content_image/365752.jpg
the chucking rate k$_{c}$ in our MC simulations are in units of [MC cycles] − $^{1}$. This dynamical MC scheme allows us to represent the solute particles as penetrable hard spheres and easily to insert new solute particles, both of which would be difficult in a standard Brownian Dynamics scheme. 

The chucker and the solute particles interact according to the Asakura-Oosawa-Vrij (or penetrable hard sphere) model [31–33]: the solute particles cannot overlap with the chucker but do not interact with each other: 

<img src='content_image/365752.jpg'>

where v$_{ss}$ and v$_{sc}$ are the solute-solute and solute-chucker interaction energies, and r$_{sc}$ is the distance between the centres of the solute and chucker particles. 

Figure 1 shows snapshots from our MC simulations. To prevent the number of solute particles from growing indefinitely during the simulations, solutes need to be removed at some large distance from the chucker. Our system reaches a steady state when the rate of solute particle generation at the chucker surface equals the rate of solute absorption at the boundary. We achieve this in two different ways. For simulations with a fixed wall (as shown in the right-hand panel of Figure 1), we define a fixed cubic simulation box and remove any solute particles which stray outside this box. For simulations in the bulk (as shown in the left panel of Figure 1), we remove any solute particles that stray outside a cubic box with sides of length 2 L , centred on the current position of the chucker. The box size is large enough to have no effect on the results reported here ( L = 6 R$_{1}$ ). We have also verified that for our parameter set, the results are independent of the box size. Figure 2 shows the steady-state concentration profile of solute particles around the (moving) chucker, for several different values of L : for L ≥ 6 R$_{1}$ , the solute concentration profile is virtually independent of L . 

## B. Langevin Dynamics simulations 

To facilitate the simulation of larger systems, and to better understand the underlying physics, we have also simulated our system using an overdamped Langevin dynamics algo- 

