Microfluidic slug transport on traveling-wave surface topographies by mechanowetting

Nature often uses capillary forces to manipulate fluids, which has inspired scientists to develop new applications, such as in microfluidics and laboratory-on-a-chip systems. Here we present a method to transport fluids in microfluidic channels, by exploiting the capillary interaction of fluid interfaces with traveling surface waves, called mechanowetting. We found that the three-phase lines of fluid slugs dynamically attach to the crests of the waves, resulting in fluid velocities that are equal to the wave speed. By comparing this microfluidic slug flow to conventional peristaltic fluid propulsion, we demonstrate that fluid velocities can be reached that are one order of magnitude larger. We quantified the efficiency numerically and theoretically in terms of the generated pressure gradient using a closed channel and measured the evolution of the pressure distribution as the wave progresses. The method was shown to work for a very wide range of contact angles. We anticipate that our results will lead to new microfluidic applications based on switchable topography technology.

Figure 1

(a) Schematics of the slug flow setup, highlighting the parameters in this study. For the closed-channel simulations, no-slip and no-flux boundary conditions are applied to the striped area at the right, while the boundary conditions at the right are traction-free. For the infinite-channel approach, the striped area is connected to the channel inlet at the left through periodic boundary conditions. (b) Streamlines (black lines, center-of-mass frame), velocity profile (white arrows, laboratory frame), and the pressure distribution (colors) of the infinite channel approach. Here $L=200\mu \mathrm{m}$, ${\theta }_{\mathrm{Y}}={90}^{\circ }$. For an animation of the infinite channel simulation. (c) Streamlines (black lines, laboratory frame), velocity profile (white arrows, laboratory frame), and the pressure distribution (colors) of the peristaltic case, i.e., the wave topography applied to a channel filled with a single fluid. For the configurations shown in (b) and (c), the blue and red colors denote regions of low and high pressure, respectively, with absolute values that depend on the applied wave speed. Qualitatively the fields remain the same. (d) Steady-state slug speeds depending on slug length ratio $L/\lambda$ and $\mathrm{Ca}\mathrm{St}$ for the infinite-channel approach. $U/\lambda f=1$ corresponds to fluid transport at the wave speed. Here ${\theta }_{\mathrm{Y}}={90}^{\circ }$, $\lambda =100\mu \mathrm{m}$. The red lines correspond to the flow speed of single fluids ($\mathrm{a}$ and $\mathrm{b}$) in the microchannel, subjected to the same traveling wave.

Figure 2

Pressures in the closed-channel approach to quantify the efficiency of the (a) steady-state pressure evolution as a function of time corresponding to the three regions indicated in (b)–(d). The conformations at three different instances indicated by the dashed lines are shown in (b)–(d). Here $L=200\mu \mathrm{m}$, $\lambda =100\mu \mathrm{m}$. (b)–(d) Pressure distributions at times denoted in (a). (e) The maximum pressure built up on the right side of the slug related to the slug length for the closed-channel simulations (triangles) and corresponding theory [Eq. (11), solid line]. The two filled upward-pointing and downward-pointing triangles correspond to the situations in (b) and (g), respectively. (f), (g) Pressure distributions for $L=200\mu \mathrm{m}$, $\lambda =133\mu \mathrm{m}$. Here the curvatures of the two interfaces create a pressure jump of opposite sign, resulting in $p_1=p_3$ at all times and no pressure build up occurs, while $p_2$ is fluctuating between the situations shown in (f) and (g).

Figure 3

Numerical results for the closed-channel approach. Contour plot showing the dependence of the generated maximum pressure difference $\mathrm{\Delta }{p}_{\max }$ on the normalized slug length and the contact angle ${\theta }_{\mathrm{Y}}$ for the closed channel (see Fig. 2). Here $L=200\mu \mathrm{m}$ and the wavelength $\lambda$ was varied.

Figure 4

Numerical results for the closed-channel, containing two slugs. (a) Numerical dual-slug simulation in a closed channel for ${\theta }_{\mathrm{Y}}={90}^{\circ }$. Here $L=S=200\mu \mathrm{m}$. The wavelength $\lambda$ and slug spacing $S$ were varied. Because $S/\lambda =2$, the slugs are both contributing constructively in the pressure build up. (b) Dual-slug simulation in a closed channel for $S/\lambda =1.5$. The pressure that was built up by two consecutive slugs destructively interferes, which results in an end pressure of $p_5\approx p_1$, where $p_5$ is the pressure at the right side of the channel and $p_1$ at the left (as indicated in the figure). (c) Normalized maximum pressure difference ($\mathrm{\Delta }p=p_5-p_1$) for the two-slug case, as a function of channel parameters $L/\lambda$ and $S/\lambda$. The crosses at $S/\lambda =1.5,2$ correspond to the snapshots shown in (a) and (b), respectively.

Figure 5

Theoretical model for the closed-channel configuration based on Eq. (11), showing the ${\theta }_{\mathrm{Y}}$ dependence (a) and the $S/\lambda$ dependence (b) of the generated maximum pressure differences, showing excellent agreement with the CFD data of Fig. 3 and Fig. 4.