Question

A o/w emulsion contains mineral oil (density 0.9 kg/L) and aqueous medium (density 1.05 kg/L, viscocity 0.5 poise. If the droplets have an average diameter of 5 μm, what is the velocity (cm/day) of creaming in 24 hours, according to stokes' equation?

Answer 1

The creaming ratio for o/w emulsions can be estimated from the Stokes equation:

$\upsilon =-\frac{2r^{2}(\rho -\rho _{o})g}{9\eta }$

where, υ is the creaming (settling) rate, r is the droplet radius, ρ is the density of the droplet, ρ_o is the density of the dispersion medium, η is the viscosity of the dispersion medium (continuous phase) and g is the local acceleration due to gravity.

If we put our values in the equation, we get (I've converted Poise to Pa.s for easier unit conversion later, 10 poise = 1 Pa.s):

$\upsilon =-\frac{2\cdot (2.5x10^{-6}m)^{2}(0.9\frac{kg}{L}-1.05\frac{kg}{L})\cdot 9.81\frac{m}{s^{2}}}{9\cdot 0.05Pa\cdot s }=4.087x10^{-11}\frac{m}{s}$

This can be converted to cm/day as:

$4.087x10^{-11}\frac{m}{s}\cdot \frac{100cm}{1m}\cdot \frac{3600s}{1h}\cdot \frac{24h}{1day}=3.53x10^{-4}\frac{cm}{day}$