The beta distribution as a generalized statistical model for adhesion force

The adhesive interaction between colloidal particles and surfaces is a fundamental phenomenon that governs a wide range of processes in natural and engineered systems. Adhesion measurements display variability and complex, often multimodal, or highly non-Gaussian force distributions. However, classical contact models and simple empirical descriptions typically assume uniform contacts and focus on a mean value of the adhesion force. In this study, we address these inconsistencies and introduce a novel approach in which we propose the beta distribution as a generalized adhesion force distribution that encapsulates the full spectrum of adhesion strengths between colloids and surfaces. By applying the beta distribution to adhesion data, we demonstrate that a more accurate and flexible description of surface forces can be implemented without the need to pre-assume a specific statistical distribution. By quantitatively describing the adhesion variability, the proposed model offers improved predictive capability for adhesion-mediated phenomena (such as filtration fouling, coating adhesion, and particle resuspension) under realistic surface conditions for the design of advanced materials and microdevices.