Fick's laws of diffusion

1. Fick’s First Law of Diffusion: This law states that the diffusive flux is proportional to the negative gradient of concentration. It implies that diffusion occurs in the direction of decreasing concentration and can be mathematically expressed as: [J = -D \frac{\partial \phi}{\partial x}] where $J$ is the diffusion flux, $D$ is the diffusion coefficient (a measure of the diffusivity of the substance), $\varphi$ is the concentration, and $\partial \varphi /\partial x$ is the concentration gradient.

2. Fick’s Second Law of Diffusion: This law provides a description of how diffusion causes the concentration to change over time. It is derived from Fick’s first law and the conservation of mass, leading to a partial differential equation that describes the time evolution of concentration: [\frac{\partial \phi}{\partial t} = D \frac{\partial^2 \phi}{\partial x^2}] This equation indicates that the rate of change of concentration at a point in space is proportional to the second derivative of concentration with respect to space, accounting for the spread of particles.