### Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 28

28.1 A 1.75-cm diameter naphthalene mothball is suspended in an air stream at 280 K, 1.0 atm, and constant velocity of 1.4 m/s. Solid naphthalene exerts a vapor pressure of 2.8 Pa at 280 K. Consequently, the naphthalene very slowly sublimes into the passing air stream, with the rate limited by convective mass transfer. The density of solid naphthalene is 1.14 g/cm3, and the molecular weight is 128 g/mole.
a. What is the initial evaporation rate of naphthalene mothball?
b. How long will it take for the mothball to shrink to half of its original diameter? Remember: as the mothball shrinks, its diameter is decreasing, which in turn affects the Reynolds and Sherwood numbers.

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28.2 Pure liquid benzene (C6H6) at 290 K flows as a thin film down the outside of a vertical, 0.08-m-diameter cylinder at a flow rate of 4.0 kg/hr. Dry air at 290 K and 1.0 atm flows perpendicular to the cylinder at a velocity of 4.0 m/s. The liquid benzene exerts a vapor pressure of 8100 Pa. Determine the length of the cylinder if the entire outer surface of the cylinder is used for the evaporating process, and all of the benzene flowing down the cylinder evaporates. Assume that the surrounding air serves as an infinite sink for mass transfer.
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28.3 An engineer proposes to use the mass-transfer equipment shown in the figure (next page) to prepare a water stream containing dissolved oxygen. Liquid water containing no dissolved oxygen is fed to the tank at a rate of 50 gmole/s. The inlet water is passed through a flow diffuser that makes the velocity of the liquid uniform in the tank. The tank contains 10 silicone-walled tubes of 100 cm length and 2.0 cm outer diameter. The silicone walls are permeable to O2 gas but not to water. The long width of the tank (L) is also 100 cm, and the depth of the tank is 50 cm, so that the cross-sectional area for liquid flow is 5000 cm2. You may assume that the concentration of dissolved O2 in the tank is equal to the concentration of dissolved oxygen in the liquid outlet stream—i.e., the liquid volume is well mixed.Potentially useful data: c AL = 5:0 gmole O2=m3 (4.0 atm 100% O2 gas on tube side); rL = 998.2 kg/m3; nL = 0.995 10?6 m2/s; DAB = 2.0 10?9 m2/s (A = O2, B = H2O).
a. Develop a material balance model to predict the concentration of dissolved oxygen in the outlet liquid (cAL). State all assumptions. Your final model must be in algebraic form. Your model development should contain the following variables: cAL,o, inlet concentration of dissolved oxygen; c AL, concentration of dissolved oxygen in liquid at the tube surface; D, outer diameter of tube; v∞, bulk velocity of liquid; L, length of tube, long width of tank; W, width of tank, short dimension; kL, liquid film mass-transfer coefficient; Nt, number of tubes.
b. What is the mass-transfer coefficient kL? Does masstransfer process represents an external flow convection or internal flow convection?
c. Based on your results for parts (a) and (b) above, estimate the outlet concentration of dissolved oxygen. Based upon your analysis, do you think that this mass-transfer device works very well? Mention two doable options to increase cAL.
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28.4 A spherical drug capsule dispenses Dicyclomine (an irritable bowel syndrome drug) to the body’s gastrointestinal tract over time. Initially, 2.00 mg of Dicyclomine (mAo) is loaded into the 0.50-cm-diameter capsule. In the bulk fluid surrounding the capsule, the Dicyclomine has a residual constant concentration (cA∞) of 0.20 mg/cm3 = The solubility of Dicyclomine in the capsule polymer is the same as that in the surrounding fluid, which approximates the properties of liquid water. The molecular diffusion coefficient of Dicyclomine in water is 1.0 10?5 cm2/s, whereas the effective diffusion coefficient of Dicyclomine in the capsule matrix material is 4.0 10?6 cm2/s. At 37°C, the density and viscosity of liquid water are 1.0 g/cm3 and 0.0070 g/cm s, respectively. Fluid movement inside the intestinal tract as has “mass-transfer Biot number” of nominally 5.0, and is defined by Bi = kcR/DAe, where DAe is the effective diffusion coefficient associated with the solid surface in contact with the fluid, and R is the radius of the spherical capsule.
a. What is the concentration of Dicyclomine remaining in the center of the spherical capsule after a time of 4.34 hr (15,625 s)?
b. What is the estimated Biot number if the velocity of the bulk fluid is 0.50 cm/s? Does the diffusion process within the drug capsule have any convective mass-transfer resistances associated with it?

