Figure 2

Time dependence. (a) Results, obtained by integrating Equations 5 to 7, for the time dependence of the areal density of trapped impurities (continuous lines) at the entrance of the channel n(x = 0,t) and at its exit point n(x = L,t), and also the global average areal density of trapped impurities$\bar{n}\left(t\right)=L^{-1}{\int }_0^{L}n(x,t)\text{d}x$. The areal density axis is normalized by the saturation value n^sat. The time axis is normalized by the half-saturation time, defined by$\bar{n}\left(t_{1/2}\right)=n^{\text{sat}}/2$. The parameter values used are as follows (see main text for details): ρ₀ = 13 nm, ρ₁ = 0. 11, λ_D = 5. 1 nm,$n^{\text{sat}}=1.5\times 10^{15}/{\text{m}}^2=0.25/{\rho }_0^2$, r₀ = 500 nm,$r_1=8.8\times 10^{-24},{\text{m}}^3=4{\rho }_0^3$, Ω₀ = 0, Ω₁z₀ = 1. 2 × 10⁵/m, L = 7. 25 mm, P = 3×10⁵ Pa, η = 10⁻³ Pa·s, and$C_{\text{imp}}(x=0,t)=10^{10}/{\text{m}}^3$. We also show the linear, logarithmic, and saturated behaviors (as dashed, dotted, and dot-dashed lines respectively). (b) Time dependence of the logarithmic removal value (LRV), calculated using the same parameter values as in Figure2a.