Viscosity coefficient gases

Similar analysis of momentum transfer in the gas was used to obtain an expression for the viscosity coefficient... 

Gas Formation Volume Factor — The Coefficient of Isothermal Compressibility of Gas — The Coefficient of Viscosity of Gas... 

Selection of Separator Conditions—Formation Volume Factor of Oil—Solution Gas-Oil Ratio — Formation Volume Factor of Gas—Total Formation Volume Factor— Viscosities — Coefficient of Isothermal Compressibility of... 

The widening of the shock wave front in this case can also be foreseen from the viewpoint of Leontovich and Mandelstam [7] who indicate that delayed excitation corresponds to an anomalously large second gas viscosity coefficient. However, this approach is approximate being qualitatively valid for small-amplitude waves (of the type in Fig. 3), the concept of the viscosity coefficient is inappropriate to describe the more complicated structure of large-amplitude waves (of the type in Fig. 5). 

One would think a solution to increase the productivity would be to use oxygen enrichment, not just during the choke-out period but also during the remainder of the fermentation in order to sustain the productivity. This does not work because of broth viscosity and gas holdup problems. In highly mycelial systems, a 15% increase in cell mass doubles the viscosity. The volumetric oxygen mass transfer coefficient and the bubble rise velocity—... 

It should be noted again that the numerical coefficient above has units of mole. According to this equation, the gas viscosity coefficient should be independent of pressure and should increase with the square root of the absolute temperature. The viscosities of gases are in fact found to be substantially independent of pressure over a wide range. The temperature dependence generally differs to some extent from because the effective molecular diameter is dependent on how hard the molecules collide and therefore depends somewhat on temperature. Deviation from hard-sphere behavior in the case of air (diatomic molecules, N2 and O2) is demonstrated by Eq. (4-19). 

Dependence on Flow Velocity. With regard to the tacit assumption that the viscosity coefficient is independent of flow velocities and gradients of flow velocities, it must be remembered that the molecular velocities are essentially Maxwellian in a gas under... 

The formula for the viscosity coefficient of a gas can be derived in a way similar to that used f or heat conduction. We imagine two very large parallel flat plates, one lying in the xy-plane, the other at a distance Z above the xy-plane. We keep the lower plate stationary and pull the upper plate in the + x direction with a velocity U. The viscosity of the gas exerts a drag on the moving plate. To keep the plate in uniform motion, a force must be applied to balance the viscous drag. Looking at the situation in another way, if the upper plate moves with a velocity U, the viscous force will tend to set the lower plate in motion. A f orce must be applied to the lower plate to keep it in place. 

Again, the numerical factor is not quite correct, since the flow of gas produces a nonequilibrium situation. For elastic spheres, the factor should be The unit of the viscosity coefficient is 1 newton second per square metre (N sm ) = 1 pascal second (Pa s) = 1 kg m s (The cgs unit is 1 poise = 1 g cm s = 10 kg m s )... 

The isothermal flow of incompressible liquid is described by equations (5.13) and (5.21), and the viscosity coefficient n = const. Hence, there are four equations for four unknowns - the pressure p and three velocity components u, v, and w. Thus, the system of equations is a closed one. For its solution it is necessary to formulate the initial and boundary conditions. Let us discuss now possible boundary conditions. Consider conditions at an interface between two mediums denoted as 1 and 2. The form and number of boundary conditions depends on whether the boundary surface is given or it should be found in the course of solution, and also from the accepted model of the continuum. Consider first the boundary between a non-viscous liquid and a solid body. Since the equations of motion of non-viscous liquid contain only first derivatives of the velocity, it is necessary to give one condition of the impermeability u i = u 2 at the boundary S, where u is the normal component of the velocity. The equations of motion of viscous liquid include the second-order derivatives, therefore at the boundary with a solid body it is necessary to assign two conditions following from the condition of sticking u i = u 2, Wii = u i where u is the tangential to S component of the velocity. If the boundary S is an interface between two different liquids or a liquid and a gas, then it is necessary to add the kinematic condition Ui = U2 =... 

In the equation, Kx, Ky, Kz are the coal seam permeability along the x, y, z direction respectively, x is gas viscosity coefficient. 

Where Q = Gas seepage flow Pa = the atmospheric pressure L = Length of the specimen PI = Specimen inlet gas pressure P2 = Specimen export gas pressure A = he cross-sectional area of specimen = the gas viscosity coefficient. 

Here a22 is the tangential momentum accommodation coefficient, a2g and are "second-order" coefficients, is the Chapman-Enskog first-order approximation to the viscosity coefficient. Equation (2.68) is, of course, valid for general gas-surface scattering kernels (2.49). Equation (2.68) reduces approximately to... 

