Diffusivity for liquids

Table 6.1 Comparison of densities, viscosities and diffusivities for liquid, supercritical fluid and gas...

Table 2.3.2 gives the thermal conductivity and diffusivity of some common liquids. Table 2.3.3 gives the same quantities for air and liquid sodium. An interesting observation from the data of Table 2.3.3 is that the thermal diffusivity for liquid sodium and air, which is a measure of the rate at which heat is transported, is of the same order, although the thermal conductivity of sodium is some thousand times larger. 

If the mixing involves liquids rather than gases, the effect is more pronounced. The molecular diffusion for liquids would be very much lower (i.e.. Dab = 1 X 10 m /s. Since t is inversely proportional to Dab. the time required will increase by a factor of 2 x 10". The velocity in the liquid system will be lower... 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Lee-Thodos presented a generahzed treatment of self-diffusivity for gases (and liquids). These correlations have been tested for more than 500 data points each. The average deviation of the first is 0.51 percent, and that of the second is 17.2 percent. 8 = PyVr, s/cm and where G = (X - X)/(X - 1), X = p,/T h and X = p /T evaluated at the solid melting point. 

Riazi-Whitson They presented a generahzed correlation in terms of viscosity and molar density that was apphcable to both gases and liqmds. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-194)] for the low-pressure diffusivity and the Stiel-Thodos correlation for low-pressure viscosity ... 

Caldwell and Babb used virtually the same equation to evaluate the mutual diffusivity for concentrated mixtures of common liquids. 

TABLE 5-19 Correlations of Diffusivities for Concentrated/ Binary Mixtures of Nonelectrolyte Liquids... 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

In connection with the earlier consideration of diffusion in liquids using tire Stokes-Einstein equation, it can be concluded that the temperature dependence of the diffusion coefficient on the temperature should be T(exp(—Qvis/RT)) according to this equation, if the activation energy for viscous flow is included. 

For liquid/liquid separators, avoid severe piping geometry that can produce turbulence and homogenization. Provide an inlet diffuser cone and avoid shear-producing items, such as slots or holes. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

The amorphous orientation is considered a very important parameter of the microstructure of the fiber. It has a quantitative and qualitative effect on the fiber de-formability when mechanical forces are involved. It significantly influences the fatigue strength and sorptive properties (water, dyes), as well as transport phenomena inside the fiber (migration of electric charge carriers, diffusion of liquid). The importance of the amorphous phase makes its quantification essential. Indirect and direct methods currently are used for the quantitative assessment of the amorphous phase. 

The estimation of the diffusional flux to a clean surface of a single spherical bubble moving with a constant velocity relative to a liquid medium requires the solution of the equation for convective diffusion for the component that dissolves in the continuous phase. For steady-state incompressible axisym-metric flow, the equation for convective diffusion in spherical coordinates is approximated by... 

The influence of interfaeial potentials (diffusion or liquid junction potentials) established at the boundary between two different electrolyte solutions (based on e.g. aqueous and nonaqueous solvents) has been investigated frequently, for a thorough overview see Jakuszewski and Woszezak [68Jak2]. Concerning the usage of absolute and international Volt see preceding chapter. 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

At constant conditions, different fluids will diffuse at different rates into a particular elastomer (with their rates raised proportionally by increasing the exposed area), and each will reach the far elastomer-sample surface proportionally more rapidly with decreasing specimen thickness. Small molecules usually diffuse through an elastomer more readily than larger molecules, so that, as viscosity rises, diffusion rate decreases. One fluid is likely to diffuse at different rates through different elastomers. Permeation rates are generally fast for gases and slow for liquids (and fast for elastomers and slow for thermoplastics and thermosets). 

Diffusion rates for liquids in an elastomer are easily measured by absorption (immersion) testing, a simple process as indicated in Figure 23.6. An initially weighed immersed sheet sample of elastomer is removed from the liquid periodically, rapidly dabbed with tissue paper, reweighed, and replaced. A plot of mass increase versus root time is drawn (also see Figure 23.6), root time being chosen due to the form of appropriate solutions of Fick s laws. 

Flayduk, W. and Minhas, B.S. (1982) Correlations for prediction of molecular diffusivities in liquids. Can.]. Chem. 

Mass transfer in the continuous phase is less of a problem for liquid-liquid systems unless the drops are very small or the velocity difference between the phases is small. In gas-liquid systems, the resistance is always on the liquid side, unless the reaction is very fast and occurs at the interface. The Sherwood number for mass transfer in a system with dispersed bubbles tends to be almost constant and mass transfer is mainly a function of diffusivity, bubble size, and local gas holdup. 

Diffusion in liquids is very slow. Turbulent transport or very narrow channels are necessary for good contact between the phases. The droplets must also be very small to minimize transport hmitations within the drops. An estimation of the time constant for diffusion in a 1-mm drop is (f (10-3)2... 

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