A theoretical analysis is conducted of the retention of a dispersed phase fluid within a (multiphase) fluidised bed, in terms of the behaviour of mixed phase particles, or composite particles of the solid and dispersed fluid phases. By analysis of the thermodynamic stability of such particles due to interfacial tension - in the general case considering an "n-plet" (n solid grains surrounding a dispersed phase droplet) -solutions are obtained for the Gibbs free energy of several detachment processes as sets of dimensionless equations which are solved numerically. The analysis indicates that all geometrically possible mixed particles require energy for their rupture, of which the minimum energy rupture process (for a preferentially nonwetting dispersed phase) is isolated solid particle detachment. Thus, if sufficient energy is available, an n-plet will shed solid particles in successive rupture processes, such that if these reach the point at which the n-plet is either buoyant or elutriable, it will be released from the bed. The analysis determines the energy required for mixed-phase particle rupture and the limits of retention of such particles in any given fluidised bed. The derived energy functions are compared to the energy available for mixed particle rupture in Part II (Niven, Khalili & Hibbert, 2000).