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Updated: Aug 21, 2026

Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
Published on: November 4, 2021
Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory
Panu Danwanichakul1, Eduardo D Glandt
1Department of Chemical Engineering, Faculty of Engineering, Thammasat University, Klong-Luang, Pathumthani 12120, Thailand. dpanu@engr.tu.ac.th
Abstract:
We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.
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