Fig. 2
Illustration of the time-adaptive BD algorithm. a Particle motion in the bulk fluid. The small green circle represents a nanoparticle, and the large gray circles represent cells. The radius of the dashed circle, R, represents the distance between a particle’s current position and its nearest cell boundary. In the bulk fluid, particle jump S is taken adaptively so that |S|<R−a. |S| is determined by the time step Δ t: S=S v +S d , where S v =v Δ t (displacement due to advection), and \(\boldsymbol {S}_{d} = \sqrt {4D\Delta t}\boldsymbol {e}\) (displacement due to diffusion). b Particle motion near a cell boundary. |S| is determined by a constant but fine resolution time step δ t=10−3 seconds. The cell boundary represents a sticky wall that captures or reflects a colliding particle with probability ρ and 1−ρ, respectively