2019-02 14/02/2019 ForsChem Research Reports 2019-02 (1 / 18) www.forschem.org Probability of Collision of Random Inertial Particles with a Flat Wall Hugo Hernandez ForsChem Research, 050030 Medellin, Colombia hugo.hernandez@forschem.org doi: 10.13140/RG.2.2.22874.80320 Abstract In this work, a mathematical derivation of the probability of collision of a particle moving at constant velocity against a flat wall is obtained, assuming that the velocity of the particle is random, and its position at an initial time is either known or also random. A general expression is obtained for the probability of collision as a function of the probability distribution of the velocity and position of the particle, as well as the size of the wall. Depending on the particular geometry and random distribution considered (e.g. uniform and normal distributions), different shapes of the probability as a function of the expected collision time (time required by the particle to reach the plane wall) are obtained. It is expected that the expressions obtained can be used for analyzing the behavior of different types of particles including colloids, ideal gases, subatomic particles and photons. Keywords Change of Variable Theorem, Collision, Inertial Particles, Normal Distribution, Motion, Probability Density Function, Randomistics, Randomness, Standard Transformations, Uniform Distribution. 1. Introduction The purpose of this work is obtaining a mathematical description of the probability of collision of a particle moving at a random but constant velocity against a flat rectangular wall. The results obtained might be useful for a better description of the flux of molecules across boundaries, reaction kinetics, transport phenomena, and also for understanding optical phenomena.