Discontinuous clogging in gently tapered microchannels reveals a transient Markov process

Abstract

Colloidal clogging is typically studied in pores with constrictions arranged in parallel or series. In these systems, clogging statistics are governed by Poisson processes; the time interval between clogging events exhibits an exponential distribution. However, an entirely different phenomenon is observed in a gently tapered pore geometry. Unlike in non-tapered constrictions, rigid particles clogging tapered microchannels form discrete and discontinuous clogs. In a parallelized system of tapered microchannels, we analyze distributions of clog dimensions for different flow conditions. Clog width distributions reveal a lognormal process, arising from concurrent clogging across independent parallel microchannels. Clog lengths, however, which are analogous to growth time, are exponentially distributed. This indicates a Poisson process where events do not occur simultaneously. These two processes are contradictory: clogging events are statistically dependent within each channel while clogs grow simultaneously across independent channels. The coexistence of Poisson and lognormal processes suggests a transient Markov process in which clogs occur both independently of, and dependently on, other clogs. Therefore, discussions of the stochastic character of clogging may require holistic consideration of the quantities used to assess it. This study reveals small adjustments to pore spaces can lead to qualitative differences in clogging dynamics, suggesting the importance of geometry.