# 6.021/Notes/2006-10-10

### From OpenWetWare

## Diffusion

**Fick's 1st law**:

**Continuity**:

**Diffusion Equation**:

Solution of diffusion equation to impulse stimulus is Gaussian:

Time for half the solute to diffuse *x*_{1 / 2}:

**Fick's law for membranes**: ;

Membrane steady state time constant:

Solution for dissolve and diffuse: ;

## Osmosis

**Van't Hoff Law**: π(*x*,*t*) = *R**T**C*_{Σ}(*x*,*t*)

**Darcy's Law**:

**Continuity**:

Hydraulic conductivity:

Flux: Φ_{V} = *L*_{V}((*p*^{i} − π^{i}) − (*p*^{o} − π^{o}))

Cells: with solution

## Carrier Transport

Solution to simple symmetric 4-state carrier model:

;