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Objective:
After reading this unit, you should able to Know the analogy of heat and mass transfer.Know the mechanism of mass transfer process.
Know the diffusion and convection mass transfer processes.
Reading 1. Mass and Heat transfer Analogy.
We have, so far, dealt with heat transfer by convection, radiation, and diffusion. The word diffusion refers to transport by random molecular action. Heat diffuses as hotter molecules mix or agitate colder ones.
Mass diffuses as molecules of one kind randomly penetrate regions occupied by molecules of another kind. A wall exposed to a hot air stream may be cooled by bleeding water through its surface. Water vapor may condense out of damp air onto cool surfaces. Heat will flow through an air-water mixture in these situations, but water vapor will diffuse or convect through air as well.
During mass transfer processes, an individual chemical species travels from regions where it has a high concentration to regions where it has a low concentration. When liquid water is exposed to a dry air stream, its vapor pressure may produce a comparatively high concentration of water vapor in the air near the water surface. The concentration difference between the water vapor near the surface and that in the air stream will drive the diffusion of vapor into the air stream. We call this evaporation.
In this and other respects, mass transfer is analogous to heat transfer. Just as thermal energy diffuses from regions of high temperature to regions of low temperature (following the temperature gradient), the mass of one species diffuses from regions high concentration to regions of low concentration (following its concentration gradient.) Just as the diffusional (or conductive) heat flux is directly proportional to a temperature gradient, so the diffusional mass flux of a species is often directly proportional to its concentration gradient.
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TASK 1. COMPREHENSION QUESTIONS Answer the questions below1. When does diffusion occur?
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2. Share with your friend about the analogies between mass transfer and heat transfer?
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Reading 2. Simple diffusion
Let's examine the behavior of ions in solution in some detail. If we place some salt, NaCl, into one of two compartments separated by a removable partition, as shown in Figure 7-1, and add equal volumes of water to both compartments, we can determine how solutes move in solutions. Within a few minutes after removal of the partition, the solutions in both compartments will contain salt, and the solutions will have the same concentrations. The salt must have moved throughout the compartments; this movement is called diffusion.
Molecules in solution at temperatures above absolute zero are in random motion, so-called Brownian motion. The direction of motion of any one molecule can be changed by collision with another molecule or the side of the vessel, but once in motion the molecule will travel in a straight line until a collision occurs. The higher the temperature, the greater is the velocity of movement; the higher the concentration of the solution, the greater is the likelihood of a collision. Some collisions will result in molecules moving toward the interface between the two compartments and crossing it. The probability that a given molecule will cross the interface is therefore proportional to both temperature and the concentration of the solution.
Thus, the flux from one compartment to the other, J, is given by:
J = kC (7.1)
where k is a constant for a given temperature and C is the concentration in the compartment from which the flux is occurring.
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Figure 7.1. Diffusion and diffusion potentials. A container, with a removable partition, contains water.
Ordinary table salt, NaCl, is added to side 1 and then the partition is removed. After a time, NaCl is found in equal concentrations of both sides.
TASK 2: TRUE OR FALSE
Decide whether the following statements are true (T) or false (F).
1. Diffusion rate is propornational with concentration gradient?
2. Brownian motion is the random motion occurs when the temperature of the mixture is greater than absolute zero.
3. Diffusion rate will be faster if the temperature of the mixture is high.
4. The probability that a given molecule will cross the interface is proportional to temperature but is inversely proportional to the concentration of the solution.
Reading 3. Convection
Convection is the movement of molecules within fluids (i.e. liquids, gases) and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids. Convection is one of the major modes of heat transfer and mass transfer. Convective heat and mass transfer take place through both diffusion, the random Brownian motion of individual particles in the fluid, and by advection in which matter or heat is transported by the larger-scale motion of currents in the fluid. In the context of heat and mass transfer, the term "convection" is used to refer to the sum of advective and diffusive transfer.
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Advection refers to transport with the mean fluid flow. For example, if the wind is blowing toward the east, advection will carry any pollutants present in the atmosphere toward the east. Similarly, if a bag of dye is emptied into the center of a river, advection will carry the resulting spot of dye downstream.