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28.5 horizontal chemical vapor deposition (CVD) reactor for growth of gallium arsenide (GaAs) thin films is shown in the figure (next page). In this process, arsine (AsH3), trimethyl gallium, Ga(CH3)3, andH2 gases are fed into the reactor. Inside the reactor, the silicon wafer rests on a heated plate. The reactant gases flow parallel to the surface of the wafer and deposit a GaAs thin film according to the simplified CVD reactions:...If the process is considerably diluted in H2 gas, then the mass transfer of each species in the H2 carrier gas can be treated separately. The surface reaction is very rapid, and so the mass transfer of the gaseous reactants to the surface of the wafer limits the rate of GaAs thin film formation. In the present process, the edge of a 10.0 cm silicon wafer is positioned 4.0 cm downstream of the leading edge of the susceptor plate. The wafer is inset within this plate so that a contiguous flat surface is maintained. The process temperature is 800 K, and the total system pressure 101.3 kPa (1.0 atm). Consider a limiting case where the flow rate of the H2-rich feed gas to the reactor results in a bulk linear velocity of 100 cm/s, where trimethylgallium is present in dilute concentration. Determine the local mass-transfer coefficient (kc) for trimethylgallium in H2 gas at the center of the wafer using boundary-layer theory. The binary gas-phase diffusion coefficient of trimethylgallium in H2 is 1.55 cm2/s at 800 K and 1.0 atm....
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28.6 A pond containing a suspension of microorganisms is used to biologically degrade dissolved organic materials in wastewater, as shown in the figure (right column). The pond contains 1000 m3 of liquid. Recently, inflow and outflow pipes were installed. The inlet volumetric flow rate of water is 0.05 m3/ s, and the outflow is the same to maintain a constant liquid volume. The concentration of dissolved oxygen in the inlet liquid water is 10.0 mmole/m3. The present process uses an air sparger to deliver 2.0 mm air bubbles into the wastewater. The rising bubbles uniformly mix the entire liquid phase of the pond. Only a very small portion of the O2 gas within the air bubbles (containing 0.21 atm O2) dissolves into the liquid, where it is consumed by the microorganisms. The Henry’s law constant to estimate the solubility of O2 dissolved in the wastewater that is in equilibrium with the partial pressure of O2 the aeration gas is H = 8.0 10?4 atm-m3/mmole (1000 mmole = 1.0 gmole). The interphase mass-transfer area of the bubbles per unit volume of liquid is equal to 10 m2/m3 for this process. The process is 100% liquid film controlling. At the current conditions of operation, the current biological oxygen consumption demand, or “BOD,” associated with the microbial respiration in the pond is 0.200 mmole O2/m3-s.
a. Develop a steady-state material balance model to predict the dissolved concentration of O2 in the holding pond.
b. What is the liquid-phase mass-transfer coefficient kL for O2?
c. What is the steady-state concentration of dissolved oxygen in the pond?
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28.7 As society searches for technical solutions to global warming, vast ponds of photosynthetic algae are seen as one possible solution for the removal of CO2 from combustion of fossil fuels. Consider the process shown in the figure (next page), where a flue gas containing a binary mixture 10 mole% CO2 and 90 mole% N2 is bubbled into a pond containing photosynthetic, single-celled algae that are uniformly suspended in the liquid water. The agitation provided by the rising bubbles keeps the liquid suspension well mixed. The algae consume dissolved CO2 according to a first-order reaction of the form...where RA is the CO2 consumption per unit volume of liquid suspension (gmole CO2/m3 · s, k1 is the rate constant for CO2 uptake by the algal cells (m3/g cells hr), X is the algal cell density (g cells/m3), cAL is the concentration of dissolved CO2 (gmole CO2/m3), and k1 is the apparent rate constant for CO2 uptake (k1 = k1 · X; hr?1). In the present process, there is no inflow or outflow of water into the pond. However, there is a constant delivery of CO2 to the liquid suspension by the bubbled-in flue gas, and a constant consumption of dissolved CO2 by the photosynthetic algae, with k01 = 0:06435 m3=g cells hr. Furthermore, since CO2 is not very soluble in water, it was found that the composition of CO2 gas inside the gas bubble decreased only slightly as it traveled up the water column. Therefore, the partial pressure of CO2 gas inside the gas bubble (pA) is considered constant.However, there is still a significant rate of transfer of CO2 into the liquid phase. The open pond is maintained at 20°C. At 20°C, the Henry’s law constant for the dissolution of CO2 gas in the liquid is 0.025 atm m3/gmole, the mass density of liquid is 1000 kg/m3, and the viscosity of the liquid is 993 × 10?6 kg/m·s. The aeration system is designed so that the average bubble size is 7.0 mm and the desired interphase area/liquid volume is a = 5.0 m2/m3. The mass density of the gas mixture is 1.2 kg/m3. The total liquid volume of the pond is kept constant.
a. What is the molecular diffusion coefficient of CO2 in water?
b. What is the mass-transfer coefficient for CO2 on the liquid film side of the gas bubble, kL?
c. Develop a material balance model for predicting the dissolved CO2 concentration in the pond water. The model must be in algebraic form and contain the following variables: cAL, pA, H, kL, a, k1.
d. If the cell density in the pond is maintained at 50 g cells/m3, what is the predicted concentration of dissolved CO2 in the pond, cAL?
e. If the total pond volume is 1000 m3, what is the total CO2 removal rate in kg CO2/hr?
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28.8 The well-mixed bubbler tank shown in the figure below is used to prepare carbonated water needed for the production of soft drinks. The tank volume is 2.0 m3, and the tank diameter is 1.0 m. The process operates at steady state. Pure water containing noCO2 is continuously added to the tank, and carbonated water containing dissolved CO2 continually exits the tank. Pure carbon dioxide gas at 2.0 atm is bubbled into a tank at a rate of 4.0m3 gas per minute. At these conditions, the “gas holdup” inside the tank is 0.05 m3 gas/m3 liquid, and the average bubble diameter delivered by the fine bubble sparger is 2.0 mm. The CO2 gas not absorbed by the water exits the tank. The process temperature is kept constant at 293 K. The process is liquid film controlling since only pureCO2 is present in the gas phase. The Henry’s law constant for dissolution of CO2 in water is 29.6 atm m3/kgmole at 293 K. The inlet water flow rate of 0.45m3 per minute (25 kgmole H2O/min) contains no dissolved CO2.
a. What is the liquid film mass-transfer coefficient associated with the bubbling of CO2 gas into water?
b. Is the inlet flow rate of CO2 gas sufficient to insure that the CO2 dissolution is mass transfer limited? Hint: What is the saturation concentration of dissolved CO2?
c. What is the outlet concentration of dissolved CO2? Hint: Develop a well-mixed, steady-state material balance for CO2 in the liquid phase before performing any numerical calculations.
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28.9 Consider the remediation trench shown in the figure on the next page, a simple process to treat contaminated wastewater before discharge to a lake or river. The remediation trench consists of a narrow outdoor open channel with an air sparger aligned along the bottom of the trench. Wastewater containing a volatile contaminant dissolved in the water enters one end of the trench. As the wastewater flows down the trench, the aeration gas strips out the dissolved volatile solute and transfers it to the surrounding atmosphere by an interphase mass-transfer process. Consequently, the concentration of the solute in the wastewater decreases down the length of the trench. Remediation trenches can be long, and may extend from a holding pond to the discharge point. We wish to design an aerated remediation trench to treat wastewater contaminated with trichloroethylene (TCE) at a concentration of 50 mg/L (50 g TCE/m3) wastewater. The trench is open duct of width (W) 1.0 m and depth (H) 2.0 m, and the volumetric flow rate of wastewater added to the trench is 0.10m3/s. Air is sparged into the bottom of the duct at a rate that provides a gas holdup of 0.02 m3 of gas per 1.0 m3 of water, and the average bubble diameter is 1.0 cm (0.01 m). Determine the length of the trench necessary to reduce the effluent TCE concentration to 0.05 mg/L. The process temperature is 293Kand the total systempressure is 1.0 atm. TCE is only sparingly soluble in water, and the Henry’s lawconstant for TCE in liquid water is 9.98 atm m3/kgmole and the molecular weight of TCE is 131.4 g/gmole....
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28.10 The convective mass-transfer device shown in the figure (above right) is used to generate a gas stream containing a mixture of phosphorous oxychloride (POCl3) vapor diluted in inert helium (He) gas. This gas mixture is sent to a diffusion furnace to serve as the primary dopant for the manufacture of silicon-based solar cells. In the present process, pure (100%) He gas at a volumetric flow rate of 110 cm3/s enters the 2.0-cm inner diameter tube at 50°C and 1.0 atm. The length of the tube is 60 cm. Liquid POCl3 enters a reservoir that surrounds the porous ceramic tube. The liquid POCl3 enters into the porous ceramic like a wick. At the inner surface of the tube, the POCl3 liquid vaporizes, with its vapor pressure determined by the process temperature. The process is maintained at a constant temperature of 50°C by a controlled heater surrounding the POCl3 reservoir. Therefore, the transfer of POCl3 to the gas stream is limited by diffusion across the convective boundary layer on the inside of the tube. The process can be considered dilute. The diffusion coefficient of POCl3 vapor (A) in He gas (B) is 0.37 cm2/s at 1.0 atm and 50°C. The vapor pressure of POCl3 is PA = 0.15 atm at 50°C. The kinematic viscosity of He gas at 1.0 atm and 50°C is 1.4 cm2/s....
a. Propose a model in final algebraic form to predict the outlet concentration of POCl3 vapor (CA,out) from the tube. The model should contain the following process variables: gas-phase inlet concentration of A, CA,in; gas phase outlet concentration of A, CA,out; kc, tube mass-transfer coefficient; L tube length; D, tube inner diameter; v∞, gas velocity; C A, equilibrium vapor concentration in the gas stream.
b. What is the convective mass-transfer coefficient, kc, at an inlet He volumetric flow rate of 110 cm3/s?
c. What is the outlet mole fraction of POCl3 vapor (yA,out) at an inlet He volumetric flow rate of 110 cm3/s?
d. If the inlet volumetric flow rate remains fixed at 110 cm3/s, but the diameter d is doubled, what is the new kc and yA,out? e. What is the maximum possible outlet mole fraction of POCl3 vapor for an infinitely long tube?

