Sedimentation in a centrifugal field

A similar equation can be derived for batch centrifuge. A schematic of a batch 

Schematic of the batch centrifuge separating two immiscible fluids 

A force balance equation for a fluid in the rotating bowl rotating at angular velocity, w leads to pressure gradient equation given below 

Integrating this equation provides an equation for pressure P exerted by the liquid on the walls of the bowl of radius R when the radius of the inner surface of the liquid is ro as 

The retention time, C for the mixture with feed rate equal to Q is given by 

Because centrifuges are normally used for separating fine particles and droplets, it is necessary to consider only the Stokes law region in calculating the drag between the particle and the liquid. 

It is seen in Chapter 3 that, as a particle moves outwards towards the walls of the bowl of a centrifuge, the accelerating force progressively increases and therefore the particle never reaches an equilibrium velocity as is the case in the gravitational field. Neglecting the inertia of the particle, then  

The time taken to settle through a liquid layer of thickness h at the walls of the bowl is given by integration of equation 9.11 between the limits r = r0 (the radius of the inner surface of the liquid), and r = R to give equation 3.121. This equation may be simplified where R — r0 (= h) is small compared with R, as in equation 3.122. 

It may be seen that equation 9.14 is the time taken to settle through the distance h at a velocity given by equation 9.13. tR is then the minimum retention time required for all particles of size greater than d to be deposited on the walls of the bowl. Thus, the maximum throughput Q at which all particles larger than d will be retained is given by substitution for tR from equation 9.8 to give  

For cases where the thickness h of the liquid layer at the walls is comparable in order of magnitude with the radius R of the bowl, it is necessary to use equation 3.121 in place of equation 9.14 for the required residence time in the centrifuge or  

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If the motion of the molecule is one of translation, as it is during sedimentation in a centrifugal field, the velocity of every bead is the same, and in the free-draining case the difference in velocity Aw, for each bead relative to the solvent is the same as the (relative) translational velocity u of the molecule as a whole. Fig. 138 is illustrative of this case. The total force on the molecule is then... 

Sedimentation in a centrifugal field has been demonstrated to be a useful tool in the investigation of micellization in block copolymers, as first demonstrated by Tuzar etal. (1974). In this method, the velocity at which a solute species (unimer or micelle) is displaced under the influence of a strong centrifugal force is measured (Brown et al. 1995). For a given centrifugal force, the sedimentation velocity of a solute depends on its molecular weight, its buoyancy and friction... 

Svedberg. (S). A unit of measure of the rate at which a particle sediments in a centrifugal field. 

Matter, energy, charge, momentum, etc., can be transported with observable effects. The transport of matter occurs by diffusion in the earth s gravitational field, by sedimentation in a centrifugal field, and, for example, by electrophoresis in an electrical field. The viscosity of gases is due to the transfer of momentum. Energy is, for example, transported by heat conduction. 

A density difference between a liquid and suspended particles leads to a sedimentation in a centrifugal field (Fig. 4). The speed of sedimentation in radial direction... 

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