Fluctuating pressure gradient

In the Godrej-Lurgi process, olefins are produced by dehydration of fatty alcohols on alumina in a continuous vapor-phase process. The reaction is carried out in a specially designed isothermal multitube reactor at a temperature of approximately 300°C and a pressure of 5—10 kPa (0.05—0.10 atm). As the reaction is endothermic, temperature is maintained by circulating externally heated molten salt solution around the reactor tubes. The reaction is sensitive to temperature fluctuations and gradients, hence the need to maintain an isothermal reaction regime. 

Sleiched278 has indicated that this expression is not valid for pipe flows. In pipe flows, droplet breakup is governed by surface tension forces, velocity fluctuations, pressure fluctuations, and steep velocity gradients. Sevik and Park 279 modified the hypothesis of Kolmogorov, 280 and Hinze, 270 and suggested that resonance may cause droplet breakup in turbulent flows if the characteristic turbulence frequency equals to the lowest or natural frequency mode of an... 

The external electric field is in the direction of the pore axis. The particle is driven to move by the imposed electric field, the electroosmotic flow, and the Brownian force due to thermal fluctuation of the solvent molecules. Unlike the usual electroosmotic flow in an open slit, the fluid velocity profile is no longer uniform because a pressure gradient is built up due to the presence of the closed end. The probability of the particle position is obtained by solving the Fokker-Planck equation. The penetration depth is found to be dependent upon the Peclet number, which is a measure of significance of the convective electroosmotic flow relative to the Brownian diffusion, and the Damkohler number, which is a ratio of the characteristic diffusion-to-deposition times. 

In measurement and visualization of gas-solid flow in fast fluidization, various techniques have been developed and used, such as pressure gradient, pressure fluctuation, capacitance probe, optical fiber probe, momentum probe, laser Doppler velocimeter, night-television, and video camera. The resulting data on local gas and solid velocity, solids concentration and its... 

Let the pressure gradient in a duct between two parallel plates periodically fluctuate,... 

Possible influences of nonequilibrium cross-diffusion effects on the mixing process were investigated by means of direct numerical simulations (DNS) of mass fraction fluctuations in stationary isotropic turbulence for binary mixtures under supercritical conditions (26,27). The authors have shown that after some time, the initially perfectly mixed species become segregated owing to the presence of temperature and pressure fluctuations and the resulting Soret mass cross-diffusion fluxes Jj and /f, induced by temperature and pressure gradients. Based on DNS results (26,27), we propose a phenomenological model that predicts the rate of production of the concentration variance as... 

The physical properties of foams are changed by both the fluctuations in the surface rates of components and the temperature and pressure gradients the foam experiences as it travels down the wellbore and into the formation. Bottomhole treating pressures (BHTP) can be calculated as follows ... 

Moholkar and Pandit (2001b) have also extended the nonlinear continuum mixture model to orifice-type reactors. Comparison of the bubble-dynamics profiles indicated that in the case of a venturi tube, a stable oscillatory radial bubble motion is obtained due to a linear pressure recovery (with low turbulence) gradient, whereas due to an additional oscillating pressure gradient due to turbulent velocity fluctuation, the radial bubble motion in the case of an orifice flow results in a combination of both stable and oscillatory type. Thus, the intensity of cavitation... 

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