Fluid motion

The simplest type of centrifugal device is the cyclone separator (Fig. 3.4), which consists of a vertical cylinder with a conical bottom. The centrifugal force is generated by the fluid motion. The mixture enters in a tangential inlet near the top, and the rotating motion so created develops centrifugal force which throws the particles radially toward the wall. 

Figure 3.4 A cyclone generates centrifugal force by the fluid motion.

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

External stimulus flow meters are generally electrical in nature. These devices derive their signal from the interaction of the fluid motion with some external stimulus such as a magnetic field, laser energy, an ultrasonic beam, or a radioactive tracer. 

Momentum Flow Meters. Momentum flow meters operate by superimposing on a normal fluid motion a perpendicular velocity vector of known magnitude thus changing the fluid momentum. The force required to balance this change in momentum can be shown to be proportional to the fluid density and velocity, the mass-flow rate. 

R. S. Brodkey, The Phenomena of Fluid Motions, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967. 

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

Inline motionless mixers derive the fluid motion or energy dissipation needed for mixing from the flowing fluid itself. These mixers iaclude orifice mixing columns, mixing valves, and static mixers. 

At the shear plane, fluid motion relative to the particle surface is 2ero. For particles with no adsorbed surfactant or ionic atmosphere, this plane is at the particle surface. Adsorbed surfactant or ions that are strongly attracted to the particle, with their accompanying solvent, prevent Hquid motion close to the particle, thus moving the shear plane away from the particle surface. The effective potential at the shear plane is called the 2eta potential, It is smaller than the potential at the surface, but because it is difficult to determine 01 To usual assumption is that /q is effectively equal to which can be... 

Mechanical Gleaning. A cleaner is a hydrocyclone device utilizing fluid pressure to create rotational fluid motion (20). Pulp is introduced tangentially near the top of the cleaner. Contaminants denser than water such as chemically treated toner inks and sand migrate toward the outer wall of the cleaner and exit in a separate (reject) stream. For most forward cleaners, optimal ink removal efficiency is obtained at a pulp consistency of 0.2—0.3%. Most forward cleaners deinking efficiency declines at pulp feed consistencies greater than 0.4%. However, a cleaner said to be efficient at 1.2% pulp consistency has been reported (39). 

M. Van A.lbum of Fluid Motion The ParaboHc Press, Stanford, Calif., 1982. 

Velocity The term kinematics refers to the quantitative description of fluid motion or deformation. The rate of deformation depends on the distribution of velocity within the fluid. Fluid velocity v is a vector quantity, with three cartesian components i , and v.. The velocity vector is a function of spatial position and time. A steady flow is one in which the velocity is independent of time, while in unsteady flow v varies with time. 

Mixing of fluids is a discipline of fluid mechanics. Fluid motion is used to accelerate the otherwise slow processes of diffusion and conduction to bring about uniformity of concentration and temperature, blend materials, facihtate chemical reactions, bring about intimate contact of multiple phases, and so on. As the subject is too broad to cover fully, only a brier introduction and some references for further information are given here. 

General References Brodkey, The Fhenomena of Fluid Motions, Addison-... 

Relationship between Fluid Motion and Process Performance. 18-11... 

Close-Clearance Stirrers For some pseiidoplastic fluid systems stagnant fluid may be found next to the -essel walls in parts remote from propeller or turbine impellers. In such cases, an anchor impeller maybe used (Fig, 18-6), The fluid flow is principally circular or helical (see Fig, 18-7) in the direction of rotation of the anchor. Whether substantial axial or radial fluid motion also occurs depends on the fluid iscosity and the design of the upper blade-supporting spokes. Anchor agitators are used particularly to obtain irnpro ed heat transfer in high-consistency fluids,... 

Relationship between Fluid Motion and Process Performance Several phenomena which can be used to promote various processing objectives occur during fluid motion in a vessel. 

Some Observations on the Use of Nys With D/T ratios of less than 0.4, uniformity throughout the rest of the tank is minimal. In D/T ratios greater than 0.4, the rest of the tank has a very vigorous fluid motion with marked approach to complete uniformity before Njs is reached. 

The seeond Helmholtz law states that the vortieity of a frietionless fluid does not ehange with time. Henee, if the flow at the inlet to an impeller is irrotational, the absolute flow must remain irrotational throughout the impeller. As the impeller has an angular veloeity lu, the fluid must have an angular veloeity—lu relative to the impeller. This fluid motion is ealled the relative eddy. If there were no flow through the impeller, the fluid in the... 

Irrotational flow occurs when the fluid motion rotates about its axis (e.g., water flowing in a bend in a pipe). 

A fluid can be considered as being liquid, which is incompressible, or a gas, which is easily compressible. When a force of sufficient magnitude is applied to a fluid, motion will occur provided the frictional resistance within an open system is overcome. 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Boundary layer A layer of fluid, extending from the boundary into the bulk of the fluid, in which fluid motion is influenced by the frictional drag at the boundary. 

Turbulence Fluid motion made up of random eddies as opposed to streamline flow. 

Thus the Stokes diameter of any partiele is that of an equivalent sphere having same terminal settling veloeity and is a useful additional partiele eharaeteristie for partieulate systems involving fluid motion. 

Thus, a plot of IjN against t is a straight line (Figure 6.13) and is independent of the agitation rate. Perikinetie motion is generally thought to apply to partieles of less than ea. 1-10 pm, depending on the partiele-fluid motion. 

Camp, T.R. and Stein, P.C., 1943. Velocity gradients and internal work in fluid motion. Journal of the Boston Society of Civil Engineers, 30, 219. 

Book II investigates the dynamical conditions of fluid motion. Book III displays the law of gi avitatioii at work in the solar system. It is demonstrated from the revolutions of the six known planets, including Earth, and their satellites, though Newton could never quite perfect the difficult theory of the Moon s motion. It is also demonstrated from the motions of comets. The gravitational forces of the heavenly bodies are used to calculate their relative masses. The tidal ebb and flow and the precession of the equinoxes is explained m terms of the forces exerted by the Sun and Moon. These demonstrations are carried out with precise calculations. 

Mixing is accomplished by the rotating action of an impeller in the continuous fluid. This action shears the fluid, setting up eddies w hich move through the body of the system. In general the fluid motion involves (a) the mass of the fluid over large distances and (b) the small scale eddy motion or turbulence which moves the fluid over short distances [21, 15]. 

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