2 Centrifugation Celeste l. todaro 1.0 INTRODUCTION The solids-liquid separation process can be accomplished by filtration or centrifugation. Centrifuges magnify the force of gravity to separate phases, solids from liquids or one liquid from another. There are two general types of centrifuges Sedimentation Centrifuges-where a heavy phase settles out from a lighter phase, therefore requiring a density Filtering Centrifuges-where the solid phase is retained by a medium like a filtercloth, for example, that allows the id phase to pass through 2.0 THEORY Centrifuges operate on the principle that a mass spinning about a central axis at a fixed distance is acted upon by a force. The force exerted on any mass is equivalent to the weight of the mass times its acceleration rate in the direction of the force 558
12 Centrifugation Celeste L. Todaro 1.0 INTRODUCTION The solids-liquid separation process can be accomplished by filtration or centrifugation. Centrifuges magnify the force of gravity to separate phases, solids from liquids or one liquid from another. There are two general types of centrifuges: Sedimentation Centrifuges-where a heavy phase settles out from a lighter phase, therefore requiring a density difference and Filtering CentriBges-where the solid phase is retained by a medium like a filtercloth, for example, that allows the liquid phase to pass through. 2.0 THEORY Centrifuges operate on the principle that a mass spinning about a central axis at a fixed distance is acted upon by a force. The force exerted on any mass is equivalent to the weight of the mass times its acceleration rate in the direction of the force. 558
Centrifugation 559 Eq(1) m- mass a acceleration rate This acceleration rate is zero without a force acting upon it, however it will retain a certain velocity, v. If forced to move in a circular path, a vector velocity v/r exists as its direction is continually changing a= centrifugal acceleration Eq1(3) v= velocit w= angular velocity Should a mass be rotated within a cylinder, the resulting force at the cylinder wall is called a centrifugal force, F F=mw2?r this is away from the center of rotation. The equal and opposite force Eq,(5) is the centripetal force. This is the force required to keep the mass on its circular path Ifa cylindrical bowl holding a slurry is left to stand, the solids will settle out under the force of l g or gravity. By spinning the bowl the solids will settle under the influence of the centrifugal force generated as well as the force of gravity which is now negligible. Solids will collect at the wall with a liquid layer on top. This is an example of a sedimentation in a solid bowl syster
Centrifugation 559 F=ma m = mass a = acceleration rate F = force This acceleration rate is zero without a force acting upon it, however, it will retain a certain velocity, v. If forced to move in a circular path, a vector velocity v/r exists as its direction is continually changing. where a, = centrifugal acceleration v = velocity r = radius w = angular velocity Should a mass be rotated within a cylinder, the resulting force at the cylinder wall is called a centrifugal force, F,. Eq. (4) F, = mw2r this is away from the center of rotation. The equal and opposite force: is the centripetal force. This is the force required to keep the mass on its circular path. Ifa cylindrical bowl holding a slurry is left to stand, the solids will settle out under the force of 1 g orgravity. By spinning the bowl the solids will settle under the influence of the centrifugal force generated as well as the force of gravity which is now negligible. Solids will collect at the wall with a liquid layer on top. This is an example of a sedimentation in a solid bowl system
560 Fermentation and Biochemical engineering Handbook By perforating the bowl or basket and placing a filtercloth on the inside wall, one has now modeled a filtering centrifuge similar in principle to an ordinary household washing machine This amplification of the force of gravity is commonly referred to as the number of gs. The centrifugal acceleration(a )referenced to g is w2r/g ven e equation Eq(6) Relative Centrifugal Force(G)=1.42 x 10-5n2D where n= speed in revolutions/minute D,= diameter of the bowl in inches The driving force for separation is a function of the square of the rotational speed and the diameter of the bowl; however, there are restrictions in the design of centrifuges that will limit these variables An empty rotating centrifuge will exhibit a stress in the bowl called a elf-stress, S where w= angular velocity r= radius of the bowl Pm= density of the bowl material The contents of the bowl also generate a stress or pressure on the inner wall of the bowl. Assuming the radius of the bowl (r)is equal to the outer radius of the bowl contents(r2), we have Eq(8) S=w22(r2-n12)c/r where Pc=density of contents of the bowl r1=inner radius of the bowl contents(solids and liquid) r2=outer radius of the bowl contents(solids and liquid
