Dipolar thermocapillary motor and swimmer

The study of thermocapillary driven flows is typically restricted to “open” systems, i.e., ones where a liquid film is bounded on one side solely by another fluid. However, a large number of natural and engineered fluidic systems are composed of solid boundaries with only small open regions exposed to the surrounding. In this work we study the flow generated by the thermocapillary effect in a liquid film overlaid by a discontinuous solid surface. If the openings in the solid are subjected to a temperature gradient, the resulting thermocapillary flow will lead to a nonuniform pressure distribution in the film, driving flow in the rest of the system. For an infinite solid surface containing circular openings, we show that the resulting pressure distribution yields dipole flows which can be superposed to create complex flow patterns, and demonstrate how a confined dipole can act as a thermocapillary motor for driving fluids in closed microfluidic circuits. For a mobile, finite-size surface, we show that an inner temperature gradient, which can be activated by simple illumination, results in the propulsion of the surface, creating a thermocapillary surface swimmer.

Figure 1

Schematic of the system's geometry: (a) Side view of the suspended surface with the circular opening. A temperature gradient is induced from left to right, resulting in a gradient in surface tension in the opposite direction. (b) Top view of the annulus.

Figure 2

(a) Theoretically predicted streamlines obtained from Eq. (20). (b) Experimentally measured streamlines for a thermocapillary doublet flow induced in a Hele-Shaw cell by a circular opening of radius $R=5$ mm subjected to a temperature gradient of 8.8 K/cm. (c) Measurement of the temperature gradient across the Hele-Shaw cell, using a 100 $\mu \mathrm{M}$ rhodamine B solution. For clarity of imaging, the measurement was take in a closed cell without a circular opening. The location of the circular opening corresponding to the dipole experiments is marked with a white circle. The color scale bar corresponds to the temperature in ${}^{\circ }\mathrm{C}$.

Figure 3

Experimentally measured streamlines resulting from the superposition of two 5 mm dipoles under a uniform temperature gradient of 8.8 K/cm. The flow between the circular openings is directed from left to right, while above and below the openings the flow is directed from right to left. As expected, two saddle points in the velocity field are formed on the center line between the two openings. Any number of dipoles can be superposed to dictate the flow pattern in the Hele-Shaw chamber.

Figure 4

(a) Schematic of the TCM experiment: a confined dipole configuration is subjected to a temperature gradient $\vec{\nabla }T$, inducing thermocapillary flow across the circular opening. The resulting pressure difference drives the liquid through a closed channel. (b) Experimentally measured maximal velocity as a function of $\mathrm{\Delta }$.

Figure 5

(a) Side-view schematic illustration of the surface swimmer experimental setup. The illumination source is located at a distance $D$ from the swimmer, controlling the power density on the swimmer. (b) Top-view schematic of the surface swimmer. The projected light heats the black stripe on the inner side of the annulus, inducing a temperature gradient across the opening. (c) A set of time-lapse overlaid images showing the swimmer's propagation under uniform illumination. (d) Experimental measurements of the maximal velocity of the swimmer as a function of power density, actuated in tap water.

Figure 6

(a) The dimensional average velocity of the surface swimmer as a function of the power density of the light source. Circles, squares and asterisks correspond to $R_1=5$, 4, and 3, respectively. (b) The dimensional average velocity of the surface swimmer normalized by $\delta$. Dashed lines correspond to a best fit of each data set to a linear curve forced through the origin. The overlap of the curves in the normalized case shows good agreement with the scaling given by Eq. (28).

Figure 7

Photograph of the experimental setup for the thermocapillary dipole experiment. The setup consists of an 80 mm aluminum plate, one end of which was heated by a Peltier device while the other end was cooled by a liquid cooler. The temperature was controlled using feedback from two thermocouples placed at each end. On top of the aluminum plate we placed a Hele-Shaw chamber consisting of two glass plates separated by distance $d=0.4$ mm using a PDMS gasket, with one or several circular openings of radius $R=5$ mm in the upper plate.

Figure 8

Calibration curve relating temperature to rhodamine B intensity (in arbitrary units). We placed the fluidic chamber on top of an indium-tin-oxide (ITO) heating device providing a controlled uniform temperature. We changed the temperature at fixed intervals of $5^{\circ }$, and for each one imaged the dye intensity in the chamber. The images were flat-field corrected according to the intensity at room temperature, and then averaged over a fixed area. We fit the data to a linear curve, and use it to measure the temperature gradient in the dipole experiments.