(a) Schematic of microchannels sealed with thin membrane with liquid plugs moving in the main channel. (b) Cross sectional image of the microchannel. and are the pressure outside and inside the channel, is the flexible wall thickness, and and are the height and width of the channel. (c) Schematic of compliance measurement (i.e., pressure-volume relationship). is the pressure drop imposed in the target channel and is the corresponding volume change. (d) Schematic of the experimental setup on the plug generation and propagation.
(a) Pressure vs dimensionless volume for microchannels with flexible membrane and with glass slide. The empty (filled) symbols with error bars in volume are for the rigid (flexible) channel. (b) vs from the deformation of the thin membrane by subtracting the two data sets in (a), as shown in symbols and comparison with the large deflection theory in the line curve.
Selected images of plug propagation in a microchannel with a rigid upper wall and a flexible lower wall with extracted wall positions for different plug lengths and plug speeds. The lines on top of the image are the extracted wall shapes with the top one being the rigid wall, and the bottom one being the flexible wall. The lower figure in each image is the quantitative extraction and polynomial fitting of the wall position. The wall deformation is larger for longer plug with larger speed and is measured to be (a) , (b) , (c) , (d) , and (e) .
Schematic of the model system of a liquid plug of length driven by a pressure drop through a planar fluid-filled channel with a upper rigid wall located at and a lower flexible wall located at . The wall deformation when the wall deforms inward (outward). Here is the unit normal vector to the interface, , , , and are the far end film thickness, and is the plug tip speed during its steady propagation. The front gas pressure is set to be 0 as the reference pressure as well as the external pressure .
(a) The streamlines (black solid lines) and pressure fields (color contour) in a 2D channel with rigid top wall and flexible bottom wall for , , and . (b) Pressure and shear stresses along top rigid and bottom flexible walls. Magnification of films in the (c) rear and (d) front transition regions near the flexible wall. The white arrows are velocity vectors. S1–S6 are stagnation points along the interfaces for the liquid plug flow.
Streamline pattern (black solid lines) and pressure fields (color contour) in the plug near the flexible wall for different longitudinal tensions , 1.0, 2.0, and 4.0 with and .
(a) The flexible wall position for , 0.01, and 0.02 with and . (c) The flexible wall position for , 0.5, 1, and 2 with and . (d) The effect of plug length on the maximum wall deformation difference vs Ca.
The effect of longitudinal tension on (a) normal stress, (b) normal stress gradient, (c) shear stress, and (d) shear stress gradient along the wall, where is the arc length ( corresponds to ) with , , and .
(a) The measured maximum wall deformation vs Ca for different plug lengths, , 1.0, 0.5, 0.25, and 0.1. The error bars in the and directions indicate the standard deviations of measurements of plug velocity and wall deformation of three to five experiment sets. (b) The simulated maximum wall deformation difference vs Ca for different plug length.
(a) The overall pressure drop vs Ca when the plug propagates through the rigid channel (◇) and the flexible channel (◆). Two lines are fitted curve to show the general trends for both cases. (b) The simulated pressure drop vs Ca for . The measured macroscopic pressure drop vs Ca for different plug length in (c) rigid and (d) flexible channels. (a) is the combination of (c) and (d). The error bars in the and directions are the standard deviations of the measured plug velocity and pressure drop across the plug with three to five experimental cases.
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