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28.11 Consider the novel device for oxidative treatment of waste water shown in the figure (right column). In this device, O3 will serve as the oxidant source, which must be carefully dosed into the liquid. The device consists of a vertical slit, where the walls of the slit consist of polymeric membranes that are selectively permeable to ozone gas (O3). As liquid water flows through the slit, O3 dissolves into the liquid. Assuming that the membrane offers no substantial resistance to O3 transfer, the concentration of water at the inner surface of the membrane in the liquid is adequately described by Henry’s law. For example, x A = pA/H, where pA is the partial pressure of O3 on the gas side of the membrane, and x A is the mole fraction of dissolved O3 in the liquid right at the inner liquid surface side of the membrane, and the Henry’s law constant is H = 3760 atm at 20°C. At the present conditions of operation, a single slit has a slit opening h = 1.0 cm, and slit width w = 2.0 cm. The volumetric flow rate of liquid water into a single slit is 100 cm3/s. The inlet water contains no dissolved O3. The process is dilute, with total molar concentration of the liquid equal to 0.056 gmole/cm3. At 20°C, the diffusion coefficient of dissolved O3 (solute A) in liquid water (solvent B) is DAB = 1.74 10?5 cm2/s, and the kinematic viscosity of liquid water is 0.010 cm2/s. The partial pressure of pure O3 gas on the gas side of the membrane is maintained constant at 15.0 atm.
a. The mass-transfer coefficient associated with “flow through a slit” can be converted to “flow through a tube” by simply considering an equivalent hydraulic diameter d = 2h/p. What is the convective mass-transfer coefficient kL for O3 transfer for the water inside the slit?
b. Develop a material balance model, in final integrated form, to predict the dissolved concentration of O3 at the outlet (z = L). State your primary assumptions, and clearly show the development of your differential model before you perform the final integration. The material balance model must reflect the geometry of the process. What is the required length L for cAL = 2.0 gmole/m3?
c. If PA for O3 on the gas side of the membrane is increased from 15 to 30 atm, what is the new required length L to achieve a desired cAL of 2.0 gmole/m3?
d. Modify the process to include a UV light source shining into the slit through the semitransparent membrane material, and then repeat part (b). The UV light promotes a homogeneous first-order degradation reaction of O3 dissolved in solution, with the rate equation given by RA = ?k1 cAL. At the conditions of illumination, k1 = 0.00050 s?1. Plot out cAL vs. z until the curve is flat, and compare this plot to a plot of cAL vs. z for the model in part (b).
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28.12 A concept for removing CO2 from power plant flue gas is shown in the figure (next page). A gas stream containing 5.0 mole% CO2 and 95 mole% N2 flows down into a vertical tube of 25 cm (0.25 m) inner diameter and 30 m length at a total molar flow rate (F) of 0.54 kgmole/hr. The gas is maintained at 27°C and 4.0 atm total pressure. The tube is bored into a rock formation with a porous annular space filled with a brine solution that absorbs the CO2 gas. The tube wall itself is porous so that gas can diffuse through the wall and contact the brine solution, but the brine solution itself does not permeate through the tube wall. The brine solution is continuously replenished to serve as a constant sink for CO2, but the gas does not bubble through the brine. At the porous tube wall, the concentration of CO2 of the gas within the porous wall is near zero, as the brine immediately reacts with the CO2. As the flue gas travels down the length of the tube, the concentration of CO2 in the bulk gas decreases. You may neglect the pressure drop down the length of the tube. The process may be considered dilute with respect to CO2, and the CO2 is assumed to be completely soluble in the brine solution.Potentially useful data at 1.0 atm and 27°C: the molecular diffusion coefficient of CO2 in N2 is 0.166 cm2/s; viscosity of CO2 gas, mCO2 = 1.51 10?4 g/cm s; viscosity of N2 gas, mN2 = 1.78 10?4 g/cm s; molecular weight of CO2 = 44 g/gmole; molecular weight of N2 = 28 g/gmole.
a. What is the convective mass-transfer coefficient kL for CO2 inside the tube?
b. What is the mole fraction of CO2 exiting the tube, assuming that convective mass transfer inside the tube limits the overall mass-transfer rate? As part of the problem solution development, provide a mathematical model in final algebraic form that contains the following variables: gas velocity v∞, total gas molar concentration C, inlet CO2 mole fraction yA,in, outlet CO2 mole fraction yA,out, mass-transfer coefficient kc, tube inner diameter D, tube length L. In parts (c) and (d), please now consider that the mass-transfer resistance associated with the diffusion of CO2 through the porous tube wall may play a role in the overall mass-transfer process.
c. If the tube wall thickness is 1.2 cm, the porosity (void fraction) of the ceramic tube wall material is 0.6, and the mean pore diameter is 0.8 microns (0.8 mm), what is the effective diffusion coefficient of CO2 through the tube wall?
d. Based on your result from part (c), what is the “overall mass-transfer coefficient” Kc that includes the convective mass-transfer resistance and the mass-transfer resistance through the porous tube wall? You may neglect curvature effects associated with the cylindrical nature of the tube wall.
e. Based on consideration of parts (c) and (d), what is the new exit mole fraction of CO2 (yA,out)?
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28.13 A wetted-wall column of 2.0-cm inner diameter and 50-cm wetted length is used to oxygenate blood as a continuous, steady-state process, as shown in the figure below. Blood containing 1.0 gmole/m3 of dissolved oxygen enters the top of the wetted-wall column at a volumetric flow rate of 300 cm3/min. Pure, 100% O2 gas at 1.0 atm and 25°C enters the bottom of the column at a volumetric gas flow rate of 600 cm3/min. A very simplified description for estimating the equilibrium solubility of O2 dissolved in blood is...where pA is the partial pressure of O2 in the gas phase, H = 0.8 atm m3/gmole for O2 in the blood plasma, k = 28 atm?1 for the blood hemoglobin, and cAL,max = 9.3 gmole O2/m3 for the...hemoglobin. At 25°C, the kinematic viscosity of blood is 0.040 cm2/s and the density of blood is 1.025 g/cm3. You may assume that the diffusion coefficient of O2 in blood approximates the diffusion coefficient of O2 in liquid water, which is 2.0 10?5 cm2/s at 25°C.
a. What is the mass-transfer coefficient for O2 into the flowing liquid film?
b. What is the concentration of dissolved oxygen in the liquid exiting the bottom of the column, cAL,out?

