Is the relationship between penetration ratio and skin thickness first-order (proportional) or inverse?

Is the relationship between penetration ratio and skin thickness first-order (proportional) or inverse?

• A. Inverse
• B. First-order (proportional)
• C. Zero-order
• D. Logarithmic

Answer: (A)

The effect comes from diffusion through a barrier. For a membrane like skin, steady-state flux follows Fick’s law: J ≈ D ΔC / h, where h is the thickness. If you look at the permeability (the flux per unit driving concentration), P ≈ D/h (times the partition coefficient, if you include it). This shows the penetration ratio is inversely proportional to thickness: doubling the skin thickness cuts the penetration by about half, assuming D and other factors stay the same. The other shapes—proportional to thickness, constant regardless of thickness, or logarithmic—don’t match this diffusion-driven behavior.

The effect comes from diffusion through a barrier. For a membrane like skin, steady-state flux follows Fick’s law: J ≈ D ΔC / h, where h is the thickness. If you look at the permeability (the flux per unit driving concentration), P ≈ D/h (times the partition coefficient, if you include it). This shows the penetration ratio is inversely proportional to thickness: doubling the skin thickness cuts the penetration by about half, assuming D and other factors stay the same. The other shapes—proportional to thickness, constant regardless of thickness, or logarithmic—don’t match this diffusion-driven behavior.