560 Fermentation and Biochemical Engineering Handbook By perforating the bowl or basket and placing a filtercloth on the inside wall, one has now modeled a filtering centrifuge similar in principle to an ordinary household washing machine. This amplification ofthe force ofgravity is commonly referred to as the number of g's. The centrifugal acceleration (a,) referenced to g is w2r/g which is given by the equation: Relative Centrifugal Force (G) = 1.42 x n2 Di n = speed in revolutions/minutes Di = diameter of the bowl in inches The L.iving force for separation is a function of the square oL the rotational speed and the diameter of the bowl; however, there are restrictions in the design of centrifuges that will limit these variables. An empty rotating centrifuge will exhibit a stress in the bowl called a self-tress, S, . where w = angular velocity ri = radius of the bowl pm = density of the bowl material The contents of the bowl also generate a stress or pressure on the inner wall of the bowl. Assuming the radius of the bowl (ri) is equal to the outer radius of the bowl contents (r2), we have where t = thickness of the bowl p, = density of contents of the bowl r1 = inner radius of the bowl contents (solids and liquid) r2 =outer radius of the bowl contents (solids and liquid)
561 The total stress in the bowl wall is Sr=s+S 2-1 with D,= 2r, and in common units Eq,(9) Sr=41×0n2DD Centrifuges are designed such that S, is 45 to 65% of ST ST P lb/ft) Increasing the bowl speed and its diameter increases the g force, but also increases the self stress and the stress induced by the process bowl. The design is, therefore, really limited by the material of construction available, however, for a given bowl stress, the centrifugal acceleration is an inverse function of bowl diameter. For example, doubling the rotational speed and halving the bowl diameter, doubles the acceleration while keeping the total stress relatively constant. It is for this reason that the smallest diameter centrifuges operate at the highest g forces. Tubular centrifuges operate at 2-5 inches diameter withg forces over 60,000. Disk centrifuges operate at 7-24 inches at 14,000 to 5500 gs, while continuous decanter centrifuges with helical conveyors are designed with bowl diameters of 6-54 inches and g forces of 5, 500-770 gs. Filtering centrifuges with diameters of 12 to 108 inches have corresponding g forces of 2000 to 260 3.0 EQUIPMENT SELECTION pon review of Table l, it is evident that there are several types of equipment that can be used for the same application. There are also many
Centrifugation 561 The total stress in the bowl wall is: with Di = 2ri and in common units: Eq. (9) Centrifbges are designed such that S, is 45 to 65% of &. Increasing the bowl speed and its diameter increases the g force, but also increases the self stress and the stress induced by the process bowl. The design is, therefore, really limited by the material of construction available, however, for a given bowl stress, the centrifugal acceleration is an inverse function of bowl diameter. For example, doubling the rotational speed, and halving the bowl diameter, doubles the acceleration while keeping the total stress relatively constant. It is for this reason that the smallest diameter centrifuges operate at the highest g forces. Tubular centrifuges operate at 2-5 inches diameter withg forces over 60,000. Disk centrifuges operate at 7-24 inches at 14,000 to 5500 g’s, while continuous decanter centrifuges with helical conveyors are designed with bowl diameters of 6-54 inches and g forces of 5,500-770 g’s. Filtering centrifuges with diameters of 12 to 108 inches have corresponding g forces of 2000 to 260. 3.0 EQUIPMENT SELECTION Upon review of Table 1, it is evident that there are several types of equipment that can be used for the same application. There are also many
562 Fermentation and Biochemical Engineering Handbook equipment vendors that can be consulted. In consulting with vendors to narrow the choices, proprietary information may be divulged regarding the nature of one's process. Be sure to sign a secrecy agreement to protect all confidential information Table 1. Product Recovery Fermentation FERMENTER ROTARY VACUUM NTER MEMBRANE DRUM FILTER BOWL OR FILTRATION (LIQUID τH一2 OLVENT CARBON XTRACTION EXCHANGE ABSORP TION WASTE CRYSTALLIZATION OR(SMALL SCALEOREVAPORATOR PRODUCT OR CENTRIFUGE OR PEELER FILTER CENTRIFUGE FILTER DIRECT NDIRECT DRYER DRYER PRODUCT
562 Fermentation and Biochemical Engineering Handbook equipment vendors that can be consulted. In consulting with vendors to narrow the choices, proprietary information may be divulged regarding the nature of one’s process. Be sure to sign a secrecy agreement to protect all confidential information. Table 1. Product Recovery Fermentation DRUM FILTER CENTRIFUGE FILTRATION INCINERATED (LIQUID) OR ANIMAL (WASTE) FEEDSTOCK EXTRACTION EXCHANGE ABSORPTION 11- WASTE I LIQUID PRODUCT SOLIDS-LIQUID LIQUID-LIQUID CHROMATOGRAPHY -1 CRYSTALLIZATION OR [TIORFl (SMALL SCALE HIGH PURITY PRODUCT dk 1 OR FI OR F] I FILTER DRY FINAL