Tunable Electrorheological Fluid Microfluidic Rectifier: Irreversibility of Viscous Flow Due to Spatial Asymmetry Induced Memory Effects

Because of the reversibility of viscous flow it is not expected to obtain a fluidic rectifier simply from geometrical asymmetry without any moving mechanical parts. Here, we found a counterexample by using spatial asymmetry combined with an electric field to inject memory effects that render the flow irreversible. This stems from the strong dependency of the electrorheological fluid particle chaining on the flow direction. A funnel-shaped microfluidic rectifier with electrorheological fluid has been shown to be easily and rapidly tuned via the applied electric field to achieve an almost order of magnitude rectification along with pressure oscillations. These findings are of importance for the realization of fluidic diodes, rectifiers, and ratchets.

Figure 1

Chip design and definition of the positive vs negative flow directions. (a) Scheme of the funnel-shaped electrode within the microfluidic channel, where the tilt angle of the electrode sides is defined as $\theta$, while the width of the funnel tip opening is defined as $h$. Chips of varying $h$ and $\theta$ were used while keeping the same average cross-section area of the funnel. (b) Image of the chip. (c) Microscopy image of the tip region under a flow of $Q=10\mu \mathrm{L}/\min$ in the positive direction and an ac voltage of 650 V and 10 Hz square-wave form. Particle blockage of the funnel tip is clearly seen. (d) Microscopy image of the tip region under the same conditions as in (c) with flow in the negative direction, where the hydrodynamic shearing of the particle chains leaves an open path for the ER fluid.

Figure 2

The effect of the funnel geometry on ER rectification. Transient pressure drop response for (a) positive and (b) negative flow direction at different voltages [400, 650, and 800 V (10 Hz frequency)]. The width of the tip opening was $h=150\mu \mathrm{m}$ and the flow rate was $Q=10\mu \mathrm{L}/\min$. Beyond the critical voltage for particle blockage of the funnel tip, the response became oscillatory. The voltage was turned on ($t_{\mathrm{on}}$) at $t=10\mathrm{s}$ and turned off ($t_{\mathrm{off}}$) after the pressure got either saturated or exhibiting several oscillations for adequate averaging (indicated by two arrows). (c) The yield pressure vs voltage for both the positive and negative directions as obtained from parts (a) and (b), respectively. (d) The rectification factor vs voltage for different widths [150, 300, 400, 600, and $2470\mu \mathrm{m}$ (straight channel)] of the funnel tip. With decreasing tip width, the voltage corresponding to the maximum rectification factor $V_{\max }$ decreased [see also inset; symbols represent experiments while dashed line represents theoretical scaling Eq. (3)], while the rectification factor increased. Error bars denote standard deviation values.

Figure 3

The effect of the flow rate on ER rectification and pressure drop oscillations for tip opening of $400\mu \mathrm{m}$. (a) The yield pressures for both positive (dashed lines) and negative (continuous lines) flow directions vs voltage, for flow rates of 5, 10, and $15\mu \mathrm{L}/\min$. (b) The rectification factor vs voltage for different flow rates of 5, 10, and $15\mu \mathrm{L}/\min$. With increasing flow rates, the voltage corresponding to the maximum rectification factor $V_{\max }$ increased [see also inset; symbols represent experiments while dashed line represents theoretical scaling Eq. (3)], as well as the maximum rectification factor. Error bars indicate standard deviation values. (c) The time period of the pressure oscillations vs the electric field squared for both positive and negative flow direction and varying flow rates. The inset depicts the universal scaling Eq. (4) of the measured data taken relative to the threshold value of the electric field ($E_{\mathrm{th}}$) for inducing oscillations (each case has its own threshold value) and the corresponding threshold periodic time ($T_{\mathrm{th}}$).

Figure 4

The underlying physical mechanism of asymmetric ER response upon the change of flow direction. (a) Microscopic image of a funnel with tip opening of $400\mu \mathrm{m}$ defining the distance $s$, where the chain is first formed under the negative flow direction. (b) The electric field (norm), as calculated using numerical simulations indicating its intensification at the electrode corners. (c) The distance $s$ is inversely proportional to $E^2$. The critical voltages for the negative flow direction $V_{c,n}$ and their corresponding critical distance of chain formation $s_c$. For $s>s_c$, the formed chains were able to escape the dielectrophoretic trap and thus do not jam the entrance to the funnel.