Salts and chemical fertilizers, such as potash, have a strong tendency to cake when exposed to humid air. This paper examines the recrystallization process between potash particles as a result of water evaporation after the particles have been previously wetted. A theoretical/numerical model is presented to simulate binary ion diffusion and crystallization near one contact point between two potash (KCl) particles during a typical drying process. The effects of three independent factors are investigated, initial moisture content, evaporation rate, and degree of supersaturation on the surface surrounding the contact point. In part I of this two-part series of papers, this problem is formulated subject to specific boundary conditions and initial conditions and the method of numerical analysis is presented.