Thermal conductivity of the bubble gas-liquid media with a high concentration

It is known that Maxwell's equation (the Clausius–Mossotti formula) is widely used for calculating the electrical and thermal conductivity, dielectric constant, and other effective transport coefficients of disperse media. This formula does not take into account the interaction of particles with each other; therefore, it is believed to be valid only for a low volume concentration of the dispersed particles. The analytical dependence for calculating the thermal conductivity of an incompressible bubble medium, with taking into account the mutual influence of the bubbles, has been obtained theoretically by the author. A comparison of the results with the calculations and experimental data of other authors has shown that Maxwell's formula, which leaves out of account the interaction of bubbles, leads to an error of less than 5% in the range of bubble concentration (by volume) from 0 to 0.55. The allowance for interaction of the bubbles almost does not improve the results of Maxwell's formula. This fact testifies that the main contribution to a change in the thermal conductivity with an increase in concentration of bubbles in the bubble medium is made by a purely geometric factor.