Advancing micro-scale cooling by utilizing liquid-liquid phase separation

Achieving effective cooling within limited space is one of the key challenges for miniaturized product design. State-of-the-art micro-scale cooling enhancement techniques incorporate flow disturbances and boiling to reach high performance. However, these methods face the inherent issues of extra pressure drop, flow instability and dry-out that limits heat flux. Here we demonstrate that substantial cooling capability enhancement, up to 2.5 times, is realized by introducing the phase separation of a triethylamine (TEA)/water mixture at the micro-scale. Our experiments show that the enhancement behavior is closely related to the system’s initial composition, temperature, and flow conditions. Moreover, the mixture system exhibits reduced pressure drop after separation, which makes it more promising in serving practical applications. The results reveal new possibilities for liquid coolant selection and provide the experimental foundation for further research in this area.

is used to calculate the system's thermal conductivity due to the unavailability of experimental data. A simple validation experiment was performed using KD2-Pro to measure the system's thermal conductivity, and both data are in good agreement.

Supplementary Note 1. Thermodynamics of solution behaviors.
Any fluid mixture system evolves toward the minimum Gibb's free energy 4,5 . The change of system's free energy is quantified by the Gibb's free energy of mixing, Δgmix.
When Δgmix is less than zero, the mixed state has lower system free energy. Therefore, the mixed state, i.e., single phase mixture, is the stable state. On the contrary, when Δgmix is greater than zero, the fluid will remain in the unmixed state as a multi-phase mixture.
For an ideal mixture, Δhmix is assumed to be zero, i.e., no change in enthalpy state before and after mixing. For random mixing, the change in entropy is expressed as Where, xA and xB are the mole fractions of component A and B, respectively, and R is the universal gas constant. Note that xA and xB are values between 0 and 1, such that ln(xA) and ln(xB) are negative and thus Δsmix is greater than zero. This leads to Thus, an ideal mixture is always miscible at any concentration and temperature.
However, the ideal mixture assumption is not always true. One deviation is that Δhmix is not always zero. Δhmix represents the difference of bonding energy between molecules of different species and of the same species, assuming random mixing. Where, z is the number of bonds between molecules, ωAB is the energy of A-B molecule interaction, ωAA is the energy of A-A molecule interaction, ωBB is the energy of B-B molecule interaction, ω is the bond energy difference between A-A interaction and B-B interaction.
Assuming the above forms of Δhmix and Δsmi yields the thermodynamics model of regular solution.
When ω<0, the system favors mixing, i.e., A-B interaction is weaker than the average of A-A and B-B interaction. However, the situation becomes complicated as ω>0, and the temperature determines the sign of Δgmix. It can be seen from Fig. N1 that as ω>0, the system is completely miscible at high temperatures, and is partially miscible at low temperatures. Thus, the phase separation is brought by reducing the mixture temperature. Such a system is an Upper Critical Solution Temperature (UCST) system. Note that the system is always miscible at extreme compositions, i.e., very close to 0 or 1. Real solution behavior deviates from the regular solution model, and needs to be analyzed case by case. Figure N1. Gibb's free energy of mixing of a binary system.

Supplementary Note 2. Thermodynamics consideration of triethylamine (TEA)/water mixture
TEA/water mixture is very special due to its Lower Critical Solution Temperature (LCST) behavior. When the system is chilled below its critical temperature and remains as a single phase mixture, hydrogen bonds form between the amine part of TEA and water molecules. Thus, the TEA-water interaction is stronger than the TEA-TEA interaction and water-water interaction, indicating a positive ω. The system needs to absorb thermal energy to break the hydrogen bonds during phase separation. Moreover, the presence of hydrogen bonds changes the entropy behavior of the system. The system processes lower entropy in the mixed state than the unmixed state, since the hydrogen bonds organize the molecules.
Thus, the single phase mixed state is less chaotic than the unmixed states. As a result, the Δsmix term is less than zero. This unfavorable behavior of entropy causes the system to undergo phase separation with increased temperature.

