Particles through Fluids

Many processing steps, especially mechanical separations, involve the movement of solid particles or liquid drops through a fluid. The fluid may be gas or liquid, and it may be flowing or at rest. Examples are the elimination of dust and fumes 

MECHANICS OF PARTICLE MOTION. The movement of a particle through a fluid requires an external force acting on the particle. This force may come from a density difference between the particle and the fluid or it may be the result of electric or magnetic fields. In this section only gravitational or centrifugal forces, which arise from density differences, will be considered. 

Three forces act on a particle moving through a fluid (1) the external force, gravitational or centrifugal (2) the buoyant force, which acts parallel with the external force but in the opposite direction and (3) the drag force, which appears whenever there is relative motion between the particle afld the fluid. The drag force acts to oppose the motion and acts parallel with the direction of movement but in the opposite direction. 

In the general case, the direction of movement of the particle relative to the fluid may not be parallel with the direction of the external and buoyant forces, and the drag force then makes an angle with the other two. In this situation, which is called two-dimensional motion, the drag must be resolved into components, which complicates the treatment of particle mechanics. Equations are available for two-dimensional motion, but only the one-dimensional case, where the lines of action of ail forces acting on the particle are collinear, will be considered in this book. 

EQUATIONS FOR ONE-DIMENSIONAL MOTION OF PARTICLE THROUGH FLUID. Consider a particle of mass m moving through a fluid under the action of an external force F. Let the velocity of the particle relative to the fluid be u. Let the buoyant force on the particle be F, and let the drag be F. Then the resultant force on the particle is F — F, — Fp, the acceleration of the particle is du/dt, and by Eq. (1.35), since m is constant, 

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On the velocity of steady fall of spherical particles through fluid medium." Proc. Roy. Soc. London, 83 (Ser. A) 357-365 Dale, A. J. 

SEPARATIONS BASED ON THE MOTION OF PARTICLES THROUGH FLUIDS... 

Separation Based on the Motion of Particles through Fluids Gravity Settling Processes Centrifugal Settling Processes Symbols Problems References... 

Force required to move particle through fluid (g cm/s )... 

Cuimingham, E. On the Velocity of Steady Fall of Spherical Particles through Fluid Medium. Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences, 1910, 83, 357. 

Hartman M, Yates JG. Free-fall of solid particles through fluids. Collect Czech Chem Commun 58 961-982, 1993. 

Stokes s law for the rate of settling of particles through fluids may be... 

The term electrophoresis refers to the movement of a soHd particle through a stationary fluid under the influence of an electric field. The study of electrophoresis has included the movement of large molecules, coUoids (qv), fibers (qv), clay particles (see Clays), latex spheres (see Latex technology), basically anything that can be said to be distinct from the fluid in which the substance is suspended. This diversity in particle size makes electrophoresis theory very general. 

Stokes law This relates to the factors that control the passage of a spherical particle through a fluid. The Stokes diameter of a particle is the diameter of a sphere of unit density, which would move in a fluid in a similar manner to the particle in question, which may not be spherical. 

We begin our discus.sion with the top-down approach. Let F be a two or three dimensional region filled with a fluid, and let v x,t) be the velocity of a particle of fluid moving through the point x = ( r, y, z) at time t. Note that v x, t) is a vector-valued field on F, and is to be identified with a macroscopic fluid cell. The fact that we can make this so-called continuum assumption - namely that we can simultaneously speak of a velocity of a particle of fluid and think of a particle of fluid as a macroscopic cell - is not at all obvious, of course, and deserves some attention. 

The solid-liquid separation of shinies containing particles below 10 pm is difficult by conventional filtration techniques. A conventional approach would be to use a slurry thickener in which the formation of a filter cake is restricted and the product is discharged continuously as concentrated slurry. Such filters use filter cloths as the filtration medium and are limited to concentrating particles above 5 xm in size. Dead end membrane microfiltration, in which the particle-containing fluid is pumped directly through a polymeric membrane, is used for the industrial clarification and sterilisation of liquids. Such process allows the removal of particles down to 0.1 xm or less, but is only suitable for feeds containing very low concentrations of particles as otherwise the membrane becomes too rapidly clogged.2,4,8... 

The concept of cross-flow microfiltration is shown in Figure 16.11, which represents a cross-section through a rectangular or tubular membrane module. The particle-containing fluid to be filtered is pumped at a velocity in the range 1-8 m/s parallel to the face of the membrane and with a pressure difference of 0.1-0.5 MN/m2 (MPa) across the membrane. The liquid penneates through the membrane and the feed emerges in a more concentrated form at the exit of the module.1617 All of the membrane processes are listed in Table 16.2. Membrane processes are operated with such a cross-flow of the process feed. 

RG Cox, SG Mason. Suspended particles in fluid flow through tubes. Annu Rev Fluid Mech 3 291-315, 1971. 

You want to use a viscous Newtonian fluid to transport small granite particles through a horizontal 1 in. ID pipeline 100 ft long. The granite particles have a diameter of 1.5 mm and SG = 4.0. The SG of the fluid can be assumed to be 0.95. The fluid should be pumped as fast as possible to minimize settling of the... 

Calculate the pressure drop (-AP/kPa) for flow of fluid through a fluidized bed of solid particles based on the following data the difference in density between solid particles and fluid is 2500 kg m-3 at mf conditions, the bed voidage (em/) is 0.4, and the bed depth (Lm ) is 1.2 m. State any assumptions) made. 

The diffusion process in general may be viewed as the model for specific well-defined transport problems. In particle diffusion, one is concerned with the transport of particles through systems of particles in a direction perpendicular to surfaces of constant concentration in a viscous fluid flow, with the transport of momentum by particles in a direction perpendicular to the flow and in electrical conductivity, with the transport of charges by particles in a direction perpendicular to equal-potential surfaces. 

Particulate contamination has been found in PN solutions and other intravenous drugs and fluids. Administration of particles through infusion solutions can result in adverse effects. The probability of these effects to occur increases proportionally with the amount of fluid administrated. 

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