  During the transport of colloidal suspensions in microchannels, the
deposition of particles can lead to the formation of clogs, typically at
constrictions. Once a clog is formed in a microchannel, advected particles form
an aggregate upstream from the site of the blockage. This aggregate grows over
time, which leads to a dramatic reduction of the flow rate. In this paper, we
present a model that predicts the growth of the aggregate formed upon clogging
of a microchannel. We develop an analytical description that captures the time
evolution of the volume of the aggregate, as confirmed by experiments performed
using a pressure-driven suspension flow in a microfluidic device. We show that
the growth of the aggregate increases the hydraulic resistance in the channel
and leads to a drop in the flow rate of the suspensions. We then derive a model
for the growth of aggregates in multiple parallel microchannels where the
clogging events are described using a stochastic approach. The aggregate
growths in the different channels are coupled. Our work illustrates the
critical influence of clogging events on the evolution of the flow rate in
microchannels. The coupled dynamics of the aggregates described here for
parallel channels is key to bridge clogging at the pore scale with macroscopic
observations of the flow rate evolution at the filter scale.