TASK 3. COMPREHENSION QUESTIONS Answer the questions below
1. Why mass convection cannot occur in solid material?
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2. Do you think that both mass transfer and heat transfer can occur simultaneously? Please give some example to illustrate your point.
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3. What is Brownian motion? What is the driving force of this motion? Is it similar to diffusion in heat transfer.
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Reading4. Turbulent flow
When fluid flows past a solid surface under conditions such that turbulence generally prevails, there is a region immediately adjacent to the surface where the flow is predominantly laminar. With increasing distance from the surface, the character of the flow gradually changes, becoming increasingly turbulent, until in the outermost regions of the fluid fully turbulent conditions prevail. We have noted also that the rate of transfer of dissolved substance through the fluid will necessarily depend upon the nature of the fluid motion prevailing in the various regions.
In the turbulent region, particles of fluid no longer flow in the orderly manner found in the laminar sublayer. Instead, relatively large portions of the fluid, called eddies, move rapidly from one position to the other with an appreciable component of their velocity in the direction perpendicular to the surface past which the fluid is flowing. These eddies bring with them dissolved material, and the eddy motion thus contributes considerably to the mass-transfer process. Since the eddy motion is rapid, mass transfer in the turbulent region is also rapid, much more so than that resulting from molecular-diffusion in the laminar sublayer. Because of the rapid eddy motion, the concentration gradients existing in the turbulent region will be smaller than those in the film. In the experiment for which these are the data, air in turbulent motion flowed past a water surface, and water evaporated into the air. Samples of the air were taken at
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various distances from the surface, and the water-vapor concentration was determined by analysis. At the water surface, the water concentration in the gas was the same as the vapor pressure of pure water at the prevailing temperature. It was not possible to sample the gas very close to the water surface, but the rapid change in concentration in the region close to the surface and the slower change in the outer turbulent region are nevertheless unmistakable.
TASK 4: TRUE OR FALSE
Decide whether the following statements are true (T) or false (F).
1. When fluid flow passes a solid surface, the flow region comprises of two regions, one is laminar region and the other is turbulence.
2. When the distance from solid surface is far enough, only turbulent region appeared.
3. The nature of fluid motion will affect dramatically the heat and mass transfer rate.
4. Eddies occur when large portions of the fluid move rapidly from one position to the other with an appreciable component of their velocity in the direction parallel to the surface past which the fluid is flowing.
5. Mass transfer in turbulent condition is much more rapid than that in laminar condition.
6. The concentration of water vapor at the water liquid surface is the same as that in the air immediately on the water surface.
Reading 5.
Theory of Reverse Osmosis Membrane
A semi-permeable membrane (RO membrane) is placed between two compartments. An RO membrane is consisted of a supporting layer with 50 μm in thickness and a barrier layer with about 0.2 μm in thickness.
The phenomenon of osmosis occurs when pure water flows from a dilute saline solution in one compartment through the RO membrane into a higher concentrated saline solution in the other causing a rise in the height of the salt solution in the compartment of the higher concentrated solution. The water flow will stop when the pressure of the column of the salt solution equals to the difference in chemical potential between the two aqueous solutions. The equilibrium point of the water column height in terms of water pressure against the membrane is called osmotic pressure. If a force is applied to this column of water, the direction of water flow through the membrane can be reversed. This phenomenon is called reverse osmosis. This reversed flow produces pure water from the salt solution, since the membrane is not permeable to salt.
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(a) (b)
Figure 7.2. Schematic of osmosis experiment: (a) Without existing external pressure, and (b) presence of external pressure.
TASK 5. COMPREHENSION QUESTIONS Answer the questions below
1. In the above osmosis experiment, which direction does water flow in case a?
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2. What is the osmosis pressure?
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3. What happen if the external pressure is sufficiently high
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TASK 6: How to find good keywords
Find the keywords in reading paragraphs 3 and 4 TASK 7: Summary
In about 5 sentences, summarize the main idea in paragraphs 3 and 4
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TASK 8: GlossarySearch your knowledge, look up your dictionary, internet or ask your instructor to clarify the definition and Vietnamese meaning of the following terminologies.
No Terminology Definition Vietnamese
1 agitate 2 bulk current 3 chemical potential 4 collisions
5 concentration 6 condense 7 downstream 8 dye
9 eddy 10 evaporation 11 laminar
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membrane
13 permeable 14