An immersed boundary-lattice Boltzmann model for simulation of deposited particle patterns in an evaporating sessile droplet with dispersed particles

Abstract

Use of numerical approach by tracking the particle dynamics and contact line motion to study the complex coffee-ring phenomenon can reveal the underlying transport mechanisms. Here we propose a lattice Boltzmann model coupled with the immersed boundary method to simulate the assembly and deposition of particles suspended inside a drying sessile droplet on a hot substrate. The model deals with sufficiently small size of particles with consideration of the surface contact angle hysteresis. Our simulations show that during the droplet evaporation process, the suspended particles are dragged to the contact line by the evaporation-induced flow, thereby forming the coffee-ring pattern. The formation of ring cluster, in turn, promotes the outward flow due to the capillary force. Furthermore, most of the deposited particles are present around the droplet initial contact line, and the particle ring cluster volume increases almost linearly with particle volumetric fraction. Also, when the contact line is more slippery on the surface, a more uniform deposited particle pattern is formed after the droplet gets dried out. If the substrate temperature is sufficiently high enough, the ring location changes from the droplet's edge to its center to form the “coffee eyes” because of the shorter pinning time of the initial contact line and the Marangoni convection flow inside the droplet. In addition, we discuss the evaporation mode transition from the constant contact radius (CCR) to the mixed mode during the droplet evaporation process.