Stationary medium

Equation 10.4, which describes the mass transfer rate arising solely from the random movement of molecules, is applicable to a stationary medium or a fluid in streamline flow. If circulating currents or eddies are present, then the molecular mechanism will be reinforced and the total mass transfer rate may be written as ... 

By considering of the appropriate element of a sphere show that the general equation for molecular diffusion in a stationary medium and in the absence of a chemical reaction is ... 

This expression applies to the transport of any conserved quantity Q, e.g., mass, energy, momentum, or charge. The rate of transport of Q per unit area normal to the direction of transport is called the flux of Q. This transport equation can be applied on a microscopic or molecular scale to a stationary medium or a fluid in laminar flow, in which the mechanism for the transport of Q is the intermolecular forces of attraction between molecules or groups of molecules. It also applies to fluids in turbulent flow, on a turbulent convective scale, in which the mechanism for transport is the result of the motion of turbulent eddies in the fluid that move in three directions and carry Q with them. 

In normal atmospheric conditions, fire usually is initialed by a combustible material coming in contact with a heat source. The spread of fire occurs due to direct flame impingement or the transfer of heat to the surrounding combustible materials. Heat transfer occurs by three principal mechanisms - conduction, convection, and radiation. Conduction is the movement of heat through a stationary medium, such as solids, liquids or gases. Steel is a good conductor of heat as is aluminum, therefore they can pass the heat of a fire if left unprotected. 

For mass transfer by molecular diffusion from a single sphere of diameter d to an infinite stationary medium, it can be shown that... 

Let us consider an initially stationary medium and a plane shock front propagating with a velocity U, and the initial and... 

Several metal 0-diketonates may be separated by liquid-liquid chromatography in a ternary system consisting of water, 2,2,4-trimethylpentane and ethanol [60]. The water-rich phase is used as the stationary medium, while the water-poor phase serves as the eluent. 

In the hydrodynamic theory, the diffusion coefficient of a solute molecule A or single particle through a stationary medium B, DAB, is given by the Nemst-Einstein equation ... 

For non-stationary heat conduction in a semi-infinite stationary medium the onedimensional transient heat conduction without heat production, we have next parabolic differential equation... 

The validity of the generalized Langevin equation (22) is restricted to a stationary medium. In other situations, for instance when the diffusing particle evolves in an aging medium such as a glassy colloidal suspension of Laponite [8,12,55,56], another equation of motion has to be used. 

Let us consider again the particular case of a particle diffusing in a stationary medium, in order to see how the generalized Langevin equation (22) can be deduced from the more general equation (169). When the medium is stationary, the response function x (M0 reduces to a function of t — t (% (t, t ) = X (f — t j). Introducing then the causal function y(f) as defined by... 

Special Case Ideal Gas MixtJtes 779 Pick s Lav/ of Diffusion Stationary Medium Consisting of Tv/o Species 779... 

Analysis We can consider the total molar concentration to be constant (C = Ca+ Cfl - Cfl = constant), and the container to be a stationary medium since there is no diffusion of nickel molecules (Ng - U) the concentration of the hydrogen in the container is extremely low (C D.Then the molar flow rate of hydrogen through this spherical shelf by diffusion can readily be determined from Eq. 14-28 to be. . 

Transient mass difliision in a stationary medium is analogous to transient heat transfer provided that the solution is dilute and thus the density of the medium p is constant. In Chapter 4 we presented analytical and graphical solutions for one-dimensional transient heat conduction problems in solids with constant properties, no heat generation, and uniform initial temperature. The analogous one-dimensional transient mass diffusion problems satisfy these requirements ... 

Analogy between the quantities that appear in the formulation and solution of transient heat conduction and transient mass diffusion in a stationary medium... 

The special case V - 0 corresponds to a stationary medium, which can now be defined more precisely as a medium whose mass-average velocity is zero. Therefore, mass transport in a stationary medium is by diffusion only, aud zero mass-average velocity indicates that there is no bulk fluid motion. 

Under steady conditions, the molar flow rates of species A and B can be determined directly from Eq. 14-24 developed earlier for one-diinensional steady diffusion in a stationary medium, noting that P CRJT and thus C = PIRJ" for each constituent gas and the mixture. For one-dimensional flow through a channel of uniform cross sectional area A with no homogeneous chemical reactions, they arc expressed as... 

The special case K = 0 corresponds to a stationary medium. Using Pick s law of diffusion, the total mass fluxes J = m/A in a moving medium are expressed as... 

SC Define the following tei/ns mass-average velocity, diffusion velocity, stationary medium, and moving medium. 14-76C What is diffusion velocity How does it affect the mass-average velocity Can the velocity of a species in a moving medium relative to a fuxed reference point be zero in a moving medium Explain. 

An equation holding between the rate of heat transfer per unit volume per unit time by the thermal conduction in a stationary medium, i.e., in a solid, in reality, and, the rate of increase in temperature of the solid is given in the following form. 

As an exercise, the reader can verify that equation (2.73) satisfies both real and imaginary parts of equation (2.70). This development represents the starting point for both the Warburg impedance associated with diffusion in a stationary medium of infinite depth and the diffusion impedance associated with a stationary medium of finite depth. 

---