Sedimentation analysis may be used over a size range of 1 to 200 μm to obtain a size-weight distribution curve and to permit the calculation of particle size. The sedimentation analysis is based on the dependence of the rate of sedimentation of the particles on their size as expressed by Stokes’s equation.
Stokes’s law is an expression of the drag factor in a fluid and is linked to the flow conditions characterized by the Reynolds number. Drag is one of three forces acting on a particle sedimenting in a gravitational field. A drag force, Fd, acts upwards, as does a buoyancy force, Fb; a third force is gravity, Fg, which acts as the driving force of sedimentation. At the constant terminal velocity, which is rapidly achieved by sedimenting particles, the drag force becomes synonymous with particle motion. Thus for a sphere of diameter d and density ρs, falling in a f luid of density ρf, the equation of motion is:
$$ F_d=\frac{π}{6}(ρ_s-ρ_f)F_gd^3 $$
According to Stokes,
$$ F_d=3πd_hηv_{St} $$
where vSt is the Stokes terminal velocity, i.e. sedimentation rate. That is,
$$ v_{St}=\frac{(ρ_s-ρ_f)F_gd^2}{18η} $$
as vSt = h/t, where h is the sedimentation height or distance and t is the sedimentation time. By rearrangement, Stokes’s equation is obtained:
$$ d_{St}=\sqrt{\frac{18ηh}{(ρ_s-ρ_f)F_gt}} $$
Andreasen Pipet Method In Sedimentation Analysis
The Andreasen pipet method is the simplest means of incremental particle size analysis. A 1% suspension of the powder in a suitable liquid medium is placed in the pipet. At given intervals of time, samples are withdrawn from a specified depth without disturbing the suspension and are dried so that the residue may be weighed.
By means of Stokes’ equation, the particle diameter corresponding to each interval of time is calculated, with (h) being the height of the liquid above the lower end of the pipet at time t when each sample is withdrawn. As the sizes of the particles are not uniform, the particles settle at different rates.
The size-distribution and concentration of the particles vary along the length of the suspension as sedimentation occurs. The larger particles settle at a faster rate and fall below the pipet tip sooner than the smaller particles, thus, each sample drawn has a lower concentration and contains particles of smaller diameter than the previous sample.
From the weight of the dried sample, the percentage by weight of the initial suspension is calculated for particles having sizes smaller than the size calculated by Stokes’ equation for that time. The weight of each sample residue is called the weight undersize, and the sum of the successive weights is known as the cumulative weight undersize.
Centrifugation In Sedimentation Analysis
When particles are small, normal sedimentation methods are very slow and factors such as Brownian movement interfere with the results. This can be overcome by applying the same basic principles, but utilizing centrifugal force instead of gravitational force, where settling velocities can be increased greatly. The rate of sedimentation may be observed by methods similar to those used for gravitational sedimentation. Calculation of results is by Stroke’s law, with an appropriate factor to indicate the number of times the centrifugal force is greater than the gravitational force. It will be realized that the method is most useful for dealing with very small particles.
Elutriation
Eluriation is a procedure in which the fluid moves in a direction opposite to the sedimentation movement, so that in the gravitational process. For example, the particles will move vertically upwards. Then the velocity of the fluid is less than the settling velocity of the particle, the latter will move downwards against the stream of the fluid. If however, the reverse applies, the settling velocity of the particle will be insufficient to overcome the velocity of the fluid, and the particle will be carried upwards. In case of sedimentation, the separation is dependent upon the time for settling of particles while in elutriation the separation depends on the velocity of the fluid and is independent of time.
Separation into several fractions may be effected by using a number of vessels of increasing diameter, with the suspension entering the bottom of the narrowest column, overflowing from the top to the bottom of the next widest column, and so on. Since the mass flow remains the same, the greater diameter will cause the fluid to flow at a lower velocity. As the tubes become wider, therefore, particles of decreasing size will be separated.
Reference:
- Aulton, M. (2018). Aulton’s pharmaceutics, the design and manufacture of medicines. Edinburgh. : Elsevier
- Khar, R.,Vyas, S., Ahmad, F., & Jain, G. (2016). Lachman/Lieberman’s The Theory and Practice of Industrial Industrial Pharmacy. New Delhi, ND: CBS Publishers & Distributors Pvt Ltd
