# Dissolution Measurement Equation

Many dissolution equations are well described in the text. Most of the equation are based on the well - known Fick’s law. Here, we discuss about the well-known Noyes –Whitney equation for dissolution rate calculation is given as:

dm/dt = A × D/d × (Cs – Cb)

Where,

dm/dt = solute dissolution rate (kg .s-1)

m = mass of dissolved material (kg)

t = time (s)

A = surface area of the solute particle (m2)

D = diffusion coefficient (m.s-1), which is related, in part, to the viscosity of the solvent, and will be discussed further below.

d = thickness of the concentration gradient (m)

Cs = particle surface (saturation) concentration (kg or moles/L)

Cb = concentration in the bulk solvent/solution (kg or moles/L).

#### Noyes–Whitney parameters for dissolution rate

Dissolution (with rate dm/dt) occurs from a solid with mass = m and surface area = A, from the saturation concentration at the particle surface (Cs) to the concentration in the bulk solution (Cb). Concentration follows a gradient d with a coefficient D.

If the bulk volume is large and the concentration of drug in the fluid is much lower than the drug solubility (Cs >> Ct), it is regarded as a sink condition. In this case, the equation is much simpler and the dissolution behaviors continuously occur because the chemical potential (Cs − Ct) approximates drug solubility (Cs).

In a matrix tablet, the following Higuchi equations are given depending on the polymeric structures of the homogenous and porous matrix:

In the dissolution of granular powders, the Hixson – Crowell equation is also established as: