## **Core Concept**
Fick's law describes the diffusion process, which is crucial in understanding how substances move through membranes, such as geomembranes. The law states that the flux of a substance is directly proportional to the concentration gradient and the diffusion coefficient, and inversely proportional to the thickness of the membrane.

## **Why the Correct Answer is Right**
The correct answer, **C.**, indicates that the flux of a geomembrane increases with an increase in the diffusion coefficient. The diffusion coefficient is a measure of how easily a substance can diffuse through a medium. A higher diffusion coefficient means that the substance can move more easily through the geomembrane, thus increasing the flux. This is in line with Fick's law of diffusion, which can be expressed as (J = -D frac{dc}{dx}), where (J) is the flux, (D) is the diffusion coefficient, and (frac{dc}{dx}) is the concentration gradient.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because decreasing the thickness of the membrane would indeed increase the flux according to Fick's law, but it's not the option provided as the correct answer.
- **Option B:** This option suggests that flux increases with a decrease in the diffusion coefficient, which is incorrect. A decrease in the diffusion coefficient would make it harder for substances to diffuse through the membrane, thus decreasing the flux.
- **Option D:** This option implies that flux is unaffected by the concentration gradient or diffusion coefficient, which is not accurate according to Fick's law.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that Fick's law of diffusion is fundamental to understanding how substances move across biological and synthetic membranes. For pharmacology and toxicology, this is crucial in understanding drug absorption, distribution, and elimination. A simple mnemonic to recall factors that increase diffusion (and thus flux) is "DICK": **D**iffusion coefficient (increase), **I**ncrease in concentration gradient, **C**ross-sectional area (increase), and **K**eeping the membrane **thin** (decrease in thickness).

## **Correct Answer:** .