Microscopic mass balance

This mass balance approach in general renders good predictions for high solubility drugs but for low solubility compounds there are other more accurate approaches based on microscopic mass balance that provide better estimations [34]. 

In order to understand these aspects, it may be useful to consider the operation of a single-phase reactor of arbitrary type. The microscopic mass balance of a reactant over an element of reactor volume (Fig. 1.3) can be written in the following general form applicable to any reactor type ... 

The Microscopic Mass Balance Equations in Thermodynamics and Fluid Mechanics 43... 

THE MICROSCOPIC MASS BALANCE EQUATIONS IN THERMODYNAMICS AND FLUID MECHANICS ... 

Figure 6. The microscopic mass balance for fluid flow is schematically illustrated with a cube. The change in mass of an isotope is equal to the sum of all fluxes entering (+) or leaving (-) the cube.

Results from the practical example in Section 11-3.2 are used to estimate the maximum error incurred by neglecting the effects of curvature in the spherical coordinate microscopic mass balance. For example, it is now possible to... 

In other words, if the microscopic mass balance for each component in the reactive mixture must be satisfied at every point within the catalyst, then a volumetric average of this mass balance is also satisfied. If n is an outward-directed unit normal vector on the external surface of the catalyst, then Gauss s law transforms the volume integral on the right side of (19-32) to an integral over the external catalytic surface ... 

Obviously, the gas-liquid interface is curved, but MTBLTuquid/ /gas 1 at very high Schmidt numbers. Under these conditions, the effect of curvature is not important. The steady-state microscopic mass balance for benzene (B) in the liquid phase with one-dimensional diffusion normal to the interface and first-order irreversible chemical reaction is... 

Answer Two. The thermal energy balance is not required when the enthalpy change for each chemical reaction is negligible, which causes the thermal energy generation parameters to tend toward zero. Hence, one calculates the molar density profile for reactant A within the catalyst via the mass transfer equation, which includes one-dimensional diffnsion and multiple chemical reactions. Stoichiometry is not required because the kinetic rate law for each reaction depends only on Ca. Since the microscopic mass balance is a second-order ordinary differential eqnation, it can be rewritten as two coupled first-order ODEs with split boundary conditions for Ca and its radial gradient. 

The cxirrently used description of homogeneous diffusion of volatile by-products in polymer media during reversible polycondensations is due to Secor [44]. It considers polymer molecules immobile. The flux of small molecules has a negligible convective contribution only the diffusional flux with respect to the polymer needs be considered, and the microscopic mass balance of a generic volatile component (usually, but not always, a by-product) Y and a group A belonging to the polymer may be written, neglecting density variations, as in Eq. (27). 

Combining this expression with the microscopic mass balances in the polymer film, it is possible to predict mass transfer coefficients for simple geometries and to take into account possible coupling with chemical reactions. For instance, if the polymer film is immobile, has a constant depth L, and mass transfer occurs along the y direction with a plane geometry, time-averaged mass transfer coefficient of... 

The microscopic mass balance of polymer functional groups and volatile components given in Eqs. (27) has to be modified in order to take into account the variable reaction volume due to polymer crystallization. Here we do not follow the notation in Ref. 74 rather, we use concentrations and rates of reaction per unit volume of amorphous phase instead of concentrations per unit volume of particle [A ]p = [A ]/(l — and so on, in order to use the same kinetic rate laws [Eqs. (49)] as in the melt. 

Instead of solving microscopic mass balances for the concentration profiles, Kar-ode et al. [89, 90] use average concentrations in the reaction zone and consider its thickness Lr constant (see Figure 3.9). 

This chapter is organized as follows. In Section 4.1 we describe the fundamentals of mass transfer, such as the various definitions for concentrations and velocities. Pick s first law of diffusion, and the microscopic mass balance principle. 

This section includes the terminology for concentrations, velocities, and fluxes and their relationships. Although the discussion of new physical situations is limited, knowledge of the definitions is necessary for the next sections. Tick s first and second laws and the microscopic mass balance principle are introduced. Finally, simple cases based on the analogy between heat and mass transfer are analyzed. 

Dividing this equation by dx dy dz and shrinking the differential volume to zero, we get the microscopic mass balance (or continuity) equation as follows ... 

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