Transport phenomena driving force

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

Mass Transport at Very Low Concentrations. Heavy Water Plants. The phenomenon of mass transport at very low concentrations is not unique to the reactor coolant systems. It can occur also in the heavy water production plants. Table III compares iron transport in a reactor primary circuit and a GS plant dehumidifier circuit and illustrates the quantities of iron that can be transported each day. While the concentrations in the reactors are typically two orders of magnitude lower, the flow rates are an order of magnitude higher. The lower concentration in the reactors gives a lower driving force for deposition and the efficiency of deposition is considerably lower. 

The driving forces, or driving potentials, for transport phenomena are (i) the temperature difference for heat transfer (ii) the concentration or partial pressure difference for mass transfer and (iii) the difference in momentum for momentum transfer. When the driving force becomes negligible, then the transport phenomenon will cease to occur, and the system will reach equilibrium. 

The phenomenon of ambipolar conduction is not limited to chemical potential gradients only, and may occur in systems with several driving forces (e.g., chemical-potential and temperature gradients in combination with external electrical field). However, this phenomenon is always related to conjugate transport of several charge carriers. 

There are some special cases in FFF related to the two extreme limits of the cross-field driving forces. In the first case, the cross-field force is zero, and no transverse solute migration is caused by outer fields. However, because of the shear forces, transverse movements may occur even under conditions of laminar flow. This phenomenon is called the tubular pinch effect . In this case, these shear forces lead to axial separation of various solutes. Small [63] made use of this phenomenon and named it hydrodynamic chromatography (HC). If thin capillaries are used for flow transport, this technique is also called capillary hydrodynamic fractionation (CHDF). A simple interpretation of the ability to separate is that the centers of the solute particles cannot approach the channel walls closer than their lateral dimensions. This means that just by their size larger particles are located in streamlines of higher flow velocities than smaller ones and are eluted first (opposite to the solution sequence in the classical FFF mode). For details on hydrodynamic chromatography,see [64-66]. 

The carrier-mediated transport of sodium in exchange for protons across membranes is a virtually universal phenomenon in biology, from bacteria to man. It is carried out by a family of Na /H exchangers which is often referred to as antiporters. They are classified as secondary active transporters, since the driving force is the... 

Equation 7.2.a-5 implicitly assumes perfectly ordered flow in that V (pyD Vx ) is specific for molecular diffusion. Deviations from perfectly ordered flow, as encountered with turbulent flow, lead to a flux that is also expressed as if it arose from a diffusion-like phenomenon, in order to avoid too complex mathematical equations. The proportionality factor between the flux and the concentration gradient is then called the turbulent or eddy diffusivity. Since this transport mechanism is considered to have the same driving force as molecular diffusion, the two mechanisms are summed and the resulting proportionality factor is called effective diffusivity, D,. In highly turbulent flow the contribution of... 

The osmosis phenomenon, stemming from biological systems with biological semipermeable membrane, initially represents a nature net transport of solvent molecules from a region of higher water chemical potential (e.g., dilute solution) to a region of lower water chemical potential (e.g., concentrate solution). The driving force is the pure chemical potential difference, i.e., osmotic pressure difference, across the membrane. 

In the mid-1800s. Pick [3,4] introduced two differential equations that provide a mathematical framework to describe the otherwise random phenomenon of molecular diffusion. The flow of mass by diffusion across a plane was proportional to the concentration gradient of the diffnsant across it. The components in a mixture are transported by a driving force dnring diffusion. The molecnlar motion is Brownian. The ability of... 

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