Dynamics of the surface growth resulted from deposition of free-falling spheres at the bottom of a Hele–Shaw cell

Abstract

This paper uses experimental and simulation approaches to explore the dynamics of surface growth driven by the deposition of spherical granular particles freely falling in air within a quasi-two-dimensional system. In the experimental part, spherical polystyrene particles are released from the top of a vertical Hele-Shaw cell, forming a 1+1-dimensional growing surface. Surface roughness is quantified from captured images, and the growth and roughness exponents are determined. In the numerical simulation part, the process is simulated using the discrete element method, which accounts for particle interactions and calculates exponents. Unlike traditional simulation models that use predefined deposition laws, this method tracks the dynamics of individual particles by considering the forces that act on them throughout the process. Because of the high energy of the particles reaching the substrate, they can knock out the already deposited particles in the first few layers, leading to two different growth regimes for short and long periods, and a very smooth surface. The growth exponent in long periods is between 0.2 and 0.3, and the roughness exponent is very small (between 0.1 and 0.2), which is unusual in surface growth systems. We find different values for the exponents using different methods, which indicates that the system is multi-affine and does not obey scaling laws of affine models.