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28.14 The “soil venting” shown in the figure (at right) is used to treat soil contaminated with volatile, toxic liquids. In the present situation, the porous soil particles are saturated with liquid TCE, a common industrial solvent. The contaminated soil is dug up at the waste site and loaded into a rectangular trough. The soil consists of porous mineral particles with an average diameter of 3.0 mm, loosely compacted into a packed bed with a void fraction 0.50. Air is introduced at the bottom of the trough through a distributor and flows upward around the soil particles. Liquid TCE satiating the pores of the soil particle evaporate into the air stream. Consequently, the TCE concentration in the air stream increases. Usually, the rate of TCE evaporation is slow enough so that the liquid TCE within the soil particle is a constant source for mass transfer, at least until 80% of the volatile TCE soaked within the soil is removed. Under these conditions, the transfer of TCE from the soil particle to the air stream is limited by convective mass transfer across the gas film surrounding the soil particles. The mass flow rate of air per unit cross section of the empty bed is 0.10 kg/m2 s. The process is carried out at 293 K. At this temperature, the vapor pressure of TCE is PA = 58 mm Hg. The molecular diffusion coefficient of TCE vapor in air is given in Example 3 of this chapter.
a. What is the gas–film mass-transfer coefficient for TCE vapor in air?
b. At what position in the bed will the TCE vapor in the air stream reach 99.9% of its saturated vapor pressure? In your solution, you may want to consider a material balance on TCE in the gas phase within a differential volume element of the bed. Assume the convective mass-transfer resistances associated with air flowing over the top surface of the bed are negligible and that there is no pressure drop of the gas stream through the bed so that the total system pressure remains constant at 1.0 atm.
...Example 3Trichloroethylene (TCE), a common industrial solvent, is often found at low concentrations in industrial waste waters. Stripping is a common process for removing sparingly soluble, volatile organic solutes such asTCEfromaqueous solution.Awetted-wall column is used to study the stripping of TCE from water to air at a constant temperature of 293 K and total system pressure of 1.0 atm. The column inner diameter is 4.0 cm, and the height is 2.0 m. In the present process, the volumetric air flow rate into the column is 500 cm3/s (5.0 × 10–4m3/s), and the volumetric flow rate of water is 50 cm3/s (5.0 × 10–5m3/s). At 293 K, the density of liquid water is 998.2 kg/m3, and so the mass flow rate of water wetting the column is w = 0.05 kg/s. Estimate KL, the overall liquid-phase masstransfer coefficient for TCE across the liquid and gas film. Assume that water loss by evaporation is negligible.Relevant physical property data are provided below. The process is very dilute so that the bulk gas has the properties of air and the bulk liquid has the properties of water. The equilibrium solubility of TCE in water is described by Henry’s law of the form...whereHis 550 atm at 293 K. The binary gas-phase diffusivity of TCE in air is 8.0 × 10–6m2/s at 1.0 atm and 293 K, as determined by the Fuller–Shettler–Giddings correlation. The binary liquid-phase diffusivity of TCE in water at 293 K is 8.9 × 10–10 m2/s, as determined by the Hayduk–Laudie correlation.With this physical property information in hand, our strategy is to estimate the gas film coefficient kG, the liquid film coefficient kL, and then the overall mass-transfer coefficient KL. First, the bulk velocity of the gas is...The Reynolds number for air flow through the inside of the wetted-wall column is...and the Schmidt number for TCE in air is...where the properties of air are found from Appendix I. As the gas flow is laminar (Re<2000), equation (30-21) for laminar flow inside a pipe is appropriate for estimation of kc. Therefore,...The conversion to kG is...The liquid–film mass-transfer coefficient is now estimated. The Reynolds number for the falling liquid film is...and the Schmidt number is...where the properties of liquid water at 293 K are found in Appendix I. Equation (30-22) is appropriate for estimation of kL for the falling liquid film inside the wetted-wall column:...Since the process is dilute, the Henry’s law constant in units consistent with kL and kG is...The overall liquid-phase mass-transfer coefficient, KL, is estimated by equation (29-22):...or KL = 2.43 × 10–5 m/s. Since KLkL, the process is liquid-phase mass-transfer controlling, which is characteristic of interphase mass-transfer processes involving a large value for Henry’s law constant.
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28.15 A stirred-tank fermenter is used to cultivate aerobic microorganisms in aqueous suspension. The aerobic cells require dissolved oxygen for respiration, which is supplied by aerating the liquid medium. An important design parameter for specifying the oxygen mass-transfer rate in the fermenter is the volumetric mass-transfer coefficient, kLa. To promote the gas–liquid mass-transfer process and suspend the microorganisms within the liquid medium, a flat-blade disk turbine impeller of diameter 0.30 m rotates at 240 rev/min within a 1.0-m diameter tank of 2.0-m3 liquid volume. The aeration rate to the fermenter is 1.2 m3 of air per min, and the air bubbles are observed to be coalescing. The aerobic fermentation is carried out at 35°C and 1.0 atm system pressure. You may assume that the liquid medium approximates the properties of water.
a. Determine the volumetric mass-transfer coefficient (kLa) for O2 in water. Also, provide the aerated power input (Pg) and non-aerated power input (P) to the fermenter.
b. Based on your answer in part (a), determine the maximum oxygen mass-transfer rate (the OTR) to the liquid medium in units of moles O2 per minute. Assume that the cells immediately consume the dissolved O2, so that the dissolved oxygen concentration in the liquid medium is essentially zero. In biochemical engineering, this situation is called oxygen mass-transfer limited growth. You may also assume that the interphase mass-transfer process is liquid-phase controlling. The Henry’s law constant for the dissolution of O2 in water can be found in Table 25.1. The mole fraction of O2 in air is 0.21.

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28.16 Please refer to Problem 30.22. Now consider that a “packed column” containing 3/8-inch rings will be used instead of the wetted-wall column.
a. What is kLa, the volumetric mass-transfer coefficient?
b. What is the concentration of dissolved oxygen in the liquid exiting the bottom of the column, cAL,out? As part of this analysis, develop a material balance on a differential volume element of the column along position z.
c. Why does the packed tower perform better than the wettedwall tower in terms of overall mass transfer?
Problem 30.22A wetted-wall column of 2.0-cm inner diameter and 50-cm wetted length is used to oxygenate blood as a continuous, steady-state process, as shown in the figure below. Blood containing 1.0 gmole/m3 of dissolved oxygen enters the top of the wetted-wall column at a volumetric flow rate of 300 cm3/min. Pure, 100% O2 gas at 1.0 atm and 25°C enters the bottom of the column at a volumetric gas flow rate of 600 cm3/min. A very simplified description for estimating the equilibrium solubility of O2 dissolved in blood is...where pA is the partial pressure of O2 in the gas phase, H = 0.8 atm m3/gmole for O2 in the blood plasma, k = 28 atm?1 for the blood hemoglobin, and cAL,max = 9.3 gmole O2/m3 for the...hemoglobin. At 25°C, the kinematic viscosity of blood is 0.040 cm2/s and the density of blood is 1.025 g/cm3. You may assume that the diffusion coefficient of O2 in blood approximates the diffusion coefficient of O2 in liquid water, which is 2.0 10?5 cm2/s at 25°C.
a. What is the mass-transfer coefficient for O2 into the flowing liquid film?
b. What is the concentration of dissolved oxygen in the liquid exiting the bottom of the column, cAL,out?

