 A process used to separate or concentrate materials suspended in a liquid medium.  Centrifugation separates on the basis of the particle size and density difference between the liquid and solid phases.

 the effect of gravity on particles (including macromolecules) in suspension.  Two particles of different masses will settle in a tube at different rates in response to gravity.  Centrifugal force is used to increase this settling rate in an instrument called a centrifuge.

 Centrifuges are devices used in a variety of scientific and technical applications  The centrifugal force generated is proportional to the rotation rate of the rotor (in rpm) and the distance between the rotor center and the centrifuge tube.

 Settling: acceleration from gravity (F g )  Centrifuge:  acceleration from centrifugal force (F c )  circular motion and acceleration occurred from centrifugal force a c = acceleration from centrifugal force (m/s 2 ) r = radial distance (m) ω = angular velocity (rad/s)

 The centrifugal force, F c acting on an object of mass m, rotating in a circular path of radius R, at an angular velocity of ω is : (1) and (2) where N = rotational speed (rpm) ω= an angular velocity (rad s -1 )

 The steady-state velocity of particles moving in a streamline flow under the action of an accelerating force Where v t =terminal velicity of partical; ρ s and ρ l = density of solid and liquid ; r = distance of the particle from center of rotation; µ = viscosity of liquid.

 Time taken by the particle to move though the liquid layer is called residence time (t r ).

 flow rate (Q)

 r i = inside radius (m)  r o = outside radius (m)  b = height of centrifuge(m)  µ = viscosity (Pa.s)  ω = an angular velocity (rad s -1 )  ρ p = density of solid (kg/m 3 )  ρ = density of liquid (kg/m 3 )  D p = diameter of particle(m)

Figure 1 Liquid centrifuge (a)Pressure difference

 Consider a thin differential cylinder, of thickness dr and height b as shown in Fig. 1(a): the differential centrifugal force across the thickness dr is given by equation (1): dF c = (dm)r  2  where dF c is the differential force across the cylinder wall, dm is the mass of the differential cylinder,  is the angular velocity of the cylinder and r is the radius of the cylinder.

dm = 2πρrbdr where  is the density of the liquid and b is the height of the cylinder. The area over which the force dF c acts is 2πrb, so that: dF c /2πrb = dP =ρ  2 rdr where dP is the differential pressure across the wall of the differential cylinder.

 To find the differential pressure in a centrifuge, between radius r 1 and r 2, the equation for dP can be integrated, letting the pressure at radius r 1 be P 1 and that at r 2 be P 2, and so P 2 - P 1 = ρω 2 (r r 1 2 )/2 (3) Equation (3) shows the radial variation in pressure across the centrifuge.

Figure 1 Liquid centrifuge (b)neutral zone

ρ A ω 2 (r n 2 - r 1 2 )/2 = ρ B ω 2 (r n 2 – r 2 2 )/2 r n 2 = (ρ A r ρ B r 2 2 ) / (ρ A - ρ B ) (4) where ρ A is the density of the heavier liquid ρ B is the density of the lighter liquid  Equation (4) shows that as the discharge radius for the heavier liquid is made smaller, then the radius of the neutral zone must also decrease

FIG. 2 Liquid centrifuges: (a) conical bowl

 In liquid/liquid separation centrifuges, conical plates are arranged as illustrated in Fig. 2(a) and these give smoother flow and better separation.  Whereas liquid phases can easily be removed from a centrifuge, solids present much more of a problem.

FIG. 3 Liquid/solid centrifuges (a) telescoping bowl, (b) horizontal bowl, scroll discharge

FIG. 3 Liquid/solid centrifuges (c) nozzle (c)

 One method of handling solids from continuous feed is to employ telescoping action in the bowl, sections of the bowl moving over one another and conveying the solids that have accumulated towards the outlet, as illustrated in Fig. 3(a).

 The horizontal bowl with scroll discharge, centrifuge, as illustrated in Fig.3(b) can discharge continuously. In this machine, the horizontal collection scroll (or screw) rotates inside the conical-ended bowl of the machine and conveys the solids with it, whilst the liquid discharges over an overflow towards the centre of the machine and at the opposite end to the solid discharge.

 Another method of handling solids is to provide nozzles on the circumference of the centrifuge bowl as illustrated in Fig. 3(c). These nozzles may be opened at intervals to discharge accumulated solids together with some of the heavy liquid.

Find centrifugation time t r of a particle d=1mm. In a centrifuge Given RiRi RoRo

Find ω

Find time t r of particle d=1mm. in centrifuge≥3.25x10 -3 sec

 A bowl centrifuge is used to break an oil-in- water emulsion. Determine the radius of the neutral zone in order to position the feed pipe correctly. (Assume that the density of the continuous phase is 1000 kg/m 3 and the density of the oil is 870 kg/m 3. the outlet radius from the centrifuge are 3 cm and 4.5 cm).

 Solution

Beer with a specific gravity of and a viscosity of 1.04x10 -3 N s/m 2 contains 1.5% solids which have a density of 1160kg/m 3. It is clarified at a rate of 240 l/h in a bowl centrifuge which has and operating volume of 0.09 m 3 and a speed of rev/min. The bowl has a diameter of 5.5 cm and is fitted with a 4 cm outlet. Calculate the effect on feed rate of an increase in bowl speed to rev/min and the minimum particle size that can be removed at the higher speed.

 Solution Initial flow rate new flow rate

As all conditions except the bowl speed remain the same, Therefore, Q 2 = 0.15 l/s