Supplementary Note 3. Nucleation and spinodal decomposition
Nucleation and spinodal decomposition are two mechanisms involved in phase separation process 6,7 . Fig. N2 illustrates the relation between system's free energy and phase separation mechanisms. The top figure represents a typical twin-well shape binary system Gibb's free energy at a specific temperature. In Region I, the system starts with 100% component A. When adding small amount of component B, the system moves toward a lower free energy state, thus the system is miscible until reaching composition x1. In Region II, when adding component B, the system's free energy increases. This does not meet the global criterion for system stability. However, the Gibb's free energy curve remains concave, such that the system satisfies the local stability criterion, i.e., locally, the system's free energy after mixing is less than the free energy before mixing. As a result, Region II (space between x1 and x2) corresponds to a meta-stable state. If a system stays in a meta-stable state, phase separation is by means of nucleation. On the phase diagram, Region II corresponds to the gap between the binary curve and spinodal curve. For this process, an energy barrier needs to be overcome in order to trigger the phase transition process. As more B species is added, the curvature of the free energy changes and becomes convex (Region III). In this region, both global and local stability criteria are not satisfied. Consequently, the system is in an unstable state. Phase separation takes place by means of spinodal decomposition, which is an energy relaxation process with no energy barrier to overcome.
The nucleation process features with localized growth of spherical domains and needs to be triggered with substantial perturbations. Spinodal decomposition is a more intensive process with rapid domain growth and coalescence. For a UCST/LCST system at its critical composition, spinodal decomposition happens at wherever the mixture temperature is below/over the critical value. For quiescent fluid systems, spinodal composition is recognized by bi-continuous and dendritic domains. More detailed studies on spinodal decomposition further treat the process in two stages, diffusion and convection. The domain growth rate in the diffusion stage is proportional to t 1/3 (t is time), and linear with t in the convection stage. Under strong bulk convection and shear force, the domain morphology of spinodal decomposition is shown to be elongated droplets or string-shape. In order to estimate the separation boundary layer thickness, a conjugate heat transfer model is established. The model simulates the heat transfer in both fluid flow and device substrate. A hypothetical single phase fluid is incorporated into the model. The hypothetical fluid has the same properties as TEA/water mixture at its critical composition and at a temperature just below the critical temperature, but with a varying specific heat as shown Fig. S1(a). Such a configuration is able to simulate the effect of heat of mixing on the heat transfer and isolate the boost caused by the flow mixing. The simulation is done by COMSOL Multiphysics®, and the meshing size has been optimized to ensure accuracy and efficient computing. The comparison of average wall temperature between the experiment and simulation is shown in Fig. N4(a). At low heat fluxes, the flow remains as single phase flow, and our simulation yields good agreement with the experimental data. However, as the applied heat flux increases, the fluid mixture experiences phase transition and provides enhanced thermal transport. As a result, the actual average wall temperature is significantly lower than the single phase model prediction. There are two major reasons that account for the deviation, first, simulation cannot capture the flow mixing effect; and second, the change in physical/thermal properties after phase separation is not taken into consideration.
To overcome the abovementioned issues, an effective thermal conductivity, keff, is proposed. The keff is applied to the fluids within the separation boundary layer. This is realized by setting the mixture thermal conductivity as a function of temperature. When T<18.2 °C, the mixture k is used in the model; when T≥18.2 °C, keff is active in the model. The value of keff is set such that the simulation average wall temperature is as close as possible to the experimental value. It is possible that the value of keff is dependent upon the flowrate, residence time, heater length and heat flux (or fluid temperature). For simplicity, keff is found by trial and error with the least sum of square difference with the experimental wall temperature. The keff is found to be 0.68 W/(mK), and using keff leads to good agreement between the simulation and experimental wall temperatures at various flow conditions (Fig. N4(b)-(e)). The separation layer thickness (δs) is then predicted using the conjugate heat transfer model with both temperature dependent specific heat and thermal conductivity.