Laminar flow sometimes known as streamline flow , this type of flow of a liquid or gas occurs when the fluid flows in parallel layers, with no macroscopic disruption between the layers (exchange at the molecular level via diffusion can still occur), in accord with the Poiseuille Equation for flow through a tube of radius r, (,g and length /t be (volume flow rate U = ir.rube/8-i1-/ be)- where y is the viscosity coefficient of the fluid laminar flow is to be contrasted with turbulent flow. 

Scalar isotropic pressure Pg in the continuous phase approximately equals the mean fluid pressure, and particulate stresses P, are expressible through derivatives of w and scalar isotropic pressure p, in the dispersed phase in accordance with Equation 4.4. Pressure p, is a function of suspension volume concentration and of particle fluctuation temperature defined by equation of state (4.6) for particulate pseudogas. Osmotic pressure function G(())) appearing in Equation 4.6 is given by either Equation 4.8, 4.9, or by some other equation that follows from some other statistical pseudo-gas theory. Dispersed phase dynamic viscosity coefficient p, and particle fluctuation energy transfer coefficient q, that appear in Equation 4.4 also can be represented as functions of fluctuation temperature T and concentration < > in conformity with the formulae in Equations 5.5 and 5.7. Force nf of interphase interaction per unit suspension volume approximately equals the force in Equation 3.2 multiplied by the particle number concentration. Finally, coefficients and a are determined in Equation 4.11 and 4.12, respectively. 

In most studies dealing with heat and mass transfer, it has been generally assumed that the thermo-physical properties, such as thermal conductivity, specific heat, molecular diffusivity of non-Newtonian polymer solutions, are the same as that for water, except for their non-Newtonian viscosity. Intuitively, one would expect the surface tension to be an important variable by way of influence on bubble dynamics and shape, but only a few investigators have controlled/measured/included it in their results. The available correlations can be broadly classified into two types first, those which directly relate the volumetric mass transfer coefficient with the liquid viscosity and gas velocity. The works of Deckwer et al. [36], Godbole et al. [42] and Ballica and Ryu [60] illustrate the applicability of this approach. All of them have correlated their results in the following form ... 

The laws of Pick and Stokes are good examples on transport processes in a continuum. Adolf Pick (1829-1901), who derived the law of diffusion in 1855, was in facta physiologist from Kassel in Germany. The Irishman George Stokes (1819-1903) was a pure mathematician. For us it is important to find out how the diffusion constant (D) and the viscosity coefficient (q) are related to entities in thermodynamics and kinetic gas theory. 

Superficial gas velocity Uj (empty reactor) Partial pressure of oxygen (assumed to be constant) poi Diameter of catalyst particle dp Density of catalyst particle Pp External surface area of catalyst particle Am Kinematic viscosity of gas mixture v Molecular diffusion coefficient of o-xylene in air D .x Effective diffusion coefficient of o-xylene in the catalyst Deff.o-x Pseudo-first-order rate constant k = (fem.i + m,i)PT P02 Reynolds number Rcp — 2.46ms 0.21 bar 3mm 1800 kgm l.lm kg 5.5 X 10 m s" 2.5 X 10 m s" 2.5 X 10 m s- 2.5 X 10 m kg s 134... 

The engineering modeling of IL environments is yet to emerge, and measurements of physico-chemical properties (such as viscosities, densities, gas solubilities, diffusion coefficients, toxicology, etc.) are only available for a very limited number of compounds. Moreover, new correlations need to be developed to account for, for example, the complex equilibrium behavior of ILs and traditional solvents. 

Due to the fact that H2 has better fliermal conductivity, lower viscosity coefficient and smaller atomic radius and larger diffusion ability than that of CO. H2 diffuses faster than CO into the reaction surface in pellets, and at the same time, reaction product H2O spreads faster than CO2 from reaction surface to file outside air. Which illustrates H2 is more active than CO [14]. Therefore file elevation of mole fraction of H2 in reducing gas could enhance metallization rate and reduction degree of prereduced pellets. 

If a fluid has a velocity in the y direction that depends on z, the y component of the momentum is transported in the z direction as each layer of fluid puts a frictional force on the next layer. An analysis similar to that of self-diffusion and thermal conductivity can be carried out for a hard-sphere gas. The net flow of the momentum is computed and the result is an expression for the viscosity coefficient ... 

Calculate the viscosity coefficient of O2 gas at 292 K from its hard-sphere diameter. Compare your result with the value in Table A. 18 in the appendix. 

Transport processes in a hard-sphere gas can be analyzed theoretically. A formula for the self-diffusion coefficient was derived in this chapter, and similar formulas for thermal conductivities and viscosity coefficients were presented. Each transport coefficient is proportional to the mean free path and to the mean speed, and thus proportional to the square root of the temperature. 

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