Thermocapillary instability of an ionic liquid-water mixture in a temperature gradient

Ionic liquids have remarkable properties and are commonly harnessed for green chemistry, lubrication and energy applications. In this paper, we study a thermoresponsive ionic liquid (IL) solution which has the property of phase separating above a critical temperature, an interesting feature for the recovery of the IL-rich phase. For this purpose, we generate a temperature gradient in a microfluidic cavity where the confinement strengthens wetting effects and enhances the demixing. In this experimental configuration, we report the separation patterns along the phase diagram of the binary mixture composition. Three separation dynamics regime are identified that may display complex three-dimensional flows. In spite of this complexity, we rationalize all the observed regimes. Only two regimes lead to a complete spatial separation of the two phases. Interestingly, one is reminiscent of a Marangoni instability in radial geometry, even at confinement below $100\mu \mathrm{m}$. We believe this work will find applications in the recycling of ILs.

Figure 1

(a) Phase diagram of the IL-water mixture. The weight fractions in IL of both water-rich and IL-rich phases obtained after separation at $32{}^{\circ }\mathrm{C}$ and $45{}^{\circ }\mathrm{C}$ are indicated. (b) Sketch of the binary mixtures samples in bulk at different temperatures. The interfacial tension $\gamma$ between the two phases increases with the temperature as our system is LCST. $I{L}_W$ indicates the IL-rich phase, $W_{IL}$ the water-rich phase. The IL-rich phase is dyed in blue.

Figure 2

(a) Top view of the microfluidic cavity 1 cm in diameter. The gold connectors are in dark grey, and the chromium resistor in red ($50\times 500\mu {\mathrm{m}}^2$). (b) Radial cut of the temperature profile in the cavity around $t=70\mathrm{s}$. Inset: temperature gradient derived from the temperature profile fitted with $1/r$. (c) Interfacial tension between the two separated phases versus temperature, measured by rising drop method. (d) Viscosity of the IL solution as a function of its concentration at $25{}^{\circ }\mathrm{C}$.

Figure 3

Phase diagram of the IL-water mixture with the three phase separation patterns observed experimentally. The transition from first to second regime is indicated by the vertical dashed line centered on the consolute point. These two regimes selectively accumulate the wetting phase (IL-rich here) above the heating resistor. The transition from second to third regime is given by the dark gray area, when the composition is between 55 and $60\text{wt}\%$ in IL. The third regime does not yield a selective separation.

Figure 4

(a) Top view of the separation dynamics at 7 V (80 mW) at different times. The mass fraction in IL is 25% and the cavity height is $H=60\mu \mathrm{m}$. The separation dynamics can be divided into four regions, clearly visible at $t=5\mathrm{s}$ in the top view: (I) IL-water nonseparated mixture, (II) separation of the two phases, the droplets are mostly pushed outwards, (III) some IL-rich droplets are dragged inward across the water-rich phase, and (IV) IL-rich sessile drop. At $t=60\mathrm{s}$ when steady state is reached, an IL-rich drop is accumulated above the heating resistor. (b) Cross-sectional sketch of the phase separation dynamics. The tread-milling wetting film induces a radial Couette-Poiseuille flow. Inset: within region III, domain 1 indicates the IL-rich wetting film and domain 2 the water-rich phase above. The orange arrows indicate the interfacial stresses.

Figure 5

Time lapse of the IL-water phase separation for 7 V (80 mW). The IL mass fraction is 45%, and the cavity height is $H=80\mu \mathrm{m}$. Water droplets nucleate, coalesce and get expelled outward. Once they cross the separation temperature isotherm (spotted as the outer radius of the darker circular zone) they stop and sit still on the periphery forming a crown of drops. This crown is delimited by its inner radius $r_c$ and its outer diameter $R$. Due to high enough water fraction, those drops remain side by side, and their adjoining interfaces oriented radially are submitted to thermal interfacial gradients. Thus, these interfaces drain the outer liquid inward, making the central drop (rich in IL) to expand over time.

Figure 6

(a) Spontaneous formation of Marangoni jets resulting from the thermocapillary runaway of small instabilities developing on the outer interface of the water drops. The initial positions of the perturbations are indicated by red arrows. (b) Zoom on the black dashed box of the picture $t=5\mathrm{s}$. The temperature gradient as well as the interfacial tension gradient are indicated along the finger interface.

Figure 7

Phase separation pattern at $t=50\mathrm{s}$, for three heights of cavity $H=20,80,$ and 150 $\mu \mathrm{m}$ (from left to right) and three compositions 40, 45, and 50 $\text{wt}\%$ (from top to bottom). The voltage is 7 V (80 mW).

Figure 8

(a) Number of jets $n_j$ measured at $t=70\mathrm{s}$ for six heights $H=20,$ 40, 60, 80, 150, 200 $\mu \mathrm{m}$ and three compositions: 40, 45, and 50 $\text{wt}\%$ in IL. The dark cross and the dark star symbols are the number of jets from the lutidine-water experiments (see Fig. 12 in Appendix pp1). (b) $1/n_j$ (proportional to the wavelength) vs $H(R-r_c)$.

Figure 9

Sinusoidal perturbation of the circular interface in $r=R$. The amplitude of the perturbation is $\zeta$. The central drop is the light blue disk of radius $r_c$.

Figure 10

(a) Mean interfacial tension along a jet for the three compositions. (b) Viscosity ratio between the two phases: the water-rich ${\mu }_1$ and the nonseparated mixture ${\mu }_2$. (c) Growth rate $\beta$ calculated with the Brinkman model for all three compositions at six cavity heights: 20, 40, 60, 80 150, and 200 $\mu \mathrm{m}$. We use $d_{r}T=3000\mathrm{K}{\mathrm{m}}^{-1}$ and the values of ${\gamma }_m$ and $\eta$ from (a) and (b). (d) Comparison between the number of jets measured and the prediction given by the Brinkman model. The shaded areas include all wave numbers of the model where the growth rate is within 1% of the maximal growth rate.

Figure 11

(a) Time lapse of the phase separation dynamic for an IL mass fraction of 60%. Above 55 $\text{wt}\%$ in IL, the water droplets nucleate and migrate radially outward because of thermocapillary actuation. As they go down the temperature gradient, their size shrinks as they redissolve and eventually vanish. The inset highlights the clear trails left behind the moving droplets as they release water-rich material in the IL-rich matrix. The voltage is 7 V (80 mW), and the cavity height is $H=80\mu \mathrm{m}$. (b) Motion of a water drop in the temperature gradient. The drop is initially stuck at a surface. The black crosses give respectively the drop's front ($+$) and rear ($\times$). Inset: temporal evolution of the drop's radius. (c) Calculated and measured drop velocity vs time. We inject the temperature gradient values from Fig. 2 inset in Eq. (18). The gray shaded area gives a 20% variation in the value of $d_{r}T$.

Figure 12

Time lapse of the phase separation dynamic for two lutidine-water mixtures in two different cavities: $20\text{wt}\%$ in lutidine for the hydrophilic cavity (oxygen plasma treated) and $40\text{wt}\%$ in lutidine for the hydrophobic one (pristine PDMS cured at $130{}^{\circ }\mathrm{C}$ at least 2 h). The lutidine-rich phase is slightly darker than the water-rich one. We recover the flower pattern formed by the periodic digitation. In the hydrophilic cavity the water-rich phase is accumulated at the center and the lutidine-rich phase gives the petals, while in the hydrophobic cavity roles are swapped. The voltage is 9.2 V (135 mW) and the cavity height is $H=60\mu \mathrm{m}$. Insets: zoom on the Marangoni jets.