Thermally Enhanced Electro-osmosis to Control Foam Stability

Liquid foam is a dense dispersion of liquid bubbles in a surfactant solution. Because of its large surface area, it is an out-of-equilibrium material that evolves with space and time because of coarsening, coalescence, and liquid drainage. In many applications, it is required to control the lifetime of a foam by limiting the drainage or triggering the collapse at a specific location or a given time. We show here that applying an external electric field at the edge of the foam induces some liquid flows. Depending on the flow magnitude, it controls either gravity driven drainage, the foam stability, or the foam collapse at a specific location. Thus, applying an electric field to a liquid foam can control its stability. The experimental results are quantitatively described by a simple model taking into account first the electro-osmotic transport in such a deformable medium and second the Marangoni flows induced by heterogeneous heating due to Joule effect. More specifically, we show for the first time that electro-osmosis can be strongly enhanced due to thermal gradients generated by the applied electric field.

Popular Summary

Liquid foams are inexpensive, light, and insulating, making them useful in a wide range of applications such as cosmetics, depollution processes, and the building industry. However, it is difficult to tune their stability because various spontaneous and structural mechanisms induce foam destruction. To circumvent this hurdle, we propose a way to control liquid foam stability by using an electric field, which can induce flows that counteract gravity-driven drainage and foam collapse.

Applying an electric field to a porous membrane filled with liquid results in a so-called electro-osmotic flow. This flow originates at the interface: An electrical force acts on ions close to the interface and moves all the liquid. But a liquid foam is more complex than a simple porous membrane because of its deformability. Its porosity is instead variable, leading to uneven heating from an applied electric field. For the first time, we characterize the thermal gradients that arise in this situation. We show that they boost classical electro-osmosis by 1 order of magnitude. Thanks to these mechanisms, we can locally tune and decrease the amount of liquid in the foam to control its destabilization.

More generally, this work has strong implications in nanofluidics: Whereas heterogeneous nanofluidic channels have been widely investigated for ion pumping, desalination, and energy harvesting, no one has yet considered how these systems respond to thermal effects from electric-field heating. These new nonlinear responses may be of major interest for these emerging applications.

Figure 1

(a) Scheme of electro-osmotic flow that takes place in a foam film. (b) Experimental setup allowing the study of electrokinetic transport in a macroscopic foam. (c) Side view picture of the foam between the electrodes; the focus is on the front plate.

Figure 2

(a) Conductance $G$ of the foam as a function of time for different applied electric fields. In each case, two curves in the same conditions are superimposed. $R=4.3\mathrm{mm}$, ${\varphi }_i=0.26\%$, $L=20\mathrm{mm}$. The time ${\tau }_{\max }$ corresponds to the time at which the conductance reaches a maximum. (b) Snapshots of foam for $\mathrm{\Delta }V=100\mathrm{V}$ (top) and $\mathrm{\Delta }V=500\mathrm{V}$ (bottom), $R=2.6\mathrm{mm}$, ${\varphi }_i=0.47\%$, $L=20\mathrm{mm}$. (c) Infrared camera images of the foam for different applied voltages (from bottom to top: 200, 400, 600, 800, 1000 V). $R=3.7\mathrm{mm}$, ${\varphi }_i=0.11\%$, $L=29\mathrm{mm}$. Image height corresponds to 22.6 mm.

Figure 3

(a) Stationary temperature profile (after 50 s) for different applied voltage ($L=19\mathrm{mm}$, $R=3.7\mathrm{mm}$, and ${\varphi }_i=0.11\%$). Voltage varies from 0 to 1000 V with a 100 V step from bottom to top. The black line shows the fit used to extract the temperature gradient for 1000 V. (b) Temperature gradient at the top of the foam deduced from a linear fit of temperature profile [see (a)]. The line is a linear fit, ${\partial }_{x}T=-kE+b$, with $k=0.034\mathrm{K}/\mathrm{V}$ and $b=0.18\mathrm{K}/\mathrm{mm}$.

Figure 4

(a) Evolution of the dimensionless liquid fraction $\overline{\varphi }$ as a function of the dimensionless altitude $X$ obtained numerically for a Bond number equal to 5.3 and different effective capillary numbers Ca. (b) Theoretically predicted dimensionless liquid fraction at the bottom of the sample $\overline{\varphi }(0)$ as a function of the effective capillary number Ca for different Bond number Bo.

Figure 5

Ca versus Bo experimental phase diagram. Symbols are associated to the mean bubble radius: red, $R=1.0\mathrm{mm}$; blue, $R=2.6\mathrm{mm}$; green, $R=4.3\mathrm{mm}$. Plain circles represent stable foams and crosses represent foams where avalanches are reported. The continuous gray area is obtained numerically and corresponds to (Bo;Ca) values for which $\varphi (0)=0.1\%$ given the initial liquid fraction dispersion.

Figure 6

Side view images (diffused reflected light) of the foam under 0 (left), 200 (middle) and 400 V (right) with a color camera ($L=24\mathrm{mm}$, $R=3\mathrm{mm}$, image height is 20 mm.)