Growth of clogs in parallel microchannels

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.

Figure 1

(a) Schematic of the microfluidic device with one channel. (b) SEM images of the colloidal particles used in the experiments showing the presence of a large contaminant ($d_c\simeq 12\mu \mathrm{m}$). Scale bar is $30\mu \mathrm{m}$.

Figure 2

(a) Time evolution of clogging by sieving and the growth of the aggregates in 40 parallel microchannels taken at (a) $t=5\mathrm{s}$, (b) $t=25\mathrm{s}$, (c) $t=60\mathrm{s}$, (d) $t=120\mathrm{s}$, (e) $t=200\mathrm{s}$, and (f) $t=400\mathrm{s}$. The flow of the colloidal suspension is from top to bottom and the experimental parameters are $\mathrm{\Delta }p=13.8\mathrm{kPa}, \alpha =0.4\%, w=40\mu \mathrm{m}$, and $N=40$. The scale bar is $500\mu \mathrm{m}$.

Figure 3

Time evolution of the aggregate following the initial clogging in a single microchannel device with $\mathrm{\Delta }p=13790$ Pa and $\alpha =0.2\%$. The contaminants clogged the constricting channel at (a) $t=0\mathrm{s}$. The later particles build an aggregate: (b) $t=50\mathrm{s}$, (c) $t=150\mathrm{s}$, (d) $t=350\mathrm{s}$, (e) $t=950\mathrm{s}$, (f) $t=1950\mathrm{s}$, (g) $t=2950\mathrm{s}$, and (h) $t=4450\mathrm{s}$. Scale bar is $100\mu \mathrm{m}$.

Figure 4

Time evolution of the length of the aggregate for (a) two different widths $w, \mathrm{\Delta }p=13.7\mathrm{kPa}$, and $\alpha =0.2\%$, the colored regions show the standard deviation over all the averaged experiments; (b) different pressure $\mathrm{\Delta }p$, a width of the channel $w=40\mu \mathrm{m}$ and a concentration $\alpha =0.2\%$; and (c) different concentrations $\alpha , w=40\mu \mathrm{m}$, and $\mathrm{\Delta }p=34.4\mathrm{kPa}$.

Figure 5

Evolution of $\ell \left(t\right)/\sqrt{\alpha \mathrm{\Delta }p}$ for varying concentration and pressure in a channel of width $w=40\mu \mathrm{m}$. The hollow circles corresponds to $\alpha =0.2\%$ and $\mathrm{\Delta }p=13.8,27.6,34.5,48.2\mathrm{kPa}$ and the filled squares are obtained for $\mathrm{\Delta }p=34\mathrm{kPa}$ and varying concentrations $\alpha =0.1\%,0.2\%,0.4\%$. The dash-dotted line is the expression (7) obtained with $\varphi =0.70$ and $k$ obtained from the Carman-Kozeny relation.

Figure 6

(a) Mean time interval between two clogging events $\langle t_{\mathrm{clog}}\rangle$ for varying number of channels $N$. The circles are the results of the numerical model, the blue dotted line is the analytical solution given in Eq. (9), and the continuous black line is the simplified solution (10). (b) Mean clogging time for the entire clogging of the microfluidic device $\langle t_{\mathrm{final}}\rangle$ for varying number of channels $N$. The parameters are $\mathrm{\Delta }p=13.8\mathrm{kPa}, \alpha =0.2\%, c=5.6\times {10}^8{\mathrm{m}}^{-3}$, and the values of the hydraulic resistance and compacity of the clog are the same as in the previous section.

Figure 7

Dimensionless distribution of the clogging times for microfluidic devices made of $N=2, N=5, N=20$, and $N=40$. The experimental parameters are the same as in Fig. 6. The dotted line shows the expression (15).

Figure 8

(a) Distribution of clogging time intervals $t_{\mathrm{clog}}$ for $N=20$ channels and the same experimental parameters as in Fig. 6. The dark blue squares correspond to the clogging of the first channel, and the red squares correspond to the clogging of the 17th channel (the other points corresponds to the clogging of the 5th, 9th, and 13th). The dotted lines are the best fit assuming a Poisson distribution. (b) Number of clogged channels as a function of time for a device consisting of $N=20$ microchannels in parallel and the same parameters as in Fig. 6.

Figure 9

(a) Time evolution of the aggregate length for $N=20$ channels. The clogs form from red to blue. Inset: rescaled evolution of the aggregate. (b) Time evolution of the flow rate in the microfluidic device consisting of $N=20$ microchannels in parallel averaged over 1000 numerical experiments. The dotted line is the analytical expression (19). Inset: evolution of the flow rate in each individual microchannels obtained in a numerical experiment. In all figures, the parameters are the same as in Fig. 6.

Figure 10

(a) Mean clogging time for the entire clogging of the microfluidic device $\langle t_{\mathrm{final}}\rangle$ for varying number of channels $N$ when the hydraulic resistance of the reservoir is neglected (red circles) or not neglected (blue squares). The parameters are $\mathrm{\Delta }p=13.8\mathrm{kPa}, \alpha =0.2\%, c=5.6\times {10}^8{\mathrm{m}}^{-3}$, and the continuous line is the Eq. (22). Inset: Mean time interval between two clogging events $\langle t_{\mathrm{clog}}\rangle$ in the same situation. The continuous line is the Eq. (21). (b) Dimensionless distribution of the clogging times for devices having $N=40$ microchannels in parallel when the hydraulic resistance of the reservoir is neglected (red circles) or not neglected (blue squares). The dotted line shows the expression (15).

Figure 11

(a) Time evolution of the aggregate length for $N=40$ channels when considering the presence of the reservoirs. The clogs form from red to blue. Inset: rescaled evolution of the aggregate. (b) Time evolution of the averaged flow rate in the microfluidic device consisting of $N=40$ microchannels. The dotted line is the analytical expression (19). Inset: evolution of the flow rate in each individual microchannel obtained in a numerical experiment.