We present a novel algorithm to simulate the release of nanoparticles from a microcapsule as it rolls along an adhesive substrate, as well as the subsequent particle adsorption on the wall. We use our recently developed method to simulate nanoparticles in the presence of a substrate, microcapsules and an externally driven flow. Here, the microcapsules consist of an elastic shell that encloses a fluid with either a dissolved chemical component or a suspension of nanoparticles that are small enough to be treated as so-called tracer particles (mutually non-interacting particles without excluded volume). We immersed this microcapsule in an external host fluid that is confined between two parallel walls. A pressure gradient is then applied to drive the flow. We focus on a single vesicle, which interacts with the substrate through a non-specific Morse potential. This potential mimics an adhesive interaction that keeps the capsule rolling along the surface.

We used the lattice Boltzmann method to simulate the dynamics of both the encapsulated and the host fluid. The capsule's shell was modeled by the lattice spring model, which simulates the dynamics of a continuum elastic material. We implemented solid-fluid interactions that give stick boundary conditions for the fluid and allow for a dynamic interaction between the elastic shell and the adjacent fluid. The nanoparticles are modeled with a Brownian dynamics algorithm to simulate particle trajectories. The shell is modeled as a porous medium, allowing the nanoparticles to permeate through the membrane. We implemented three types of boundary conditions at the external walls to simulate non-reacting walls, perfectly adsorbing walls, and chemical reactions at the walls.

Starting with the simplest case of a planar perfectly adsorbing substrate, we examine how the rate of adsorption is affected by the adhesion strength between the capsule and the substrate and the membrane stiffness. We will show that even for this simple system, the compliant nature of the capsule significantly affects the rate of deposition at the surface. We then exploit the fact that the adhesion strength between the capsule and the substrate could be different for an "untreated" surface and a surface with a coating of nanoparticles. We will discuss how this could be utilized to repair an area where the coating is damaged. In particular, we will show that an uncoated area of the substrate can act to arrest the motion of the microcapsule, thus localizing it near the damaged region. Releasing new nanoparticles from the microcapsule then allows one to "repair" the area, before the capsule continues its motion along the surface. Thus, the findings yield guidelines for efficient localized delivery of an active ingredient onto a substrate. The ability to regulate and localize the delivery of nanoparticles or reactants to specific areas at a substrate can allow researches to design effective micro-scale delivery systems.