Dynamic scaling in magnetophoretic separation

摘要

Using numerical solutions of the Langevin equations, to simulate a magnetic separation of colloidal suspensions under an external magnetic-field gradient, we show the existence of a regime of dynamic scaling. We find that the separation time depends strongly on the size (or length) of aggregates taking place in the separation process. In the irreversible aggregation regime, we show that linear chains of particles steadily grow and their average size, S, increases with time as a power low. The chain-size (s) distribution-function (c_s) approaches (for long times) the following scaling form c_s(t)∝s-2f(s/S). The exponent, z, of the mean chain size S(t)∝tz is compatible with Smoluchowski's coagulation equation, with a homogeneous kernel, even if the separation is a process with particle migration. We also show that the regime corresponding to the dynamic scaling is limited in time due to the separation. Furthermore, we find a characteristic time, which we identify as a similarity variable, and we relate it to the separation time.