high
gas temperatures, is ultimately able to obliterate all evidence of the
original (''primary'') particles. We here exploit the notion that, pr
ovided an aggregate is sufficiently large, it can be treated like a sp
atially non-uniform porous medium, undergoing finite-rate surface ener
gy driven viscous flow sintering leading to final collapse to a single
dense sphere. For this purpose, after a D-f congruent to const stage
of sintering [associated with a corresponding increase in mean apparen
t primary particle ('grain') size], we use an extension of the sinteri
ng rate models of Mackenzie and Shuttleworth (1949) and Scherer (1977)
, treating the material of the restructuring aggregate to be a Newtoni
an viscous fluid. We predict and report here the time-dependent increa
se in fractal dimension, D-f, and associated decreases in: aggregate o
uter (maximum) radius, mobility radius, and changes in accessible surf
ace area with dimensionless time [real time in multiples of the charac
teristic sintering time, mu (R-1)(t=0)/sigma, where mu is the material
's viscosity (R-1)(t=0)is the effective initial grain radius and sigma
the material surface tension]. In these units, we find that the total
required coalescence time does not increase with N as sensitively as
N-1/3... an important observation for processes involving very large a
ggregates. With validation and the indicated extensions, our pseudo-co
ntinuum methods are efficient enough to be used for estimating the mor
phological-and transport property-evolution of entire populations of r
estructuring aggregates. perhaps characterized by some nonseparable pr
obability density function pdf(N,D-f,R-1), locally, in non-isothermal
combustion-synthesis reactors.