Figure 1

Model of surface-mediated diffusion in a sphere of radius $R$ containing a perfectly adsorbing cap (a target). For finite values of $k$, particles (represented as small spheres) diffusing in the bulk randomly bind to or bounce from the remaining (nonadsorbing) part of the sphere surface (outside the target cap). The target is reached either from the bulk [shown by the green (light gray) particle] or from the surface [shown by the blue (dark gray) particle].Reuse & Permissions

Figure 2

Comparison between the coarse-grained (symbols) and exact (lines) surface GMFPT $\langle t_1\rangle$ as a function of the desorption rate $\lambda$, for $\epsilon =0.02$, $N=3\times {10}^4$, and several values of $kR=6.4\times {10}^{-4},6\times {10}^{-3},6.4\times {10}^{-2}$ (from [23]), with $D_2=D_1=1$ (a) and $D_2=4D_1=4$ (b) in arbitrary units in which $R=1$.Reuse & Permissions

Figure 3

Comparison between the coarse-grained (symbols) and exact (lines) surface GMFPT $\langle t_1\rangle$ as a function of the desorption rate $\lambda$, for $\epsilon =0.02$, $N=3\times {10}^4$, and several values of $kR=1,10,100$, with $D_2=D_1=1$ (a) and $D_2=4D_1=4$ (b). The dotted curves illustrate the perturbative solution (62) which is accurate for moderate $\lambda$ but strongly deviates for very large $\lambda$.Reuse & Permissions

Figure 4

The regions of optimality for the surface GMFPT $\langle t_1\rangle$. (a) The critical ratio $D_2/D_1$ as a function of the adsorption coefficient $k$ for a fixed value of the target half-width $\epsilon =0.02$. (b) The critical ratio $D_2/D_1$ as a function of the target size $\epsilon$, for the adsorption coefficient $kR=10$. Below the lower bound (dashed red line), surface diffusion is preferred. Above the upper bound (solid blue line), the GMFPT is smaller in the desorbed state than in the adsorbed state. In between, the surface GMFPT is an optimizable function of $\lambda$. Series are truncated at $N={10}^4$.Reuse & Permissions

Figure 5

The norm $N_K$ (blue solid line and circles) and the correlation angle $\Theta$ in radians (red dashed line and squares) as functions of the adsorption coefficient $k$, for the truncation sizes $N=3000$ (lines) and $N=1000$ (symbols).Reuse & Permissions

Figure 6

The surface GMFPT $\langle t_1\rangle$ as a function of the desorption rate $\lambda$, for several values of the target adsorption parameter $k_t$ (for particles hitting the target from the bulk), with $\epsilon =0.02$ and $D_2=D_1=1$ in units in which $R=1$. The nonreactive part of the surface is semireflecting with an adsorption parameter $k=100$. Note that the target is perfectly reactive for particles adsorbed on the surface. Series are truncated at $N=3\times {10}^4$.Reuse & Permissions

Figure 7

The surface GMFPT $\langle t_1\rangle$ in the disk as a function of the desorption rate $\lambda$, for $\epsilon =0.02$, $D_2/D_1=1$, and (a) $kR=1.09\times {10}^{-2},1.09\times {10}^{-1},1.09$ (corresponding to $\alpha =0.1k_b,k_b,10k_b$) and (b) $kR=1,10,100$. Series are truncated at $N=3\times {10}^4$.Reuse & Permissions

Figure 8

The regions of optimality for the surface GMFPT $\langle t_1\rangle$ for a disk of radius $R=1$ with an aperture of half-width $\epsilon =0.02$. Below the lower bound (solid red line) surface diffusion is preferred. Above the upper bound (dashed green line), the surface GMFPT is higher in the adsorbed state than in the desorbed state. In between, the surface GMFPT is an optimizable function of $\lambda$. Series are truncated at $N={10}^4$.Reuse & Permissions