Volumetric flux

At relatively low liquid superficial velocities, increasing the mixture volumetric flux led to longer bubbles and shorter liquid slugs, eventually leading to the merging of elongated bubbles, and the development of the slug-annular flow pattern, repre-... 

The membrane is usually dense but sometimes micro-porous. If the external resistances to mass transfer are neglected in Figure 10.10, then pFj = p F l and pi, = p P i and Equation 10.20 can be written in terms of the volumetric flux as ... 

A general expression for average void fraction in an adiabatic two-phase flow or in saturated boiling was suggested by Zuber and Findlay (1965). Defining the local superficial velocities, VSG(= Qc/A) and VSL (= QJA), as volumetric flux densities, they assumed the velocity and void distributions to be... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

The mean water residence time is equal to the water volume divided by the volumetric flux ... 

In the absence of suspended solutes or colloids, the pure solvent flux through an ultrafiltration membrane is directly proportional to the applied pressure difference and inversely proportional to the viscosity of the solvent and the membrane thickness. Transport within the pores occurs in the creeping flow regime, since kinematic viscosities of liquids are sufficient to make Re < C 1 for practical pore sizes. In the simplest case, the membrane can be considered to be a packed array of straight, equal diameter nonintersecting capillary tubes. The observed volumetric flux, nAvA (cc/sec cm2), equals the product of the mass flux of solvent based on the total membrane area, nA... 

The volumetric flux of a binary mixture of solvent and solute, jy, through a membrane can be expressed as... 

On an overall basis, we are speaking of a mass, molar, or volumetric flux—that is, the mass, molar, or volumetric flow rate per unit surface area of the membrane normal to flow, per unit pressure difference, for the entirety of the membrane thickness. 

The method of zonation was applied to the energy and material conservation equations. Based on centered finite difTerence approximations, this method can transform three partial differential equations in radial distance and time to ordinary differential equations in time only. Following this, the ordinary differential equations were solved by using Crank-Nicholson algorithm. On the basis of this, the volumetric fluxes of those tar-phase and total volatile phase components were integrated with time by using in roved Euler method to evaluate overall pyrolysis product yields, and afterwards the gas yield can be deduced. 

Fig. 12.2. Steady-state solute concentration profiles in simultaneous diffusion and convection across a membrane of uniform properties. Numbers adjacent to profiles indicate values of the Peclet number whose sign depends upon the direction of the volumetric flux relative to the extemed solution...

Date Volumetric flux (pmoles m of tidal volume) ... 

In this model, the volumetric flux J and solute flux J through the skin layer are described by two equations ... 

Tomiyama A, Sou A, Zun I, Kanami N, Sakaguchi T (1995) Effects of Eotvos number and dimensionless liquid volumetric flux on lateral motion of a bubble in a laminar duct flow , In Serizawa A, Pukano T, Bataille J (eds) Advances in Multiphase Flow 1995, pp. 3-15, Elsevier... 

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