Cell membranes are made of lipid molecules, arranged in a bilayer. In a real cell membrane many types of lipid (including cholesterol) are present, and their interactions with each other, and with other cell components, can be enormously complicated. In order to begin to understand the process by which cholesterol- enriched microdomains (so-called ''lipid rafts'') form in living cells, we study a model system in which lipid bilayers are created using variable (precisely-known) proportions of phosphatidylcholine and cholesterol. These model membranes also exhibit the formation of cholesterol-enriched patches, the size distribution of which depends on the relative proportions of lipid molecules present in the mixture. After briefly presenting the experimental findings, we formulate and solve a novel mathematical model, based on the Smoluchowski model for coagulation and fragmentation, and governed by simple thermodynamic laws. We present a comparison between the distribution of ''lipid raft'' sizes observed in our experimental lipid bilayers, and that predicted by our novel theoretical model. Excellent agreement between the experiments and theory is obtained, with minimal parameter fitting.