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Introduction
Published in Nayef Ghasem, Modeling and Simulation of Chemical Process Systems, 2018
Diffusion from the arbitrary molecular motion is known as molecular diffusion; diffusion from turbulent eddies is referred to as turbulent diffusion or eddy diffusion. The diffusion coefficient is the coefficient in Fick’s first law, where J is the diffusion flux (amount of substance per unit area per unit time). Mass flux is the measurement of the amount of mass passing in or out of the control volume. The governing equation for calculating mass flux is the continuity equation. The mass flux is defined simply as mass flow per area.
Statistical Methods
Published in Michio Sanjou, Turbulence in Open Channels and River Flows, 2022
Here, consider the relation among K, γ and the kinetic viscosity ν≡μρ, in which μ is the viscosity. A relation γ∼ν is already known for the gases such as air. Hence Kγ≃Kν∼uLν=Re↔K∼Reγ is obtained. This suggests that the eddy diffusion coefficient is proportional to the Reynolds number. Namely, larger turbulence included in a flow field promotes more significantly the diffusion. By the way, the ratio of thermal diffusion coefficient and the kinetic viscosity, Pr=νγ, is called the Prandtl number, which is about 0.7 for the air and about 7 for the water.
Liquid-Liquid Extraction
Published in John J. McKetta, Unit Operations Handbook, 2018
Considering the actual transport of solute within either phase, this may involve both molecular and eddy diffusion. The former, which is a comparatively slow process, arises from the general random movement of the molecules, this leading to a net movement of solute in the direction of any concentration gradient. Eddy diffusion can be much greater in magnitude and results from bulk movement of the fluid, usually resulting from some form of turbulence.
Bayesian State Space Modeling of Physical Processes in Industrial Hygiene
Published in Technometrics, 2020
Nada Abdalla, Sudipto Banerjee, Gurumurthy Ramachandran, Susan Arnold
Bayesian SSMs for exposure assessment incorporate direct measurements of the environmental exposure, deterministic physical models, and prior information from experts. There are several physical models varying in their level of complexity (Ramachandran 2005). Three commonly used families that we consider here are: (i) the well-mixed compartment (one-zone) model; (ii) the two-zone model; and (iii) the turbulent eddy diffusion model. We use discrete approximations to these deterministic models and introduce stochasticity to devise flexible Bayesian versions. This obviates the need for exact analytic solutions to the differential equations, which can be sensitive to the choice of initial conditions. Prior specifications for the model parameters produce Bayesian SSMs. Dynamic steady-state models are composed of (i) a measurement equation that relates the observations (or some function thereof) to the true concentrations; and (ii) a transition equation describing the concentration change from time t to time . We will derive the dynamic models from the respective differential equations for three popular physical models in industrial hygiene.
Static turbulence promoters in cross-flow membrane filtration: a review
Published in Chemical Engineering Communications, 2020
Chiranjit Bhattacharjee, V. K. Saxena, Suman Dutta
In membrane filtration processes, turbulence is defined as the process of increasing the flow rate of the feed or changing the flow path or to create additional mixing to disrupt the boundary layer which enhances the mass transfer rate in the module. In cross-flow systems this disruption leads to minimal accumulation of rejected particles over the membrane surface and hence results in increased permeate flux. This can be achieved by incorporating static inserts in membrane modules. In literature, these static inserts are referred to as static mixers or static turbulence promoters. Static turbulence promoters effectively change the hydrodynamics conditions of the module without significantly increasing energy consumption and investment costs. The intensity of turbulence plays an important role in changing the fluid dynamics in the system. Turbulent intensity is a measure of extent of turbulence dissipation which is used to signify the strength of turbulence in promoter-filled channels. One characteristic of turbulent flows is their irregularity or randomness. Stretching of three-dimensional vortices plays an important role in turbulence. This mechanism is also known as vortex stretching. Turbulence enhances the mixing of fluid and generates an additional diffusive effect termed as eddy diffusion. This diffusive effect of turbulence is the driving force for rapid mixing and simultaneous increase in momentum and mass transfer.