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28.17 A “rotating disk” shown in the figure (at right) is used to plate a thin film of copper onto a silicon wafer by an electroless plating process at 25°C. The disk is 8.0 cm in diameter and rotates at a speed of 2.0 rev/s. The plating bath liquid volume is 500 cm3. In the electroless plating process, copper metal is deposited on a surface without an applied electrical potential. Instead, copper is deposited on a surface by the reduction of an alkaline solution containing copper (II) ions (Cu.2) stabilized by chelation with ethylene-diaminetetraacetic acid (EDTA), using formaldehyde (CH2O) dissolved in solution as the reducing agent. The overall reaction stoichiometry is...where Y represents the EDTA chelation agent. In a large excess of chelation agent, formaldehyde, and NaOH, the surface reaction for reduction of Cu.2 is first-order with respect to the dissolved copper concentration, with surface rate constant of ks = 3.2 cm/s at 25°C. The kinematic viscosity of liquid water is 0.01 cm2/s at 25°C. The diffusion coefficient of Cu.2 is 1.20 10?5 cm2/s at 25°C and infinite dilution. The density of copper is 8.96 g/cm3.
a. What is the convective mass-transfer coefficient (kL) for copper ion diffusion across the liquid boundary layer formed by the spinning disk?
b. Develop a model to describe the flux of Cu.2 from the bulk solution to the rotating disk surface that accounts for the rate of surface reaction. What is the rate of copper deposition (mol/cm2-s) if the Cu.2 concentration is 0.005 gmole/L? Which process is controlling, surface reaction or boundary-layer diffusion?
c. Develop an unsteady-state material balance model to describe the depletion of copper ions in solution with time. How long will it take to deposit a 2.0 mm solid thin film of Cu0, if the initial Cu.2 concentration is 0.005 gmole/L and there is initially no copper deposited on the surface? Clearly state all assumptions.
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### Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 27

27.1 The table below presents equilibrium distribution data for four gaseous solutes dissolved in water, using air as the carrier gas:......
a. Using a spreadsheet to perform the calculations, prepare a graph of the equilibrium distribution data for each solute as partial pressure in the gas vs. molar concentration dissolved in the liquid (pAcAL), and also in mole fraction coordinates (yAxA) at 1.0 atm total system pressure. Which solute is the most soluble in water? Which solute dissolved in water can be stripped into air the easiest?
b. For each solute at the appropriate concentration range, estimate the Henry’s law constant (H) based on the definition ..., and the distribution coefficient m based on the definition ... at 1.0 atm total system pressure.

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27.2 Hydrogen sulfide (H2S) is a common contaminant in natural gas. The dissolution of H2S gas in water is a linear function of partial pressure, as is described by Henry’s law of the form .... Values of H vs. temperature are provided below:...Given the relatively low solubility of H2S in water, an aminebased chelating agent is added to the water to improve the solubility of H2S. Equilibrium distribution data for H2S in a 15.9 wt% solution of monoethanolamine (MEA) in water at 40 °C is provided below:4...
a. Describe the effect of temperature on the solubility of H2S gas in water.
b. Prepare equilibrium distribution plots, in mole-fraction coordinates (yAxA), for the solubility of H2S in water vs. H2S in 15.9 wt% MEA solution at 40 °C and 1.0 atm total system pressure. Comment on the relative solubility of H2S in water vs. MEA solution.

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27.3 Consider an interphase mass-transfer process for the chlorine dioxide (ClO2)-air-water system at 20 °C, where ClO2 gas (solute A) is sparingly soluble in water. At the current conditions of operation, the mole fraction of ClO2 in the bulk gas phase is yA = 0.040 and the mole fraction of ClO2 in the bulk liquid phase is xA = 0.00040. The mass density of the liquid phase is 992.3 kg/m3 and is not dependent on the very small amount of ClO2 dissolved in it. The molecular weight of water is 18 g/gmole, and the molecular weight of ClO2 is 67.5 g/gmole. The total system pressure is 1.5 atm. The liquid film mass-transfer coefficient for ClO2 in water is kx = 1.0 gmole/m2 · s, and the gas film mass-transfer coefficient ClO2 in air is kG = 0.010 gmole/m2 · s · atm. The equilibrium distribution data for the ClO2-water-air system at 20 °C are provided below:...
a. Plot out the equilibrium line in pAcAL coordinates, and the operating point (pA, cAL). Is the process gas absorption or liquid stripping?
b. What is the equilibrium relationship as m equal to?
c. What is kL for the liquid film?
d. If the ClO2 mole fraction in the bulk gas phase is maintained at 0.040 under 1.5 atm total system pressure, what is the maximum possible dissolved ClO2 concentration (gmole A/m3) in the liquid phase that could possibly exit the process—i.e., ...?
e. What are the compositions at the gas–liquid interface, pA, i and cAL, i?
f. What is Ky, the overall mass-transfer coefficient based upon the overall gas phase mole fraction driving force? There are several valid approaches for calculating Ky based on the information provided. Show at least two approaches that lead to the same result.
g. What is the mass-transfer flux NA for ClO2 in units of gmole/m2 · s?

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27.4 It is desired to recover hexane vapor (solute A) from air using an absorption process. The absorption solvent is a nonvolatile mineral oil, which has a mass density of 0.80 g/cm3 and a molecular weight of 180 g/gmole. In the dilute concentration range, the equilibrium relationship for the dissolution of hexane vapor in the mineral oil at 20 °C is described by pA,i = HxA,i, where H = 0.15 atm. At the present conditions of operation, the hexane partial pressure in the bulk gas stream is 0.015 atm, and the dissolved hexane in the bulk absorption solvent is 5.0 mole%. The total system pressure is 1.50 atm, and the temperature is 20 °C. The liquid film mass-transfer coefficient kx is 0.01 kgmole/m2 · s, and the gas film mass-transfer coefficient ky is 0.02 kgmole/m2 · s.
a. What is the overall mass-transfer coefficient based on the liquid phase, KL, and molar flux NA?
b. What is the composition of hexane at the gas–liquid interface, in terms of pA,i and xA,i?

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27.5 A packed-bed tower is used for absorption of sulfur dioxide (SO2) from an air stream using water as the solvent. At one point in the tower, the composition of SO2 is 10% (by volume) in the gas phase, and 0.30 wt% in the liquid phase, which has a mass density 61.8 lbm/ft3.The tower is isothermal at 30 °C, and the total system pressure is 1.0 atm. The convective mass-transfer coefficients are kL = 2.5 lbmole/ft2 · h · (lbmole/ft3) for the liquid film, and kG = 0.125 lbmole/ft2 · h · atm for the gas film. Equilibrium distribution data for the SO2-water-air system are provided in Problem 29.1.
a. Plot out the equilibrium line in units of pA (atm) vs. cAL (lbmole/ft3). Plot out the operating point (pA, cAL) on the same graph. Determine ... and ... and plot on the same graph.
b. Determine the gas–liquid interface compositions pA,i and cAL,i;
c. Estimate KG and KL, Ky and Kx at the operating point, and the molar flux NA.
d. Determine the % resistance in the gas phase at the operating point.
Problem 29.1The table below presents equilibrium distribution data for four gaseous solutes dissolved in water, using air as the carrier gas:......
a. Using a spreadsheet to perform the calculations, prepare a graph of the equilibrium distribution data for each solute as partial pressure in the gas vs. molar concentration dissolved in the liquid (pAcAL), and also in mole fraction coordinates (yAxA) at 1.0 atm total system pressure. Which solute is the most soluble in water? Which solute dissolved in water can be stripped into air the easiest?
b. For each solute at the appropriate concentration range, estimate the Henry’s law constant (H) based on the definition ..., and the distribution coefficient m based on the definition ... at 1.0 atm total system pressure.

