Liquid foams consist of randomly packed bubbles separated by a thin liquid fluid. They can be found in various industrial applications including separation processes, oil recovery, water treatment, food, and material processings. They are also being considered as coolant in heat exchangers systems for heat transfer enhancement compared with single-phase air. Similarly, liquid marbles, a phase inversion of liquid foams, consisting of a liquid core stabilized by closely packed solid hydrophobic particles, have shown significant promise as functional materials exploiting their photoresponsive behavior. In all of the above mentioned applications, it is necessary to further the current understanding of transport phenomena, such as heat, mass, and radiation transfer, in liquid foam and liquid marble systems.
First, the effects of Ostwald ripening or inter-bubble gas diffusion on the steady-state thickness of aqueous foams were investigated. The governing equation for the time rate of change of bubble radius in the liquid foam accounting for Ostwald ripening was derived and non-dimensionalized. A dimensionless similarity parameter representing the ratio of the average contact time between bubbles to the characteristic time for gas permeation was identified. This dimensionless number was combined with two previously identified dimensionless numbers accounting for viscous, gravitational, and capillary forces. A semi-empirical model predicting the steady-state height of liquid foam was developed based on experimental data for liquid foams generated by sparging different gases through a porous frit into an aqueous surfactant solution contained in a glass column.
Moreover, the stability of liquid foams exposed to normally incident thermal radiation was experimentally investigated. Here again, liquid foams were generated by injecting air into an aqueous surfactant solution contained in a glass column. Results demonstrated that the steady-state foam height decreased with increasing radiative heat flux. This was attributed to the effects of the foam temperature-dependent thermophysical properties and to liquid evaporation at the top of the foam layer. In addition, a one-dimensional reduced-order thermal model accounting for combined conduction and radiation within the steady-state foam agreed reasonably well with temperature measurements taken across the foam layer.
Furthermore, experimental data and scaling analysis for laminar forced convection of liquid foams flowing in circular and rectangular tubes as well as in tube bundles were reported. First, aqueous solutions of surfactant Tween 20 with different concentrations were used to generate microfoams with various porosity, bubble size distribution, and two-phase pseudoplastic (shear thinning) power-law fluid behaviors. These different microfoams were flowed laminarly in uniformly heated circular tubes of different diameter instrumented with thermocouples. A wide range of heat fluxes and flow rates were explored. Experimental data were compared with analytical and semi-empirical expressions derived and validated for single-phase power-law fluids. These correlations were extended to two-phase foams by defining the Reynolds number based on the effective viscosity and density of microfoams. However, the local Nusselt and Prandtl numbers were defined based on the specific heat and thermal conductivity of water. Indeed, the heated wall was continuously in contact with a film of water controlling convective heat transfer to the microfoams. Overall, good agreement between experimental results and model predictions was obtained for all experimental conditions considered. Finally, the same approach was shown to be also valid for experimental data reported in the literature for laminar forced convection of microfoams in rectangular minichannels and of macrofoams across aligned and staggered tube bundles with constant wall heat flux.
Finally, the radiation characteristics of liquid marbles made of an aqueous core stabilized by a coating of highly hydrophobic and closely packed monodisperse non-absorbing or absorbing particles were predicted numerically using the superposition T-matrix method and the geometric-optics surface-waves (GOS) method. Particular attention was paid to the effects of the liquid marble's core and coating optical properties, size parameter, and core-to-coating particle radii ratio on their absorption and scattering cross-sections and on the asymmetry factor. Results were compared with predictions by the Lorenz-Mie theory for (i) the water core alone, (ii) the volume and projected area equivalent coated sphere, and (iii) the dimensionally equivalent coated sphere.