## B. Chucker diffusion 

We now discuss the diffusive behaviour of an isolated chucker, using MC simulations with two different ratios of the chucker and solute radii: R$_{1}$/R$_{2}$ = 10 and R$_{1}$/R$_{2}$ = 100 , for various chucking rates k$_{c}$ . In our simulations, the solute particles are produced isotropically so there is no net directional motion. Rather, we observe diffusive behaviour, in which the mean square displacement 〈 r ( t ) $^{2}$〉 is linear in time. This allows us to compute an effective diffusion constant D$_{eff}$ by linear fitting of the long-time behaviour of 〈 r ( t ) $^{2}$〉 . 

Figure 5 shows that in our simulations the effective diffusion constant D$_{eff}$ of the chucker varies non-monotonically with the chucking rate k$_{c}$ . Diffusive motion of the chucker is enhanced as the chucking rate increases, for low chucking rates. At high chucking rates, diffusive motion is inhibited due to crowding by the solute particles, so that D$_{eff}$ decreases with k$_{c}$ . We plot the dimensionless quantity D$_{eff}$/D$_{1}$ , where D$_{1}$ is the diffusion constant of the chucker for zero chucking rate, versus k$_{c}$R 2 $_{2}$/D$_{1}$ . The latter turns out to be the most relevant dimensionless parameter for comparison to theory: see Ref [11] and Eq.(7). R 2 $_{2}$/D$_{1}$ is the typical time for the chucker to diffuse the radius of a solute particle; this ratio therefore measures the relative magnitudes of this time and the inverse of the chucking rate. 

We believe that the mechanism behind the increase in D$_{eff}$ with chucking rate, for small k$_{c}$ , is as follows. A stationary chucker would be surrounded by a symmetric, concentration field of solute which decreases with distance from the chucker. A small random displacement of the chucker, however, positions it asymmetrically in the solute concentration field. Osmotic effects will then tend to cause the chucker to move further in the same direction, leading to a non-thermal osmotic enhancement of the effective diffusion constant of the chucker. 

Comparing the results in Figure 5 for the two different ratios of chucker and solute radius, we find that the small k$_{c}$ regime, where D$_{eff}$/D$_{1}$ increases with k$_{c}$R 2 $_{2}$/D$_{1}$ , appears not to depend strongly on the size of the solute – although the inset, plotted on a linear scale, suggests that the two plots do not actually collapse convincingly onto one curve. On the other hand, our data suggests that the regime, for large k$_{c}$ , in which diffusion decays with chucking rate, does depend strongly on the size of the crowder: crowding effects kick in at smaller k$_{c}$R 2 $_{2}$/D$_{1}$ for the smaller solute particles. This suggests that the dependence of the crowding effect on solute radius is less steep than ∼ R 2 $_{2}$. 

Golestanian’s recent theoretical work [11], which uses linearised hydrodynamics, predicts 

