We consider the SHS (self-propagating high-temperature synthesis) process for synthesizing materials. In this process a powder mixture of reactants is cold pressed into a sample, which is ignited at one end. A high temperature combustion wave then propagates through the sample converting reactants to the desired product material. In this process, melting of some or all the components is often observed. Therefore, we study combustion waves propagating through a high caloricity inorganic powder mixture whose combustion temperature exceeds the melting temperatures of many components. The solid matrix is thus destroyed by the propagating combustion wave due to melting ahead of the reaction zone, and a liquid bath is formed which contains gaseous bubbles. The waves propagate in the presence of a gravitational field. Due to the effect of gravity, there is relative motion between the rising bubbles and the descending bath, which affects the composition of the medium, its thermophysical properties, the "liquid flame" structure, and the propagation velocity. To enhance our understanding of phenomena associated with the interaction of the relative motion with the propagating combustion wave we formulate and analyze a relatively simple mathematical model of liquid flames in a gravitational field. We describe the wave structure and combustion characteristics including the combustion velocity. We compare our results to existing experimental observations and suggest new experiments to be performed. We consider the effects of gravity and, in particular, examine both microgravity and large gravity conditions.