Laminar flow pattern

Multiphase copolymers, Ziegler-Natta catalysts for, 26 535, 537-540 Multiphase laminar flow patterning, in microfluidics, 26 961 Multiphase reactions, in microbial transformations, 16 412-414 Multi-phase reactors, 21 333-335 Multiphoton effects, in photochemical technology, 19 109... 

As in the case of capillary-tube units, the shear rate (rotational speed) should be variable over wide ranges (10- to 1000-fold) and baffles or other obstructions which could interfere with the laminar-flow pattern must be absent. Since the fluid is sheared for long periods of time in these instruments, temperature control is much more critical, especially in the case of high-consistency materials, for which temperature rises of over 20°C. (W2) have been recorded. Weltmann and Kuhns (W5) subsequently presented an erudite mathematical analysis of the temperature distribution within the layers of sheared fluid. 

This derivation makes a number of assumptions. Firstly, we assume that there is no disruption to the laminar flow pattern due to a finite disc surface, finite cell size, or eccentricity in disc rotation. To what extent design factors affect measured currents will be discussed further in the section on electrode construction. It is sufficient at this point to say that the criteria for negligible disruption can be met. 

Certain criteria have to be met in the construction of hydrodynamic electrodes, such that the laminar flow pattern, which is used in the derivation of the theoretical equations, is conformed to. Thus edge effects, which are due to the fact that electrode and surrounding mantle are not of infinite size and which are also dependent on cell dimensions, must be minimised. The shape of the electrode and mantle is important the surfaces must be smooth and there must be no discontinuities or electrolyte penetration at the electrode/mantle junction. 

Inertial forces of the fluid increase with density and the square of velocity (pv2) while viscous forces decrease with increasing diameter of tube (nv/d) and increase with viscosity and velocity. High Reynolds numbers (Re>4000) result in turbulent flow with low Reynolds number (Re<2000) the flow is laminar. Laminar flow results from formation of layers of fluid with different velocities after a certain flow distance, as illustrated in Figure 2.10A. Flow at the walls is zero and increases approaching the center of the tubes. The laminar flow pattern results from layers of mobile phase with different velocities travelling parallel to each other. The maximum flow at the center is twice the average flow velocity of the fluid. Molecules in the fluid can exchange between fluid layers by molecular diffusion. Most open tubular columns operate under laminar flow conditions. 

A measure that has been the subject of extensive publication is that of microreactors with catalytically coated walls (7,8). A microreactor has been defined as a miniaturized reaction vessel with characteristic dimensions in the range 10-300 pm which has been fabricated using state-of-the-art high-precision engineering (7). Such reactors exhibit well-defined laminar-flow patterns and permit facile scale-up by simple numbering up of the number of channels and flexible... 

P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, Microfabrication inside capillaries using multiphase laminar flow patterning, Science 285, 83—85 (1999). 

Using the linear relation between drag coefficient and Reynolds number, a pure laminar flow pattern of the sedimentating particles is implied. For spherical particles, flow is considered as laminar for Reynolds number smaller than 0.1. For Reynolds numbers up to 1, the linear relation with drag coefficient is generally accepted. Several investigators accepted the linear relation as far... 

The dispersion given by Eq. 4.25 can be considered as two terms. One is due to the longitudinal diffusion and the other originates from the laminar flow patterns and from the adsorption retention. In practice, one of the terms is relatively small and may be neglected. In the conditions of present interest, it is mostly the case with the longitudinal diffusion. This omission will be implied if not stated otherwise. 

An application of microfluidic reactors is the development of a membraneless fuel cell. Two streams, one containing a fuel such as methanol, the other an oxygen-saturated acid or alkaline stream, are merged without mixing. The laminar flow pattern in the narrow channel helps to maintain separate streams without the use of membrane separators. Opposite walls function as the electrodes and are doped with catalyst. Ion exchange, protons for the add system, takes place through the liquid-liquid interface. This is an example of a solid-liquid-liquid-solid multiphase reactor. ... 

In the absence of pressure driven fluxes through the membrane and assuming a laminar flow pattern, a hexagonal free shear layer should sheath each fiber the hexagon is approximated by an equivalent circle of radius Re. 

Assuming a laminar flow pattern, the radial velocity profile in region 1 can be expressed as ... 

In CRNI the material flow is based on drag, not positive pumping. There is a low shear stress field, responsible for the absence of dispersive mixing. However, the interchange of material between the screws provides good distributive mixing. The chemical reaction proceeds on the continuously renewed surfaces, related to reorientation of the laminar flow patterns and the total strain. CRNI is well suited for the polymerization... 

Another area which applied microfluidics to materials production is reported in [10]. Here, the authors coinfused solutions of adipoyl chloride in xylene and hexamethylenediamine in 0.1 NaOH for laminar flow patterning of nylon 6,6 membranes (Fig. 4). Using this method, the reactants in the different fluid phases would diffuse to the... 

Microscale In channel structures with dimensions <200 mm (microfiuidic devices), fluids (liquids) follow predictable laminar paths characteristic of low Reynolds numbers. This allows two or more layers of fluid to flow next to each other without any mixing other than by molecular or particulate diffusion. As a result of this property, it is possible to have multiple inputs into a single chaimel and have them flow side by side in an orderly fashion (Fig. 2b). Since the channel dimensions in many cases are comparable to the size of single cells, we can use laminar flow patterning to expose subceUular regions to specific signals. Also it is possible to allow different regions of the same cell to different conditions. 

In addition, microfiuidics makes use of phenomena not available in the macroscopic world. Well-predictable and controllable laminar flow patterns can be achieved by appropriate design of microchannels. Substance transport by diffusion becomes faster as dimensions shrink. Sample volumes are on the order of microliters to picoliters, and flow on the order of pl/min to nl/min can be realized, comparable to the sima-tion in capillary blood vessels. 

Equation [2] is derived from the mass balance in a differential volume of the fluid and considers the axial and radial concentration gradients as well as the linear velocities established in a laminar flow pattern in the absence of chemical reactions. The first term (M C/Mx ) refers to the axial diffusion and the other terms to the radial diffusion. The expression... 

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