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27.6 An engineer at a pulp mill is considering the feasibility of removing chlorine gas (Cl2, solute A) from an air steam using water, which will be reused for a pulp bleaching operation. The process will be carried out in a countercurrent flow gas absorption tower filled with inert packing, where liquid water containing no dissolved Cl2 is pumped into the top of the tower (... = 0), and air containing 20% by volume Cl2 (... = 0.20) at 1.0 atm is fed into the bottom of the tower. Gas–liquid contact is promoted by the inert packing surface as the gas and liquid flow around the packing. As the gas moves to the top of the tower, the Cl2 composition decreases, and as liquid moves down the tower, the dissolved Cl2 concentration increases. At the gas and liquid flow rates of operation, the liquid leaving the bottom of the tower has a composition of 0.05 mole% (... = 0.00050), and the gas exiting the top of the tower has been lower to 5% by volume (... = 0.050). At the flow rates of operation, the gas film mass-transfer coefficient based on a mole fraction driving force (ky) is 5.0 lbmole/ft2 · hr, and the liquid film mass-transfer coefficient based on a mole fraction driving force (kx) is 20 lbmole/ft2 · hr. Equilibrium data for the Cl2-water-air system at 20 °C and 1.0 atm are provided in the table below....
a. Draw a diagram of what the packed tower might look like, labeling liquid flow with L, gas flow with G, and terminal steam mole fraction compositions ... and ... at the bottom and top of the tower.
b. Plot out the equilibrium line in mole fraction coordinates. Then plot out the operating points ... and ... for the bottom and the top of the tower respectively.
c. Determine the local overall mass-transfer coefficients Ky at the top and bottom of the tower? Why are the values for Ky different?

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27.7 Ammonia (NH3) and hydrogen sulfide (H2S) must both be stripped from wastewater in a packed tower before the wastewater can be treated for reuse. Individual mass-transfer coefficients for ammonia transfer within a packed tower are kG = 3.20 × 10–9 kgmole/m2 · s · Pa for the gas film, and kL = 1.73 × 10–9 m/s for the liquid film. At the temperature and concentration ranges of the solutes within the process, the equilibrium distribution data for the solutes NH3 and H2S are in the linear range. The Henry’s law constants are 1.36 × 103 m3 · Pa/kgmole for NH3, and 8.81 × 105 m3 · Pa/kgmole for H2S. Under the assumption that both kG and kL for H2S transfer is the same as those for NH3 transfer, estimate and compare the overall mass-transfer coefficients KG and KL for H2S and NH3, respectively.
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27.8 Wastewater containing dissolved hydrogen sulfide (H2S) at concentration of 2.50 gmole/m3 (85 mg/L) enters an open tank at a volumetric flow rate of 20 m3/h, and exits at the same volumetric flow rate, as shown in the figure on the next page. The open tank is within a large enclosed building. The ventilation for the air surrounding the open tank is such that the composition of H2S in the bulk, well-mixed air over the tank is 0.5 mole% H2S (gas-phase mole fraction of 0.005), which has a pungent odor. The total system pressure is 1.0 atm, and the temperature is 20 °C. The diameter of the cylindrical tank is 5.0 m, and the depth of the liquid in the tank is 1.0 m. At the conditions of operation, the film mass-transfer coefficients for H2S transfer are kL = 2.0 · 10–4 m/s in the liquid film, and kG = 5.0 · 10–4 kgmole/m2 · s · atm in the gas film. The solute H2S (solute A) is sparingly soluble in water, with the linear equilibrium distribution data at 20 °C described by Henry’s law with H = 9.34 m3 · atm/kgmole. At 20 °C, the mass density of the wastewater is 1000 kg/m3.The molecular weight of H2S is 34 g/gmole, and H2O is 18 g/gmole....
a. Estimate m, the equilibrium distribution constant based upon the mole fraction equilibrium relationship—e.g., yA,i = mxA,i. Plot out the operating point (xA, yA) and the equilibrium line in mole fraction coordinates. Is the process gas absorption or liquid stripping?
b. What is the overall mass-transfer coefficient Ky based upon the overall gas-phase mole fraction driving force?
c. Perform a material balance on the process. At the conditions of operation, what is the concentration of dissolved H2S exiting the tank, cAL, in units of gmole/m3?

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27.9 Ozone gas (O3, solute A) dissolved in high-purity water is commonly used in wet cleaning processes associated with semiconductor device fabrication. It is desired to produce a liquid water stream containing 3.0 gmole O3/m3 (238 mg/L) by a process that does not create any gas bubbles. One engineer’s idea is shown in the figure below. Liquid water containing 1.0 gmole O3/m3 enters a well-mixed tank at a volumetric flow rate 0.050 m3/h. A pressurized gas mixture of O3 diluted in inert N2 is continuously added the headspace of the tank at a total pressure of 1.5 atm. Both the liquid and gas inside the tank are assumed to be well mixed. The gas–liquid surface area inside the tank is 4.0 m2. The process is maintained at 20 °C. At 20 °C, the solution density is 992.3 kg/m3. For a well-mixed, non-bubbled ozonation tank, the appropriate film mass-transfer coefficients for the liquid and gas films are kL = 3.0 · 10–6 m/s andkc = 5.0 · 10–3 m/s, respectively. Equilibrium distribution data for O3 gas dissolved in water at 20 °C follows Henry’s law, with H = 68.2 m3 · atm/kgmole based on the definition pA,i = H · cAL,i....
a. What are m, and the Henry’s law constant H in units of atm? Is O3 very soluble in water?
b. What is the overall mass-transfer coefficient KG, based on the overall gas-phase driving force?
c. What is the overall mass-transfer coefficient KL based on the overall liquid-phase driving force?
d. For the process to operate as intended, what are the required partial pressure (pA) and mole fraction (yA) of ozone (O3) in the gas phase inside the tank? As part of your solution, develop a material balance model in algebraic form for solute A that contains the following terms: vo, volumetric flow rate of liquid (m3/hr); cAL,o, inlet concentration of solute A in liquid (gmole A/m3); cAL, outlet concentration of solute A in liquid (gmole O3/m3); KG, overall mass-transfer coefficient based on gas-phase driving force (gmole/m2 · s · atm), pA, partial pressure of O3 in bulk gas phase (atm); H, Henry’s law constant for O3 between gas and liquid (m3 · atm/gmole); S, surface area for interphase mass-transfer (m2).
e. What is the total transfer rate of O3, WA?
f. Is the mass-transfer process is gas film controlling, liquid film controlling, or neither? Comment on the relative contributions of the film mass-transfer coefficients and the equilibrium distribution relationship on the controlling mass-transfer resistance.

