Coalition formation is a desirable behavior in a multi-agent system, when a group of agents can perform a task more efficiently than any single agent can. Computational and communications complexity of traditional approaches to coalition formation, e.g., through negotiation, make them impractical for large systems. We propose an alternative, physics-motivated mechanism for coalition formation that treats agents as randomly moving, locally interacting entities. A new coalition may form when two agents encounter one anothe1; and it may grow when a single agent encounters it. Such agent-level behavior leads to a macroscopic model that describes how the number and distribution of coalitions change with time. We increase the generality and complexity of the model by letting the agents leave coalitions with some probability. The model is expressed mathematically as a series of differential equations. These equations have steady state solutions that describe the equilibrium distribution of coalitions. Within a context of a specific multi-agent application, we analyze and discuss the connection between the global system utility and the parameters of the model.