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Quantifying the role of surface shape and physicochemical surface conditions on the interfacial reactivity of particles and substrates is fundamental to a multitude of natural and engineered surface adsorption phenomena. We consider continuum/jump regime adsorption at the gas or liquid interface of arbitrary regular solid surfaces with heterogeneous surface features. In particular, the 3-D boundary value problem (based on Laplace's diffusion equation) is converted into a 2-D integral equation for the adsorbate concentration at the particle surface. This accommodates numerical descretization via the implementation of 2-D Gauss–Legendre quadratures on an arrangement of high- and low-adsorption patch trace sites constructed to completely cover the particle surface. A generalized computer program is developed to solve the resulting linear algebra problem for the unkown local adsorption current densities. We investigate the role of various distributions of high- and low-adsorption sites for a generalized class of spheres which includes the DNA-like shaped twisted spheres. The biological implications of the role of surface curvature on interfacial adsorption/reactivity at particle surfaces are also discussed.