Diffusion through a plate

Figure 5.1 Concentration, c(x), vs. x for steady-state diffusion through a plate.

We observe that the steady state obstracted diffusion through a plate is equivalent to a steady state normal diffusion whose flux runs out through a reduced area [EVA 52] ... 

We will now consider the pseudo-steady state mode for diffusion through a plate of thickness Y and a constant unit section. To do so, we write that the variation in the amount of diliusing species on plane i is zero, so ... 

When t = R2/a, the temperature ratio at the center of the plate (f = 0) has decayed to exp( —irV4), or 8 percent of its initial value. We conclude that diffusion through a distance R takes roughly R2/a units of time, or alternatively, the distance diffused in time t is about (at). ... 

Accordingly the kinetic theory requires that the rate of effusion of a gas through a small hole be inversely proportional to the square root of its molecular weight. This law was discovered experimentally before the development of the kinetic theory— it was observed that hydrogen diffuses through a pcwous plate four times as rapidly as oxygen. 

The geometry of the plate does not bear much relevance to real porous solid. Thus, the above equation is not of much use in diffusion of adsorption systems. To this end, we will consider the Knudsen diffusion through a long cylindrical capillary in the next section. 

The method is in principle applicable also to the measurement of micropore or intracrystalline diffusivities, but the practical difficulties of mounting and sealing a single small zeolite crystal have hitherto prevented such applications. However, these difficulties have been overcome and the results of two studies have been recently reported in which diffusion through a single (iOO /tm) zeolite crystal, mounted in a metal plate, was measured by this method. 

The plate. Consider the diffusion of a gas through a plate of thickness 1. If the boundary conditions are... 

The phenomenon of surface diffusion, demonstrated by Barter and Strachan (1955) may be used to advantage for the separation of some hydrogen-hydrocarbon mixtures (Sircar, 1993b). Thus, thin microporous carbon membranes (<5 pm), supported by macroporous sheets of graphite assembled into a plate and frame membrane module, were able to separate H2 at 63% recovery from a refinery waste gas. The feed was passed at high pressure over the membrane unit which preferentially adsorbed the hydrocarbons and facilitated surface diffusion of these species through the membrane to the low pressure side of the module. Adsorption, accompanied by surface diffusion through a thin microporous membrane, thus offers possible future applications. 

Carbon is allowed to diffuse through a steel plate O 10-mm thick. The concentrations of carbon at the... 

A species diffuses through this plate under the action of a gradient of concentration imposed by the values of the concentrations at the two boundaries. These concentrations remain constant (Figure 5.11). 

We will determine the diffusion flux of the defect M in one direction, in the case of diffusion through a thick plate X. The number of jumps is given by the number of planes between the departure and arrival, hence n=X a. 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

The filtrate from this first batch will comprise a solution of 180 to 270 kg of unprecipitated acetylsalicylic acid (1.0 to 1.5 mols), 510 kg of acetic anhydrice (5.0 mols), 600 kg of acetic acid (10.0 mols) (obtained as a by-product in the acetylation step) and 1,200 kg of the diluent toluene. Into this filtrate, at a temperature of 15° to 25°C, ketene gas is now passed through a sparger tube or diffuser plate, with good agitation, until a weight increase of 420.5 kg of ketene (10 mols) occurs. The reaction mixture wiil now contain 180-270 kg of unprecipitated acetylsalicylic acid (1.0-1.5 mols) and 1,532 kg of acetic anhydride (15 mols) in 1,200 kg of toluene. This mother liquor is recycled to the first step of the process for reaction with another batch of 1,382 kg of salicylic acid. On recirculating the mother liquor, the yield of pure acetylsalicylic acid is 1,780 to 1,795 kg per batch. 

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