Motion of particles in a fluid

A finely ground mixture of galena and limestone in the proportion of 1 to 4 by mass, is subjected to elutriation by a current of water flowing upwards at 5 mm/s. Assuming that the size distribution for each material is the same, and is as follows, estimate the percentage of galena in the material carried away and in the material left behind. The absolute viscosity of water is 1 mN s/m2 and Stokes equation should be used. 

What is the terminal velocity of a spherical steel particle of 0.40 mm diameter, settling in an oil of density 820 kg/m3 and viscosity 10 mN s/m2 The density of steel is 7870 kg/m3. 

Thus it is seen that all the mica particles settle at approximately the same velocity. 

A material of density 2500 kg/m3 is fed to a size separation plant where the separating fluid is water which rises with a velocity of 1.2 m/s. The upward vertical component of 

Processes for the separation of particles of various sizes and shapes often depend on the variation in the behaviour of the particles when they are subjected to the action of a moving fluid. Further, many of the methods for the determination of the sizes of particles in the sub-sieve ranges involve relative motion between the particles and a fluid. 

The flow problems considered in Volume 1 are unidirectional, with the fluid flowing along a pipe or channel, and the effect of an obstruction is discussed only in so far as it causes an alteration in the forward velocity of the fluid. In this chapter, the force exerted on a body as a result of the flow of fluid past it is considered and, as the fluid is generally diverted all round it, the resulting three-dimensional flow is more complex. The flow of fluid relative to an infinitely long cylinder, a spherical particle and a non-spherical particle is considered, followed by a discussion of the motion of particles in both gravitational and centrifugal fields. 

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The motion of particles in a fluid is best approached tlirough tire Boltzmaim transport equation, provided that the combination of internal and external perturbations does not substantially disturb the equilibrium. In otlier words, our starting point will be the statistical themiodynamic treatment above, and we will consider the effect of botli the internal and external fields. Let the chemical species in our fluid be distinguished by the Greek subscripts a,(3,.. . and let f (r, c,f)AV A be the number of molecules of type a located m... 

Hancock RT. The law of motion of particles in a fluid. Trans Inst Min Engrs (London) 94 114-121, 1937/38. 

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