Electrical double layer theory is used to predict ionic transport coefficients in the fluid between two parallel charged plates, which represent clay particles. The compaction of a finite quantity of mud (clay suspended in water), to form a clay filter cake, is then modelled, using double layer theory to predict the forces between the clay particles. The path followed by the water and ions is taken to be a smoothly varying channel, which is widest at the upper (least-compacted) surface of the cake, and narrowest at the (most-compacted) cake base. There is a constant surface charge density over the walls of the channel. The electrical double layers surrounding the clay particles overlap one another at the base of the cake, and act as an ion-selective membrane. When filtration commences, the ionic concentration in the filtrate is initially lower than that in the clay suspension. The mean ionic concentration of the suspension increases during the compaction: that of the filtrate first increases and then decreases. Such variations have been previously reported, and may be responsible for the observed time dependence of the clay concentration at the base of clay filtercakes. Predictions are also made of the streaming potential generated across the cake by the motion of the filtrate: these are of the same order of magnitude as those obtained experimentally.