Physica 147A (1987) 280-296 North-Holland, Amsterdam ON THE HYDRODYNAMIC RADIUS OF FRACTAL AGGREGATES Wim VAN SAARLOOS A T& T Bell Laboratories. Murray Hill, NJ 07974, USA Motivated by recent light scattering experiments by Wiltzius, we discuss the various factors affecting the hydrodynamic radius R, of fractal aggregates, underlining the need for further experiments. After a critical discussion of the results of the Kirkwood-Riseman approximation for the hydrodynamic radius, we analyze the porous sphere model of Debye-Bueche and Brinkman. For spherically symmetric aggregates this model leads to values of R H which are substantially larger than found experimentally by Wiltzius, but somewhat smaller than found in numerical simulations. We make various suggestions for the physical origin of these discripancies, and argue that they might be due to asymmetry of the aggregates. We discuss how this suggestion can be tested experimentally with depolarized light scattering as well as with sedimentation experiments, and theoretically with the aid of computer simulations. 1. Introduction In view of Peter Mazur's life-long interest in Brownian motion ~-5) and the statistical properties of particles in suspension6), it seems appropriate at this occasion to discuss a problem of this type. I will therefore discuss some aspects of a topic of current interest, the hydrodynamic radius of fractal aggregates, using some results related to an approach popularized in the seventies by Mazur and Bedeaux 7'8) in their extension of the so-called Fax~n theorems 9) for the hydrodynamic friction and torque on particles in suspension, The present work was motivated directly by recent experiments by WiltziusU~). In his experiments on slowly aggregating silica spheres, Wiltzius 1°) used static and dynamic light scattering to determine simultaneously the radius of gyration Re, and the hydrodynamic radius R H (defined through the transla- tional diffusion coefficient) of the aggregates. The aggregate formation in his experiments is reaction limited; indeed the observed fractal dimension df = 2.10_ + 0.03 of the aggregates is close to the fractal dimension obtained in simulations of the reaction limited aggregation model in three dimensions ~'12). For large cluster sizes, Wiltzius HI) found the ratio RH/R c (which we will refer to as the hydrodynamic ratio) to approach a constant value of about 0.72_+ 0.02. This experiment is therefore the first to show explicitly that the hydrodynamic radius of large fractal aggregates is indeed proportional to the 0378-4371 / 87 / $03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)