Behavior of Particulate Solids in Fluids: Gravity, Buoyancy & Drag Forces | Assignments Heat and Mass Transfer

IN A NUTSHELL

In the perspective of chemical engineers, knowledge on the behavior of solid-

fluid mixtures hold such importance in the design of operation and processes. These

mixtures behave rather differently from other mixtures, such as the solid-solid mixtures,

hence the dynamics of these mixtures are to be studied and quantified as much as

possible. Specifically, the behavior of particulate solids moving in a fluid is to be studied

and quantified.

The movement of particulate solids are quantified according to the various forces

that act upon them in a fluid. In fact, there are three major forces that account to the net

force particulate solids experience in a fluid and these are: gravitational force, buoyant

force, and drag force. First, it is obvious that particulate solids flow through a fluid under

the influence of gravity. Particularly, gravitational force acts as the primary force that

“pulls down” particles in a fluid, allowing them to settle at the bottom if not counteracted

by another force.

Second, the buoyant force that resulted from the displacement of fluid due to the

particle being submerged in a fluid acts against the gravitational force. This is because

the displaced fluid will always “go up”, counteracting the force of gravity that “pulls

down” the particles. Then, the drag force acts upon particles and this force also

counteracts against the force of gravity. Drag force is a result of the nature of the fluid to

resist motion, thus a kind of an inertial force. All in all, these three forces account for the

total net force experienced by particles in a fluid. The following equation expresses the

relationship of these three forces on one-dimensional particle motion in fluids.

It is important to note that particles differ largely in terms of shape, and this

variable drastically varies the motion of particles in a fluid. However, as a basis for the

formulation of correlations suited for different particle shapes, a spherical particle is

considered first because of its “simple-to-quantify” geometry. Another, particles

accelerate first and then come into a state where they flow with a constant velocity. This

occurrence is important later in the design of operations and processes, and also, this

velocity is referred to as the terminal settling velocity. With all these information

considered, the general equation is finally derived from equation 1. This equation

expresses the terminal settling velocity of spherical particles in a laminar, transition and

turbulent flow.

Equation 1. One-Dimensional

Motion of a Particle in a Fluid

Equation 2. Terminal Settling

Velocity of a Spherical Particle

in a Fluid.

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IN A NUTSHELL

In the perspective of chemical engineers, knowledge on the behavior of solid- fluid mixtures hold such importance in the design of operation and processes. These mixtures behave rather differently from other mixtures, such as the solid-solid mixtures, hence the dynamics of these mixtures are to be studied and quantified as much as possible. Specifically, the behavior of particulate solids moving in a fluid is to be studied and quantified. The movement of particulate solids are quantified according to the various forces that act upon them in a fluid. In fact, there are three major forces that account to the net force particulate solids experience in a fluid and these are: gravitational force, buoyant force, and drag force. First, it is obvious that particulate solids flow through a fluid under the influence of gravity. Particularly, gravitational force acts as the primary force that “pulls down” particles in a fluid, allowing them to settle at the bottom if not counteracted by another force. Second, the buoyant force that resulted from the displacement of fluid due to the particle being submerged in a fluid acts against the gravitational force. This is because the displaced fluid will always “go up”, counteracting the force of gravity that “pulls down” the particles. Then, the drag force acts upon particles and this force also counteracts against the force of gravity. Drag force is a result of the nature of the fluid to resist motion, thus a kind of an inertial force. All in all, these three forces account for the total net force experienced by particles in a fluid. The following equation expresses the relationship of these three forces on one-dimensional particle motion in fluids. It is important to note that particles differ largely in terms of shape, and this variable drastically varies the motion of particles in a fluid. However, as a basis for the formulation of correlations suited for different particle shapes, a spherical particle is considered first because of its “simple-to-quantify” geometry. Another, particles accelerate first and then come into a state where they flow with a constant velocity. This occurrence is important later in the design of operations and processes, and also, this velocity is referred to as the terminal settling velocity. With all these information considered, the general equation is finally derived from equation 1. This equation expresses the terminal settling velocity of spherical particles in a laminar, transition and turbulent flow. Equation 1. One-Dimensional Motion of a Particle in a Fluid Equation 2. Terminal Settling Velocity of a Spherical Particle in a Fluid.

Another key physical property of particles that define their motion in a fluid is their density. In fact, density also plays a major role in the terminal settling velocity of a particle in a fluid. The other variables that affect the motion of particles in a fluid aside from their physical properties are the following: particle concentration and wall effect. First, particle concentration greatly affects the terminal settling velocity of particles in a fluid. Specifically, the more particles present in a fluid, the lesser are their terminal settling velocities in comparison to that of a single particle in a fluid. This phenomenon is called as hindered settling. Traffic is a great analogy to describe this phenomenon. For example, in the morning, when you walk alone to a store where you may want to buy your breakfast ingredients, you would obviously reach the store faster than when you walk to that store at night when the streets are crowded and busy. Hence, your “velocity” is “hindered” by just having more people along your path, and this is the same as that of a particle flowing through a fluid crowded with particles. The following is the equation that expresses the hindered settling velocity of a spherical particle in a fluid in a laminar regime, where (^) ε^2 Ψ represent as the correction factors. Equation 1 expresses the terminal settling velocity of a spherical particle in a fluid where walls have negligible effect on the velocity of the particle. However, when the volume of a container that contains the mixture, surely, walls will have an effect of upon the velocity of the particle. To correct for these deviations from infinite-dilution, the following correlations were formulated when Dp Dw

With all these behaviors quantified into equations and correlations, it is important to imply that these are vital concepts in the design of various separation processes particularly sedimentation, classification, jigging and centrifugation. First, a sedimentation process is designed to take advantage the differences in density of various kinds of particles in a fluid. A specific kind of sedimentation, called the sink and float method, chooses an appropriate fluid that has a density intermediate to the Equation 3. Hindered Settling Velocity of a Spherical Particle in a Fluid. Equation 4. Correction factor for wall effect in a laminar regime. Equation 5. Correction factor for wall effect in a turbulent regime.

Behavior of Particulate Solids in Fluids: Gravity, Buoyancy & Drag Forces, Assignments of Heat and Mass Transfer

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IN A NUTSHELL