Kamack’s equation

Concentration undersize D, is determined using Kamack s equation [Kamack, Br. J. Appl. Phys., 5, 1962-68 (1972)] ... 

Kamack s equation is applied with the assumption that the attenuation is proportional to the product of the extinetion coefficient and the cross-sectional area of the particles in the beam i.e. ln(/(//) is replaced by the optical density D where ... 

Kamack offered the following solution to equation (8.12). If Q is plotted as a function of v, = rJSy with f = o9-t as parameter, a family of curves is obtained whose shape depends on the particle size distribution function. The boundary conditions are that Q - 1 when f = 0 for all r, (i.e. the suspension is initially homogeneous) and = 0 for r, = S when f>0 (i.e. the surface region is particle free as soon as the centrifuge bowl spins). Hence all the curves, except for f>0, pass through the point Q = 0, S, and they will all be asymptotic to the line / = 0, which has the equation Q = - Furthermore, from equation (8.12), the areas under the curves are each equal to F(r/., ). 

The approximation due to Kamack can be modified, for the scanning mode of operation, by replacing the constant r/S) with the variable r/S) where r is the position of the source and detector at time t i.e. equation (8.4) becomes ... 

Kamack solved the above equation for a fixed measurement radius (r) and this solution was later extended to a variable surface radius (S ). 

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