Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.