Velocity flows

The echo phase does not depend on the initial position of the nuclei, only on their displacement, vA, occurring in the interval between the gradient pulses. Analysis of the phase of the echo yields a measure of flow velocity in a bulk sample. Spatial resolution is easily obtained by the incorporation of additional imaging gradients. 

Figure B2.5.1 schematically illustrates a typical flow-tube set-up. In gas-phase studies, it serves mainly two purposes. On the one hand it allows highly reactive shortlived reactant species, such as radicals or atoms, to be prepared at well-defined concentrations in an inert buffer gas. On the other hand, the flow replaces the time dependence, t, of a reaction by the dependence on the distance v from the point where the reactants are mixed by the simple transfomiation with the flow velocity vy...

Erosion is the deterioration of a surface by the abrasive action of solid particles in a liquid or gas, gas bubbles in a liquid, liquid droplets in a gas or due to (local) high-flow velocities. This type of attack is often accompanied by corrosion (erosion-corrosion). The most significant effect of a joint action of erosion and corrosion is the constant removal of protective films from a metal s surface. This can also be caused by liquid movement at high velocities, and will be particularly prone to occur if the solution contains solid particles that have an abrasive action. 

Lagrangian-Eulerian (ALE) method. In the ALE technique the finite element mesh used in the simulation is moved, in each time step, according to a predetermined pattern. In this procedure the element and node numbers and nodal connectivity remain constant but the shape and/or position of the elements change from one time step to the next. Therefore the solution mesh appears to move with a velocity which is different from the flow velocity. Components of the mesh velocity are time derivatives of nodal coordinate displacements expressed in a two-dimensional Cartesian system as... 

The Reynolds number for flow in a tube is defined by dvpirj, where d is the diameter of the tube, V is the average velocity of the fluid along the tube, p is the density of the fluid, and rj is its dynamic viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000, turbulence is encountered. 

Electroosmotic flow velocity, Veof, is a function of the magnitude of the applied electric field and the buffer solution s electroosmotic mobility, )J,eof. 

Total Mobility A solute s net, or total velocity, Vtot, is the sum of its electrophoretic velocity and the electroosmotic flow velocity thus. 

Because micelles are negatively charged, they migrate toward the cathode with a velocity less than the electroosmotic flow velocity. Neutral species partition themselves between the micelles and the buffer solution in much the same manner as they do in HPLC. Because there is a partitioning between two phases, the term chromatography is used. Note that in MEKC both phases are mobile. ... 

McKillop and associates have examined the electrophoretic separation of alkylpyridines by CZE. Separations were carried out using either 50-pm or 75-pm inner diameter capillaries, with a total length of 57 cm and a length of 50 cm from the point of injection to the detector. The run buffer was a pH 2.5 lithium phosphate buffer. Separations were achieved using an applied voltage of 15 kV. The electroosmotic flow velocity, as measured using a neutral marker, was found to be 6.398 X 10 cm s k The diffusion coefficient,... 

When a gas or liquid flows over a surface, the pressure at the surface is reduced according to the formula shown in equation (1), in which d is the density and v is the linear flow velocity of the moving stream. 

Most of the above apphcations are in clarification duties. The use of HGMS to dewater relatively concentrated, paramagnetic mineral slurries has been demonstrated on 2 to 12 wt % feed concentration of synthetic malachite (7) concentrated to 40%. The magnetic collection was optimized at flow velocities of 1 mm/s, and product concentrations greater than 40% were not possible unless the collected material could be removed from the matrix with less than the equivalent of one canister of washwater. 

The flow velocity is thus proportional to the difference in transit time between the upstream and downstream directions and to the square of the speed of sound in the fluid. Because sonic velocity varies with fluid properties, some designs derive compensation signals from the sum of the transit times which can also be shown to be proportional to C. 

The flow velocity in this design is therefore proportional to the difference between the frequencies but independent of sonic speed within the fluid. 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Process variables also play a significant part in determination of surface finish. For example, the higher the current density, generally the smoother the finish on the workpiece surface. Tests using nickel machined in HCl solution show that the surface finish improves from an etched to a poHshed appearance when the current density is increased from ca 8 to 19 A/cm and the flow velocity is held constant. A similar effect is achieved when the electrolyte velocity is increased. Bright smooth finishes are obtained over the main machining zone using both NaCl and NaNO electrolyte solutions and current densities of 45-75 A/cm. ... 

Fig. 4. (a) Photographs of fluid flow behind cylinders at increasing flow velocities top to bottom, (b) Photomicrographs of nickel—nickel bond 2ones made at increasing coUision velocities top, 1600 m/s middle, - 1900 m/s bottom, - 2500 m/s (23). 

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