Diffusion bulk: calculation

The MD simulations show that second shell water molecules exist and are distinct from freely diffusing bulk water. Freed s analytical force-free model can only be applied to water molecules without interacting force relative to the Gd-complex, it should therefore be restricted to water molecules without hydrogen bonds formed. Freed s general model [91,92] allows the calculation of NMRD profiles if the radial distribution function g(r) is known and if the fluctuation of the water-proton - Gd vector can be described by a translational motion. The potential of mean force in Eq. 24 is obtained from U(r) = -kBT In [g(r)] and the spectral density functions have to be calculated numerically [91,97]. 

The soot temperature was found to exceed the gas temperature as measured by thermocouples in the absence of droplet injection but decayed at a similar rate. This is attributed to bulk heating effects associated with the localized burning of vaporized material. A detailed diffusion flame calculation for a cylindrical source of reactants and relative velocity on the same order as these experimental data, indicate that this bulk heating effect is reasonable. 

Not only surfactant molecules may diffuse in advance of the wetting front. Spreading of pure liquids by surfaee diffusion of molecules from a micro-doplet over a solid surface was comprehensively studied using microellipso-metric measurements [29-34]. It has been observed that on the top of the first monolayer, a second and subsequent layers form, and the corresponding coefficients of surface diffusion were calculated. For liquid polydimethylsi-loxan (PDMS) on a hydrophobed silicone wafer, coefficients of surface diffusion in the first monolayer grow with decreasing molecular mass M of the PDMS from = A x 10 cm /s for M = 28,400 to 7 x 10 cm /s for M = 6700. Correlation between the values and bulk viscosity of the liquid PDMS have been established. 

Basically, the transport resistance can be considered as a parallel circuit of the bulk and the Knudsen type of mass transport resistance. The effective bulk diffusivity was calculated from the solution of Eq. 9.11 as described above. To determine the... 

At the opposite limit, where all the pores are sufficiently large that bulk diffusion controls, a similar calculation can be performed. In this case the appropriate flux relations are equation (5.29) and its companion obtained by interchanging the suffixes. For the symmetric systems considered here these may be written in scalar form ... 

Assuming that Eq. (2.67) applies to small molecules in the limit as n 1, calculate To, using D = 3 X 10" m sec" for a typical low molecular weight molecule. Use this value of Tq to estimate t for a polymer with n = 10. Based on Eq. (2.63), evaluate diffusion coefficient for bulk... 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

Consider spherical molecules A and B having radii and Tb and diffusion coefficients Da and Db- First, suppose that B is fixed and that the rate of reaction is limited by the rate at which A molecules diffuse to the B molecule. We calculate the flux 7(A- B) of A molecules to one B molecule. Let a and b be the concentrations (in molecules/cm ) of A and B in the bulk, and let r be the radius of a sphere centered at the B molecule. The surface area of this sphere is Aitr, so by Pick s first law we obtain... 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

At a particular location in a distillation column, where the temperature is 350 K and the pressure 500 m Hg, the tnol fraction of the more volatile component in the vapour is 0.7 at the interface with the liquid and 0.5 in the bulk of the vapour. The molar latent heat of the more volatile component is 1.5 times that of the less volatile. Calculate the mass transferrates (kmol m s-11 of the two components. The resistance to mass transfer in the vapour may be considered to lie in a stagnant film of thickness 0.5 mm at the interface. The diffusivity in the vapour mixture is 2 x )() ° mV. ... 

Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

The diffusion length can thus be calculated since a is typically known, or since =(t D)1/2, the bulk lifetime provided the diffusion coefficient... 

A number of bulk simulations have attempted to study the dynamic properties of liquid crystal phases. The simplest property to calculate is the translational diffusion coefficient D, that can be found through the Einstein relation, which applies at long times t ... 

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