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27.10 Jasmone (molecular formula C11H16O) is a valuable specialty chemical that is obtained from the jasmine plant. A common method of manufacture is to extract the plant material in water, and then use benzene to concentrate the jasmone in a simple liquid-liquid extraction process. Jasmone (species A) is 170 times more soluble in benzene than in water, and so...where ... is the concentration of jasmone in benzene, and cA is the concentration of jasmone in water. In a proposed extraction unit, the benzene phase is well mixed with the film mass-transfer coefficient ... = 3.5 × 10–6 m/s. The aqueous phase is also well mixed with its film mass-transfer coefficient kL = 2.5 × 10–5 m/s. Determine
a. The overall liquid mass-transfer coefficient, ..., based on the benzene phase
b. The overall liquid transfer coefficient, KL, based on the aqueous phase
c. The percent resistance to mass-transfer encountered in the aqueous liquid film

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27.11 Ammonia (NH3) in air is being absorbed into water within the enclosed tank shown in the figure (next page). The liquid and gas phases are both well mixed, and mass-transfer occurs only at the exposed gas–liquid interface. The diameter of the cylindrical tank is 4.0 m, and the total liquid volume inside the tank is constant. The bulk gas partial pressure of NH3 is maintained at 0.020 atm, and the total gas pressure is constant at 1.0 atm. The system is isothermal at 20 °C. The inlet volumetric flow rate of water is 200 L/h (0.20 m3/hr), and there is no NH3 in the inlet liquid stream (i.e., cAL,o = 0). You may assume that Henry’s law adequately describes the equilibrium distribution of NH3 between the gas and liquid phases, given by PA,i = H · cAL,i, where H = 0.020 m3 · atm/kgmole. The mass-transfer coefficients for the gas and liquid films are kG = 1.25 kgmole/m2 · hr · atm and kL = 0.05 kgmole/(m2 · hr · (kgmole/m3)), respectively....
a. Develop a material balance equation for NH3 (solute A). Then determine cAL, the concentration of dissolved NH3 in the outlet liquid stream. In material balances involving interphase mass-transfer, base the material balance on one phase. For this process, consider a material balance on NH3 based on the liquid phase.
b. Determine pA,i the partial pressure of NH3 at the gas–liquid interface, and cAL,i, the dissolved NH3 concentration at the liquid side of the gas–liquid interface.
c. Determine WA, the total rate of ammonia transfer.
d. In the above system, the flux NA would increase by increasing which of the following: the liquid volume level in the tank at fixed surface area; the agitation intensity of the bulk liquid; the agitation intensity of the bulk gas; the inlet liquid volumetric flow rate; the system temperature.

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### Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 26

26.1 Define the Stanton and Peclet numbers and their relationships to other dimensionless groups for convection mass transfer.
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26.2 A thin (1.0-mm-thick) coat of fresh paint has just been sprayed over a 1.5-m by 1.5-m square steel body part, which approximates a flat surface. The paint contains a volatile solvent that initially constitutes 30 wt% of the wet paint. The initial density of the wet paint is 1.5 g/cm3. The freshly painted part is introduced into a drying chamber. Air is blown into the rectangular drying chamber at a volumetric flow rate of 60 m3/min, as shown in the figure below, which has dimensions L = 1.5 m, H = 1.0 m, W = 1.5 m). The temperature of the air stream and the steel body part are both maintained at 27°C, and the total system pressure is 1.0 atm. The molecular weight of the solvent is 78 g/ gmole, the vapor pressure exerted by the solvent at 27°C is 105mm Hg, and the molecular diffusion coefficient of solvent vapor in air at 27°C and 1.0 atm is 0.097 cm2/s....
a. What is the Schmidt number and the average Sherwood number (ShL) for the mass-transfer process?
b. What is the estimated solvent evaporation rate from the surface of the whole body part in units of g/min? It may be assumed that convection mass-transfer limits the evaporation rate, and that the concentration of solvent vapor in the bulk gas is finite, but can be approximated as cA; ≈ 0.
c. Using the results from part (a), how long will it take for the paint to completely dry?
d. What are the hydrodynamic (δ) and concentration boundary-layer (δc) thicknesses at x = L = 1.5 m? How does this compare to H, the height of the drying chamber?
e. What is the new required air flow rate (m3/min) if the desired solvent mass-transfer rate is 150 g/min?

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26.3 A horizontal chemical vapor deposition (CVD) reactor similar to the configuration shown in Example 3, Figure 28.6 will be used for growth of gallium arsenide (GaAs) thin films. In this process, arsine vapor, trimethylgallium vapor, and H2 gas are fed into the reactor. Inside the reactor, the silicon wafer rests on a heated plate called a susceptor. The reactant gases flow parallel to the surface of the wafer and deposit a GaAs thin film according to the simplified CVD reactions...If the reactant gas is considerably diluted in H2 gas, then the mass transfer of each species in the H2 carrier gas can be treated separately. These surface reactions are considered to be very rapid, and so the mass transfer of the gaseous reactants to the surface of the wafer limits the rate of GaAs thin film formation. In the present process, a 15 cm × 15 cm square silicon wafer is positioned at the leading edge of the susceptor plate. The process temperature is 800 K, and the total system pressure 101.3 kPa (1.0 atm). The feed gas delivered to the reactor results in a bulk linear velocity of 100 cm/s. The composition of arsine and trimethylgallium in the feed gas are both 0.10 mole%, which is very dilute. You may assume that the amount of arsine and trimethylgallium delivered with the feed gas is much higher than the amount of arsine and trimethylgallium consumed by the reactions, so that the concentration of these reactants in the bulk gas phase is essentially constant down the length of the reactor. You may also assume that the surface-reaction rates are instantaneous relative to the rates of mass transfer, so that the gas-phase concentrations of both arsine vapor and trimethylgallium vapor at the surface of the wafer are essentially zero. The binary gas phase diffusion coefficient of trimethylgallium in H2 is 1.55 cm2/s at 800K and 1.0 atm.
a. What are the average mass-transfer rates for arsine and trimethylgallium over the whole wafer?
b. Based on the ratio of the arsine and trimethylgallium mass-transfer rates, what is the composition of the GaAs composite thin film—e.g., the molar composition of gallium (Ga) and arsenic (As) in the solid? How could the feed-gas composition be adjusted so that the molar ratio of Ga to As within the solid thin film is 1:1?
.........
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26.4 Boundary-layer analysis for fluid flow over a flat plate predicts the following relationships between the local Sherwood (Shx), Reynolds (Re), and Schmidt (Sc) numbers:...with the transition beginning at Rex = 2.0 × 105. Determine what percentage of the mass transfer occurs within the laminar zone of the flow over the flat plate if the Reynolds number at the end of the plate is ReL = 3.0 × 106.
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26.5 In using the von Kármán approximate method for analyzing the turbulent boundary layer over a flat plate, the following velocity and concentration profiles were assumed:...and...The four constants—α, β, η, and ξ—are determined by the appropriate boundary conditions at the surface and at the outer edge of the hydrodynamic and concentration layers.
a. Determine α, β, η, and ξ, and provide the resulting equations for velocity and concentration profiles.
b. Upon the application of the von Kármán momentum integral equation, the thickness of the turbulent boundary layer is given by...Use this relationship, and the solution to von Kármán concentration integral equation for Sc = 1.0, to obtain the following equation for the local mass-transfer coefficient:...

