Mass transfer velocities

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

All the physics is hidden in the coefficient via/w which, because it has the dimension of a velocity (LT-1), is called the (overall) air-water exchange velocity. Air-water exchange occurs due to random motion of molecules. Equation 20-1 is a particular version of Eq. 18-4 in which the air-water exchange velocity adopts the role of the mass transfer velocity, vA/B. 

If the ratio of the evaporation velocity to the liquid phase mass transfer velocity uiiq/kiiq tends towards zero (i.e., Kiq = 1), then Eq. (81) reduces to ... 

The influence of mass-transport resistance in the particles can only be excluded if the critical reaction rate is substantially lower than the mass transfer velocity. This leads to the need for good external mass transfer (i.e. to a sufficiently rapid flow rate in the packed bed), as well as to short diffusion paths in catalyst particles. 

Vtot in the above equation is a mass transfer velocity across the air-water interface. It has units of velocity (usually cm/s), and it is made up of two parts (a) the velocity of the compound through the boundary layer in the water to the interface (denoted by vw) and (b) the velocity of the compound through the boundary layer in the air as it leaves the air-water interface (denoted by va). The total mass transfer velocity is given by... 

Now we need the air-side and the water-side mass transfer velocities ... 

In analogy with electrical conductance and as shown by Liss and Slater (1974) and as discussed by Mackay and Leinonen (1975) and Mackay (1991) the reciprocal of the mass transfer velocity is a measure of resistance to the gas transfer and is composed of two resistances in series, the liquid phase resistance, r , and the gas phase resistance, r ... 

The Sherwood number, Sh = kJ/D, that determine the ratio between the effective mass transfer velocity and the molecular diffusivity (i.e., a dimensionless concentration gradient at the interface). 

With fctot having units cm s and concentration in g or mol cm, the flux would be expressed in g or mol cm s In many cases, Ca is essentially zero and the evaporative flux would be a first order function of the bulk water concentration, C. The overall mass transfer velocity, can be perceived as the mean velocity with which the molecules cross the boundary and as demonstrated earlier, the evaporative half-life would be given by... 

The presence of two scales enables modeling the mass transfer processes both in the extent of their completion and in time. When the data of mass transfer velocities are absent, used is only the degree of the processes completion. In this case in the USA within the framework of reviewed models are distinguished direct problems, i.e., reaction path models, and inverse problems, i.e., mass balance models. 

In these models equations of the mass action law for most slow mass transfer processes are replaced by equations in partial derivatives, which include velocity. As the mass transfer velocity depends on water composition and at approach to the saturation it decreases, kinetic mass transfer equations have the nature of recurrent (see equations (2.275) and (2.278)), and that is why modeling of mass transfer kinetics is performed using a two-step method of computation described below. 

Open models with mass transfer assume that the media in the object of study are not balanced either dynamically or chemically. In these models is necessary simultaneous consideration of both mass transport and mass transfer velocities because the relaxation time At >0 and flow time At>... 

Figure 7.12 Experimental evaluation of the effect of external mass transfer. Velocity is varied by varying AO and W simultaneousy so that M /Fao (contact time) remains constant.

Forms of the Peclet number are shown with both column length L and particle diameter dp because both forms are used. It is obviously inportant to know whether L or dp is being enployed in the definition of Pe. Sometimes a dimensionless group called the Stanton number St, the ratio of mass-transfer velocity to flow velocity, is used. 

The first assumption of isotropy makes the two mass transfer velocities equal at the level of the poles ... 

The primary purpose of this handbook is to present the current state of the science concerning the estimation of these mass transfer velocities or coefficients. The material... 

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