Table III.

Summary of Expressions Used to Calculate Diffusion Parameters in SI Units

Parameter	Expression
Diffusion coefficient in SCa	$D_{\mathit{SC}}=\frac{K_p\times \delta }{K_{SC/w}}$
Diffusion coefficient in VE and Deb [8]	$D_{\mathit{VE}}=\frac{{10}^{-8.15-0.655\times \text{log}MW}}{0.68+\frac{0.32}{f_u}+0.025\times f_{\mathit{non}}\times K_{\mathit{mw}}}$
Diffusion coefficient in sebum (R2 = 0.92)c [25]	$D_{\mathit{se}}=2.48\times {10}^{-4}{e}^{-0.42\times r^2}$
Diffusion coefficient in water (Stokes equation) [26]	$D_w=\frac{k_b\times T}{6\times \pi \times \eta \times r}$

^aThe following QSPR [21] was used to calculate the permeability of the SC: ${\text{K}}_{\text{p}}=5.6\times {10}^{-6}{\text{K}}_{\text{o}/\text{w}}^{0.7}{\text{e}}^{-0.46{\text{r}}^2}$. Thickness of the SC is $\mathrm{\delta }=$ 14 μm as indicated in Fig. 1 [8]. Partition coefficient SC to water ${\text{K}}_{\text{SC}/\text{w}}$ calculated as indicated in Table II. ^bPartition coefficient lipid to water was ${\text{K}}_{\text{mw}}=\frac{{\mathrm{\rho }}_{\text{lip}}}{{\mathrm{\rho }}_{\text{w}}}{\text{K}}_{\text{o}/\text{w}}^{0.69}$ [22]. ^cMolecular radius $\text{r}=\sqrt{<}spanclass{=}^{\prime }reftyp{e}^{\prime }>[3]</span>3/4\mathrm{\pi }\times 0.9087\times \text{MW}$ [23]. ^dBoltzmann constant ${\text{k}}_{\text{b}}=$ 1.380649 $\times$ 10^–23 J/K. Temperature $\text{T}=$ 20°C. Dynamic viscosity of water $\mathrm{\eta }=$ 1.0016 mPa·s