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26.6 A well-mixed open pond contains wastewater that is contaminated with a dilute concentration of dissolved methylene chloride. The pond is rectangular with dimensions of 500 m by 100 m, as shown in the figure (above right). Air at 27°C and 1.0 atm blows parallel to the surface of the pond with a bulk velocity of 7.5 m/s. At 20°C and 1.0 atm, for the gas phase (A = methylene chloride, B = air), the diffusion coefficient (DAB) is 0.085 cm2/s, and kinematic viscosity (vB) is 0.15 cm2/s. At 27°C, for the liquid phase, (A = methylene chloride, B = liquid water), the diffusion coefficient (DAB) is 1.07 × 105 cm2/s, and the kinematic viscosity (vB) is 0.010 cm2/s.
a. At what position across the pond is the air flow no longer laminar? Would it be reasonable to assume that the mean gas film mass-transfer coefficient for methylene chloride in air is dominated by turbulent flow mass transfer?
b. As part of an engineering analysis to predict the emissions rate of methylene chloride (species A) from the pond, determine the average gas film mass-transfer coefficient associated with the mass-transfer methylene chloride from the liquid surface to the bulk air stream.
c. Compare the Schmidt number for methylene chloride in the gas phase vs. the liquid phase, and explain why the values are different.
...
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26.7 Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool. A simplified picture of the situation is provided in the figure below. Directly over this underground pool of liquid gasoline (n-octane, species A) is a layer of gravel of 1.0 m thickness and width of 10.0 m. The volatile n-octane vapors diffuse through the highly porous gravel layer, and then through a gas boundary layer formed by flow of air over the top surface of the gravel bed, and finally out to the bulk atmosphere where the n-octane is diluted to below detectable levels. There is no adsorption of n-octane vapor onto the porous gravel layer, and n-octane vapor concentration is dilute. Assume that the mass-transfer process is allowed to achieve a steady state. The temperature of the system is constant at 15°C, and the total system pressure is 1.0 atm. At this temperature, liquid n-octane exerts a vapor pressure of 1039 Pa. The void spaces in porous layer create a void fraction (ε) of 0.40, and but the pore size is large enough that Knudsen diffusion can be neglected.
a. What is the average mole fraction of n-octane vapor at the top surface of the rock layer (yAs = cAs/C) if the air velocity is very low, only 2.0 cm/s? What is the average flux of n-octane vapor emitted to the atmosphere?
b. What would be the average mole fraction of n-octane vapor at the top surface of the rock layer if the air velocity is 50.0 cm/s? What is the average flux of n-octane vapor?
c. The Biot number associated with a mass-transfer process involving diffusion and convection in series is defined as...where L refers to the path length for molecular diffusion within the porous gravel layer and DAe refers to the diffusion coefficient of species A within this porous medium, which is not the same as the molecular diffusion coefficient as octane vapor in air. Determine the Biot number for parts (a) and (b), and then assess the relative importance of convective mass transfer in determining the n-octane vapor emissions rate.
...
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26.8 Consider the process shown in the figure (next page). A bulk gas stream containing 0.10 mole% of carbon monoxide (CO) gas, 2.0mole% O2 gas, and 97.9 mole% of CO2 gas flows over a flat catalytic surface of length 0.50 m at a bulk velocity of 40 m/s at 1.0atm and 600 K. Heat-transfer processes maintain the gas stream and catalytic surface at 600 K. At this temperature, the catalytic surface promotes the oxidation reaction CO(g) + 1=2O2.(g) → CO2(g). Let A = CO, B = O2, C = CO2. The gas-phase diffusion coefficients at 1.0 atm and 300K are DAB= 0.213 cm2/s, DAC = 0.155 cm2/s, DBC = 0.166 cm2/s.
a. What are the Schmidt numbers for CO and O2 mass transfer? What species (CO, O2, CO2) is considered the carrier gas?
b. For CO mass transfer, what is the average convective mass-transfer coefficient (kc) over the 0.50mlength of the catalytic surface, and the local mass transfer coefficient (kc;x) at the far edge of the catalytic surface (x = L = 0.50 m)?
c. Using boundary-layer theory, scale kc for CO mass transfer to kc for O2 transfer.
d. At 600 K, the surface reaction constant for the first-order oxidation reaction with respect to CO concentration is ks = 1.5 cm/s. What is the average molar flux of CO to the catalytic surface, assuming that the composition of CO in the bulk gas is maintained at 0.10 mole%?
...
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26.9 A small droplet of liquid detergent, falling through air in a spray drying tower, has its diameter reduced as water evaporates from the surface. If it is assumed that the temperature of the liquid within the drop remains at 290K and the dry air is at 310 K, determine the concentration of water vapor in the surrounding bulk air stream within the drying tower. The total system pressure is 1.0 atm, and the film average gas temperature is 300 K.Potentially useful data: kinematic viscosity of air at 300 K, vair = 1.57 × 105 m2/s; thermal diffusivity of air at 300 K, α = 2.22 × 105m2/s; gas-phase diffusion coefficient of water vapor in air at 300 K, DA-air = 2.63 × 105 m2/s; density of air at 300 K, ρG = 1.18 kg/m3; heat capacity of air at 300 K, Cp,air = 1006 J/kg · K; latent heat of vaporization of water at 290 K, ∆Hv,A = 2.46 kJ/g H2O; vapor pressure of water at 290 K, PA = 1.94 × 103 Pa.
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26.10 In a spray column, a liquid is sprayed into a gas stream, and mass is transferred between the liquid and gas phases. The formation of liquid drops from the spray nozzle is considered to be a function of the nozzle diameter, gravitational acceleration, surface tension of the liquid against the gas, liquid density, liquid viscosity, velocity, and the viscosity and density of the surrounding gas medium. Arrange these variables into dimensionless groups. Should any other variables have been included?
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26.11 A falling liquid film within a gas–liquid contactor of 1.50 m length is in contact with 100% carbon dioxide gas at 1.0 atm and 25°C. The wetted surface area is 0.50 m2, and the liquid film thickness is 2.0 mm, which is thin enough to prevent ripples or waves in the falling liquid film. The liquid delivered to the contactor does not initially contain any dissolved CO2. At 25°C, the Henry’s law constant for the dissolution of CO2 gas in water is 29.5 m3 × atm/kgmole, and the molecular diffusion coefficient for CO2 in liquid water is 2.0 × 105 cm2/s. What is the average molar flux of CO2 into the film? What is the estimated bulk concentration of dissolved CO2 in the liquid exiting the process?
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