Suspension Jams in a Leaky Microfluidic Channel

Inspired by the jamming in leaky systems that arises in many physiological and industrial settings, we study the propagation of clogs in a leaky microfluidic channel. By driving a colloidal suspension through such a channel with a fluid-permeable wall adjoining a gutter, we follow the formation and propagation of jams and show that they move at a steady speed, in contrast with jams in channels that have impermeable walls. Furthermore, by varying the ratio of the resistance from the leaky wall and that of the gutter, we show that it is possible to control the shape of the propagating jam, which is typically wedge shaped. We complement our experiments with numerical simulations, where we implement an Euler-Lagrangian framework for the simultaneous evolution of both immersed colloidal particles and the carrier fluid. Finally, we show that the particle ordering in the clog can be tuned by adjusting the geometry of the leaky wall. Altogether, the leaky channel serves both as a filter and a shunt with the potential for a range of uses.

Figure 1

(a) Top: schematic of experimental setup. A particle suspension driven by constant pressure head flows through a microfluidic channel with leaky walls and an adjoining gutter. Bottom: optical micrograph of the channel interior. The leaky inner wall is comprised of pillars spaced $d=15\mu \mathrm{m}$ apart. The channel has width, $w=450\mu \mathrm{m}$, and the distance between the leaky membrane and the outer wall is ${\ell }_g=220\mu \mathrm{m}$. (b) Time series of a clog propagating against the incident particles taken in 10-second intervals. The red dotted line indicates the clog front position. (c) Schematic of incident particles (red) with flux $u_{\infty }{\varphi }_{\infty }$ forming a clog (blue) with flux $u_s{\varphi }_s$. The position of the clog, $s(t)$, is measured from the tip of the clog wedge. Near the clogging front, incident particles can develop a component of velocity transverse to the channel. (d) PIV plot of the fluid velocity field ($\mathbf{v}$) in the vicinity of a clog. The color bar is a linear scale normalized to the maximum fluid velocity ($v_{\max }$).

Figure 2

(a) $s(t)$ taken at constant pressure for different incident volume fractions, ${\varphi }_{\infty }$. The clog speed, $u_{s,m}$, is the derivative of $s(t)$. Inset: nondimensionalized clog position $\widehat{s}(t)=s(t)/w$ plotted against nondimensionalized time $\widehat{t}=t{u}_{\infty }/w$. (b) Top: micrograph of a clog with angle ${\theta }^c$ used to characterize shape indicated. Bottom: angle fluctuations (in radians) of the clog in time.

Figure 3

(a) The ratio of the normalized measured clog speed, ${\widehat{u}}_{s,m}=u_{s,m}/u_{\infty }$, plotted against the normalized predicted clog speed, ${\widehat{u}}_{s,p}=u_{s,p}/u_{\infty }$. The red dashed line is a fit to data, ${\widehat{u}}_{s,m}=0.52{\widehat{u}}_{s,p}$. Inset: simulated nondimensionalized clog speed, ${\widehat{u}}_{\mathrm{sim}}=u_s/u_{\infty }$, plotted against ${\varphi }_{\infty }$. (b) Schematic of the half plane of a clog with stationary shape with labeled velocity and length scales. (c) Plot of ${\theta }^c$ (radians) versus $\xi =w/{\ell }_g$. Red circular points correspond to devices with $d=5\mu \mathrm{m}$ and blue triangular points to $d=25\mu \mathrm{m}$. The red and blue dashed lines are fits to the data given, respectively, by ${\theta }^c=0.14{\tan }^{-1}(0.43\xi )$ and ${\theta }^c=0.16{\tan }^{-1}(0.28\xi )$. Inset: simulated clog angle plotted as a function of $\xi$ with $\alpha =0.4$ and 0.6.

Figure 4

(a) Top: optical micrograph of the particle packing near the top leaky membrane of a device with $d=15\mu \mathrm{m}$. Bottom: schematic of the leaky membrane feature spacing and particle dimensions. (b) Snapshot of a particle clog in a device with $d=15\mu \mathrm{m}$. (c) Two-dimensional fast Fourier transform of the area in the bottom rectangular box in (b). (d)–(f) Same as (a)–(c) but with $d=20\mu \mathrm{m}$ so that shunted particles close pack along the leaky wall.