It is known that the reaction between many solids and solutes is chemically controlled, at least in part by chemical control. Even the response to the transfer control, the assumptions established by Nernst theory are not completely correct. The main problem is the assumption that the diffusion layer is stationary for the solid surface and the thickness of the diffusion layer is 3 × 10 -3 cm in many different kinds of reactions.
There is strong evidence that the motion of the fluid is always very close to the solid surface and has been observed at a distance of 10 x 10 -5 cm from the solid surface. This means that the assumption that the concentration of the solute is a linear function of the distance y from the solid surface is at best an approximation. However, there is a large amount of evidence that there is a concentration gradient between the solid surface and a point at a certain distance from the liquid. This distance is still called δ in a system where mass transfer control occurs at the solid-liquid interface. The nature and thickness of this region is determined by the diffusion coefficient of the solute, the viscosity of the solution, and the manner in which the liquid flows relative to the solid surface. Therefore, the most important parameter for any particular reaction system is the degree of agitation, which is treated by fluid mechanics.
The theory of fluid mechanics applicable to the mass transfer control reaction of solids and solute ions or molecules has been reviewed, and there are also very complete treatment methods. Two main results are required: (1) the manner in which the solute concentration varies with distance from the solid surface and the scale of the region in which it changes; and (2) the rate at which the solute is mass-transferred from the bulk of the solution to the solid surface by forced diffusion. Relevant theories should point out that this mass transfer is related to which factors and their quantitative associations have obtained the above information. Unfortunately, the equations for convection diffusion are complex and can usually only be solved using semi-empirical methods. However, in the case of a turntable, due to its high degree of symmetry, it is possible to find a complete solution that provides a rate distribution across the entire fluid mass. The disk rotates about an axis perpendicular to the disk surface and at its center. The disk area is large enough to make the edge effect negligible and the solution volume is large enough to avoid wall effects.
The liquid moves toward the disk at a constant rate v y from the rotating disk away from the vertical disk surface.
v y =-0.886 
(1)
Where, the dynamic viscosity of the v-fluid;
The constant angular rate of the ω-turntable, rad∕s.
The fluid can only get a rotational motion when it reaches very close to the disk surface, and as it gets closer to the disk surface, the angular rate of the fluid increases until the angular rate of the disk itself is reached. The centrifugal force generated by the angular momentum imparts a radial velocity to the liquid, pushing the liquid outwardly away from the disk along the surface, so that the liquid is continuously drawn toward the disk and pushed away from the disk when it is very close to the disk surface. Thus the liquid is subjected to two flows, one flowing vertically to the disc at a constant rate and the other being flowing parallel to the disk. The transition from one to the other indicates the presence of a viscous boundary layer. Found that the distance from the disk surface is equal to about 2.8 The rate at which the vertical disk surface flows is 80% of its maximum value, while the rate at which the parallel disk faces flow is 10% of the flow rate of the liquid at the disk. This distance can be taken as the approximate thickness of the viscous boundary layer. For water at 25 ° C, the boundary layer thickness is about 5 x 10 -2 cm when the disc angular rate is 25 rad ∕s.
Now considering the convective mass transfer and steady state conditions, the concentration of the solute acting on the surface of the disk must be related only to the distance from the disk surface and the distance from the axis of rotation. Assuming a reasonable liquid flow pattern that is independent of the distance between the solute concentration and the axis of rotation, the following relationship should exist.
D(d 2 c∕dy 2 )=v y (dc∕dy) (2)
When y is large, v y is constant, and as long as the angular rate ω of the turntable is sufficiently large that the v y value is quite high, other processes that can change the solute concentration (such as non-convective mass transfer) change the solute concentration due to the relatively slow rate. Does not work. If the liquid of the far-high turntable flows to the turntable fast enough, the solute concentration of the bulk phase of the solution does not change. The diffusion of the solute-deficient layer to the surface of the turntable is too slow and has no effect on the surface away from the surface.
The axial flow velocity v y of the turntable very close to the surface is much smaller than its maximum value, and the diffusion rate is increased to the same order of magnitude, so that the mass transfer rate of the solute is increasingly controlled by diffusion. The solution of the above equation yields the ratio of the solute concentration c y from the surface y to the bulk phase concentration c, which is expressed as a function of the distance from the surface using the fraction of the diffusion layer thickness δ defined by the Nernst equation.
The thickness of the diffusion boundary layer depends on the thickness of the hydrodynamic boundary layer or the viscous boundary layer, which is assumed to be constant over the entire surface of the disk. This is true except for the border area of ​​the turntable. The size of the boundary zone is on the same order of magnitude as the thickness of the fluid mechanics boundary layer. Therefore, the above theory can only be used for the scale of the turntable to be much larger than the thickness of the boundary layer. The wall of the container must also be kept away from the turntable boundary so as not to interfere with the flow pattern of the liquid causing turbulence. Under these conditions, the solution of equation (2) can be used in a finite-scale system.
-dc∕dt=DA(c-c 1 )∕V(0.893δ') (3)
-dc∕dt=DA(c-c 1 )∕Vδ (4)
Where δ' is the concentration of the liquid layer that changes in concentration near the disk surface. Comparing equations (3) and (4), δ = 0.893 δ'. Integrate equation (2)
(5)
thereby
(6)
The rate at which the solute flows from the body phase to the solid surface is determined by the Nernst theory.
I=DA(c-c 1 )∕δ (7)
Therefore, in the simplest case where the surface concentration is 0
(8)
(9)
Where, the radius of the r-turntable.
Therefore, if the reaction rate is completely controlled by mass transfer, it is possible to calculate the maximum rate of action with the solute using a solid turntable. For other geometric systems, as long as the flow is non-turbulent, the dependence of δ and δ on D, v and system characteristic rate is similar to equation (6).
Heat energy (hot water, low-pressure steam or heat transfer oil) is introduced into the closed interlayer, and the heat is transferred to the dried material through the inner shell. Driven by power, the tank body rotates slowly, the materials in the tank are constantly turned and mixed, and the heat is received from the inner surface of the wall, so as to achieve the purpose of strengthening drying. The material is in a vacuum state, and the vapor pressure drops to make the water (solvent) on the surface of the material reach a saturated state and evaporate, and is discharged and recovered by a vacuum pump in time. The moisture (solvent) inside the material continuously penetrates, evaporates and discharges to the surface. The three processes are carried out continuously, and the material achieves the purpose of drying in a short time.
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