Transport Through Boundaries

Simple Bottleneck Boundaries A Simple Noninterface Bottleneck Boundary Illustrative Example 19.1 Vertical Exchange of Water in a Lake Two- and Multilayer Bottleneck Boundaries Bottleneck Boundary Between Different Media Illustrative Example 19.2 Diffusion of a Volatile Compound from the Groundwater Through the Unsaturated Zone into the Atmosphere 

Box 19.1 Equilibrium of Sorbing Solutes at the Sediment—Water Interface 

Wall Boundary with Boundary Layer (Advanced Topic) 

Illustrative Example 19.3 Release ofPCBs from the Historically Polluted Sediments of Boston Harbor 

Illustrative Example 19.4 Dissolution of a Non-Aqueous-Phase Liquid (NAPL) into the Aqueous Phase Wall Boundary with Time-Variable Boundary Concentration 

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Since the flux is independent of x, the substance which is transported along the x-axis can neither accumulate nor disappear, thus dC/dt = 0. This situation will be discussed in more detail in the next section dealing with transport through boundaries. 

We now discuss two additional solutions of Fick s second law (Eq. 18-14) for particular boundary conditions. The first one deals with diffusion from a surface with fixed boundary concentration, C0, into the semi-infinite space. The second one involves the disappearance ( erosion ) of a concentration jump. Both cases will be important when dealing with the transport through boundaries (Chapter 19). No derivations will be given below. The interested reader is referred to Crank (1975) and Carslaw and Jaeger (1959) or to mathematical textbooks dealing with particular techniques for solving Eq. 18-14. 

Heat and mass transfer takes place simultaneously in DCMD. The mass and heat transport can be described by three steps, namely transport through boundary layer on the feed side, transport through membrane, and transport through boundary layer on the permeate side. 

Particle transport through boundary layers in the presence of thermophoretic and electric forces is complex but predictable [5]. For coarse particles, thermophoretic and electric forces can usually be ignored. For fine particles, they can be very important. If the material to be tested is expected to exist in the field at >10°C cooler or warmer than the ambient, or if the surface is expected to be >100 V above or below ground potential, these effects need to be considered. Cool surfaces increase the particle deposition rate while warm surfaces decrease it (analogous to condensation but for different reasons). Experience has shown that surfaces biased at a few hundred volts can collect fine particles at >5 times the rate of grounded surfaces. 

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