External flow distribution

The simplest approach of splitting one stream into six streams is the use of a fluidic element that directly connects one inlet with six symmetrically arranged outlets [140, 141, 148], Commercial fluid distributors, however, suffer from flow maldistribution, as the smallest deviations in their manufacture have a large impact. Hence specially devices are required for flow splitting to micro devices. A liquid-flow distribution module was one first such device to be realized. 

Tolerances in diameter will, according to the Hagen-Poiseuille law, influence the flow rate to the power of 4. 

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Alternatively, reactant and product gases can be distributed to and removed from individual cells through internal pipes in a design analogous to that of filter presses, (iare must be exercised to assure an even flow distribution between the entiv and exit cells. The seals in internally manifolded stacks are generally not subject to electrical, thermal, and mechanical stresses, but are more numerous than in externally manifolded stacks. 

One method of characterising the residence time distribution is by means of the E-curve or external-age distribution function. This defines the fraction of material in the reactor exit which has spent time between t and t -i- dt in the reactor. The response to a pulse input of tracer in the inlet flow to the reactor gives rise to an outlet response in the form of an E-curve. This is shown below in Fig. 3.20. 

The first stage, called dynamic stage, is the period during which a spherical droplet is flattened and deformed into a planetary ellipsoid with its major axis perpendicular to the flow direction as a result of the external pressure distribution. The eccentricity of the elliptical profile changes with time. 

So far, we have been talking about the stability of zero pressure gradient flows. It is possible to extend the studies to include flows with pressure gradient using quasi-parallel flow assumption. To study the effects in a systematic manner, one can also use the equilibrium solution provided by the self-similar velocity profiles of the Falkner-Skan family. These similarity profiles are for wedge flows, whose external velocity distribution is of the form, 11 = k x . This family of similarity flow is characterized by the Hartree parameter jSh = 2 1 the shape factor, H =. Some typical non-dimensional flow profiles of this family are plotted against non-dimensional wall-normal co-ordinate in Fig. 2.7. The wall-normal distance is normalized by the boundary layer thickness of the shear layer. 

We therefore consider a different reaction flow model as our basic targeting model—one that can address temperature manipulation by feed mixing as well as by external heating or cooling. The model consists of a differential sidestream reactor (DSR), shown in Fig. 6, with a sidestream concentration set to the feed concentration and a general exit flow distribution function. (As mentioned in Section II, the boundary of an AR can be defined by DSRs for higher-dimensional (> 3) problems). We term this particular structure a cross-flow reactor. By construction, this model not only allows the manipulation of reactor temperature by feed mixing, but often eliminates the need to check for PFR extensions. 

One approach to the solution of this equation is to assume that the pressure does not vary with v, and so it is specified by the external velocity distribution, v is computed from the continuity equation, leaving a differential equation in u to be integrated. However, this holds only for the laminar flow since turbulent boundary layers are inherently unsteady. The subsequent sections deal with the solutions of these equations in more detail. 

The second way for scale-out refers to having, in parallel, several caterpillar channels with, ahead, a flow-distribution unit (internal numbering-up) or to simply combine a few of the devices with an external flow manifold. This has not yet been realized. The first route with a slight increase in internal dimensions into the meso range was preferred to avoid problems with flow distribution. 

The velocity field at the spherical surface corresponds to influence of an unperturbed external flow on the sphere. In its turn, the rotation of the sphere influences the distribution of velocities in the liquid. Let these perturbations u = (u j y, w ) be small in comparison with the unperturbed velocity. The velocity of... 

However, drop formation is not the only situation during which a new surface is created. Indeed, while the volume of fluid inside a drop must be ccmserved, its shape may vary and with it the surface area of its interface. For instance, a spherical drop (of minimal surface area) may be deformed by the external flow to form an oval or other shape. This creation of a new surface is coupled with the presenc e of Marangoni stresses as we shall see below, the surfac e variaticMi can create Marangoni stresses, but it can also be caused by uneven distribution of surfactant. 

Determination of flow distribution on the basis of model (40)-(43) for the given scheme and parameters. As a result of this stage the interaction between flows in the scheme branches that cause non-additivity of function F x,d) is fixed, since the flow distribution is the result of this interaction. So far as the scheme is closed, there is no interaction involving constant pressures or flows at nodes of external sources or sinks. Thermal interaction of the circuit described by equation (43) as a whole with the environment remains, but does not influences additivity of the minimized function. Transformation with the fixed interaction (distribution of flows among the branches) of the closed scheme (Fig. 3,a) to the tree (Fig. 3,b), specifying conditional external sources and sinks at break nodes (4, 4, 4", 5, 5, 5"). They make it possible to preserve material balances in the network that were determined at the previous stage. 

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