Fundamentals of Diffusion

The diffusion coefficient, or diffusivity, D, is defined by Pick s First Law. 

The diffusion coefficient of alkali ions in glasses is usually found by placing a thin layer of a source of a radioactive isotope of the ion on the surface of the sample, heating at a known temperature for a known time, t, and analyzing the concentration profile of the radioactive isotope in the glass using standard methods. The data for concentration versus distance are then fitted to the expression 

If the source of the diffusing species is a melt or a gas, the corresponding expression for the concentration profile is given by  

If the diffusing species is a gas such as helium, it is possible to expose one face of a plate of thickness, L to a known pressure of that gas, while maintaining the other face at zero pressure. Under these conditions, a steady-state flow will be reached and Eq. 8.1 can be rewritten as  

If we maintain a vacuum on the inside face of the sample, P2 is zero, and Pj equals the applied pressure, P. This expression can then be written as  

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In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

Fundamentals of Diffusion in Microfluidic Systems, Fig. 1 Simulated paths of a Brownian particle, (a) Path recorded on a large timescale and (b) same path recorded on a smaller timescale. More details emerge as we use smaller timescales... 

Fundamentals of Diffusion in Mkrofluidic Systems, Fig. 2 Sketch of an experimental flow chamber the bold arrow indicates the flow direction. Concentration profiles were obtained by looking through the top (a) at a fixed distance (50 pm) fiom the top wall. Velocity profiles were taken by scanning a horizontal plane through the side (b) of the chamber, across the SO pm width of the channel... 

Fundamentals of Diffusion in Mkrofluidk Systems, Fig. 3 Plots of the local volume fraction c() as a function of the distance across the channel for an average volume fraction c()buik = 0.05, 0.22, and 0.34 at flow rates of 0.125 )ilmin solid line,... 

Fundamentals of Diffusion in Microfiuidic Systems, Fig. 4 Plot of the relative concentration (probability density function of the particle distribution) as a function of the radial position in a round capillary tube... 

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