Capillary filling in patterned channels

We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning, which slows, or sometimes prevents, filling, whereas ridges parallel to the flow provide extra surface that may enhance filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle ${\theta }_e\lesssim 30°$. For ${\theta }_e\gtrsim 60°$, however, even a small number of posts can pin the advancing liquid front.

Figure 1

Lattice Boltzmann simulation results for capillary filling for $h=50$, ${\theta }_e=60°$, $\gamma =0.0188$, ${\rho }_A={\rho }_B=1.0$, ${\eta }_A=0.83$, ${\eta }_B=0.03$, and $M=0.05$. (a) The length of the column of the filling $A$ component plotted against time. The circles are the simulation results and the solid line is a fit to Washburn’s law using the measured advancing contact angle and correcting for the small viscosity of the displaced $B$ component. (b) The measured advancing contact angle of the liquid-liquid interface: note that $\text{cos}{\theta }_a$ varies linearly with capillary number [13].

Figure 2

Pinning of the contact line during capillary filling when the top wall is patterned with (a) squares, (b) triangles, and (c) ratchets. (d) Interface velocity $dl/dt$ when one of the walls is decorated with a single $40\times 10$ post. (e) Interface velocity when the bottom wall is decorated with three posts and the top wall is decorated with two posts. The posts have height 10 and width 5. (f) Experimental results on capillary filling in patterned channels. Local pinning temporarily holds the capillary front on one of the two microchannel sidewalls, while the interface advances along the opposite sidewall.

Figure 3

Two-dimensional surface patterning: (a) the surface geometry; (b) regions of contact line pinning and capillary flow as a function of post-separation and equilibrium contact angle. The channel height is kept constant at $h=50$. The dashed line is a guide to the eye.

Figure 4

The length of the column of $A$ liquid plotted against time for different surface patterning. The channels’ intrinsic contact angle is ${\theta }_e=30°$. Other parameters as in Fig. 1.