Water side resistance

Note i lWw measures the size of the air-side resistance relative to the water-side resistance (Eq. 20-30). 

For gases passing between the atmosphere and ocean, two resistances are important (Fig. 2). These resistances are the boimdary layers on the air and water sides of the interface. At some distance from the interface on both sides, the mediums are well mixed. As the interface is approached, turbulent mixing is damped by viscous forces and, very near the interface, diffusion becomes important for mass transfer. The resistance to transfer of any gas is the sum of the air side and the water side resistance. For gases that are highly soluble or react with water, e.g. SO2, NH3 and H2O vapor, the water side resistance becomes less important and the air side resistance dominates. In this case, it is passage through... 

Fig. 3. Schematic of the surface renewal model of gas exchange (shown, water side resistance dominant). In this model, gas diffuses across the air-water interface and establishes a gradient. Tm-bulence eddies periodically mix the gradient into the bulk water phase. Solid lines show gas concentration with distance from the interface and correspond to times, to to which represent increasing times between renewal events. The concentration of dissolved gas is C, and subscripts a and w refer to air (at equilibrium) and water, respectively. Note that the shorter the sm face renewal time, the higher the gas transfer, because transfer Orem s on average along a stronger gradient...

Likewise, water-side resistance is calculated with water diffusivities and Uio as follows (Schwartzenbach et al., 1993) ... 

Water side resistance The partial water side resistance defined as the water side diffusivity divided by the depth of the stagnant water boundary at the water s surface (sec cm ). 

A key parameter appearing in Eq. 7 is Kd, the particle-to-water chemical partition coefficient. This parameter should reflect chemical desorption from the particles rather than absorption. There is considerable evidence in the published literature which demonstrates they are different, numerically. In Eq. 7 as Kd becomes large then Kg-p/msKo so that the BBL or the water-side resistance controls the magnitude of the overall transport coefficient. Recent work by the authors supports this prediction (26), however the concept is counter intuitive. Never-the-less the theoretical behavior of the Kd effect displayed in Eq. 7 suggest that as chemical binding or sequesteration potential to the particle increases the water-side resistance controls the transport coefficient magnitude. Additional research is needed to support this predicted effect. 

For overall U cooling, assume water side fouling = 0.002 propylene side fouling = 0.001 neglect tube wall resistance... 

For conditions of turbulent flow the transfer coefficient for the water side, hi = u<>. Ri the scale resistance is constant, and h the coefficient for the condensate film is almost independent of the water velocity. Thus, equation 9.201 reduces to ... 

The air-side resistivity of the cobalt chloride modified polyimide film was Increased to the value observed with a nonmodified BTDA-ODA polyimide film while, the cobalt chloride modified BDSDA-ODA polyimide film had an increase in surface resistivity of only about three orders of magnitude after soa)cing this film in water. The variable temperature air-side surface resistivity profiles for the cobalt chloride modified BDSDA-ODA polyimide film before and after a water soa)c are shown in Figure 4. 

Another example is the air-water transfer of a compound, illustrated in Figure 1.5. This example will be used to explain volatile and nonvolatile compounds. There is resistance to transport on both sides of the interface, regardless of whether the compound is classified as volatile or nonvolatile. The resistance to transport in the liquid phase is given as Rl = 1/Kl. If we are describing chemical transfer through an equation like (1.3), the resistance to transfer in the gas phase is given as Ro = 1/(HKg). The equilibrium constant is in the Rg equation because we are using the equivalent water side concentrations to represent the concentration difference from... 

Note that the air-water exchange velocity decreases by about a factor of 2 when the temperature decreases from 25°C to 0°C. For MCF, via/w is completely water-side controlled, while for BF the relative resistance between air and water increases from 16% to 30% when the temperature decreases from 25°C to 0°C. This change of i ,Vw is due to the fact that Kia/Sv/ and thus v a drops more strongly with T than vIw. 

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

It can be seen that in this example the largest resistance, the controlling film, is that of the air, 1/U 1 /Aajr, he. U hiur, and so the air film controls the overall heat transfer process. If we wish to increase the overall rate of heat transfer by increasing U, we should look at the dominating resistance, the air film, and try to reduce it, e.g. by increasing the air-side velocity. Reducing the water film resistance has very little effect upon U. 

In this problem the water-side convection coefficient is the main controlling factor because h is so large for a condensation process. In fact, the outside thermal resistance is smaller than the conduction resistance of the steel. The approximate relative magnitudes of the resistances are... 

Fig. 9.5. Acid cooler, courtesy Chemetics www.chemetics.com Cool water flows through 1610 internal 2 cm diameter tubes while warm acid flows counter currently (and turbulently) between the tubes. The tubes are 316L stainless steel. They are resistant to water-side corrosion. They are electrochemically passivated against acid-side corrosion by continuously applying an electrical potential between the tubes and several electrically isolated metal rods. Details shell diameter 1.65 m shell material 304L stainless steel acid flow 2000 m3/hour water flow 2900 m3/hour acid temperature drop 40 K. (Green pipes = water metallic pipes = acid.) Fig. 24.6 gives an internal view.

The water vapor flux increases exponentially as the mean temperature of the system increases in accordance with the Antoine equation [Eq. (17)]. Here, T is the absolute temperature and A, B, and C are constants. Temperature also affects water flux through the thermal sensitivity of solution viscosity, solute dif-fusivity, and the diffusion co-efficient of water vapor in air-filled membrane pores. Elevated temperatures tend to lower feed-side, membrane, and strip-side resistances to mass transfer. However, operation at such temperatures may lead to a loss of product integrity through thermal degradation or volatiles loss. 

It is assnmed that the gas is completely backmixed. Gas-side resistance for mass transfer is neglected. The reaction is performed under isothermal conditions. Initially, a slurry of Ca(OH)2 in water is prepared and the liqnid is saturated with Ca(OH)2. Then CO2 gas is sparged to the reactor. It is assnmed that the number of reacting Ca(OH)2 particles per nnit volnme of the reactor is constant (no breakage or agglomeration) until the particles are completely consnmed. The instantaneous rate of reaction is integrated with respect to time until all the Ca(OH)2 is consumed. Thus, the batch time is obtained ... 

Because of negligible liquid-side resistance the flux is governed by the gas phase transport. Note that mxA,i = yAwhich implies that the interfacial gas-phase composition is in equilibrium with (he bulk liquid composition. Even if the mass transfer coefficients in the iwo phases are computable. Eqs. (2,4-IOa) aed (2.4-1 Ob) show that phase equilibrium considerations can cause one or the other phase to control." For a very soluble gas (m is small), the gas phase may control while for a sparingly soluble gas such as 02 in water the liquid phase transport generally will govern. 

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