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 <a onClick="popup('http://www.nanoscalereslett.com/content/8/1/19/mathml/M27','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/8/1/19/mathml/M27">View MathML</a>. The areal density axis is normalized by the saturation value nsat. The time axis is normalized by the half-saturation time, defined by <a onClick="popup('http://www.nanoscalereslett.com/content/8/1/19/mathml/M28','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/8/1/19/mathml/M28">View MathML</a>. The parameter values used are as follows (see main text for details): ρ0 = 13 nm, ρ1 = 0.11, λD = 5.1 nm, <a onClick="popup('http://www.nanoscalereslett.com/content/8/1/19/mathml/M29','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/8/1/19/mathml/M29">View MathML</a>, r0 = 500 nm, <a onClick="popup('http://www.nanoscalereslett.com/content/8/1/19/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/8/1/19/mathml/M30">View MathML</a>, Ω0 = 0, Ω1z0 = 1.2 × 105/m, L = 7.25 mm, P = 3×105 Pa, η = 10−3 Pa·s, and <a onClick="popup('http://www.nanoscalereslett.com/content/8/1/19/mathml/M31','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/8/1/19/mathml/M31">View MathML</a>. 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 Figure 2a.

Ramallo Nanoscale Research Letters 2013 8:19   doi:10.1186/1556-276X-8-19
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