High quantum efficiency (QE) photocathodes are useful for many accelerator applications requiring high brightness electron beams, but suffer from short operational lifetime due to QE decay. For most photocathodes, the decrease in QE is primarily attributed to the loss of a cesium layer at the photocathode surface during operation. The development of robust, long life, high QE photoemitters is critically needed for applications demanding high brightness electron sources. To that end, a controlled porosity dispenser (CPD) photocathode is currently being explored and developed to replace the cesium during operation and increase photocathode lifetime. A theoretical model of cesium resupply, diffusion, and evaporation on the surface of a sintered wire CPD photocathode is developed to understand and optimize the performance of future controlled porosity photocathodes. For typical activation temperatures within the range of 500K--750K, simulation found differences of less than 5 % between the quantum efficiency (QE) maximum and minimum over ideal homogenous surfaces. Simulations suggest more variation for real cases to include real surface non uniformity. The evaporation of cesium from a tungsten surface is modeled using an effective one-dimensional potential well representation of the binding energy. The model accounts for both local and global interactions of cesium with the surface metal as well as with other cesium atoms. The theory is compared with the data of Taylor and Langmuir comparing evaporation rates to sub-monolayer surface coverage of cesium, gives good agreement, and reproduces the nonlinear behavior of evaporation with varying coverage and temperature.