Channels dimensions

In a static system, the gel-layer thickness rapidly increases and flux drops to uneconomicaHy low values. In equation 6, however, iCis a function of the system hydrodynamics. Typically, high flux is sustained by moving the solution bulk tangentially to the membrane surface. This action decreases the gel thickness and increases the overall hydrauHc permeabiUty. For any given channel dimension, there is an optimum velocity which maximizes productivity (flux per energy input). 

A number of analytical solutions have been derived for iC as a function of channel dimensions and fluid velocity (30). In practice, the fit between theory and data for K is poor except in idealized cases. Most processes exhibit either higher fluxes, presumably caused by physical dismption of the gel layer from the nonideal hydrodynamic conditions, or lower fluxes caused by fouling (31). In addition, iCis a function of the fluid composition. 

Vacuum Flow When gas flows under high vacuum conditions or through very small openings, the continuum hypothesis is no longer appropriate if the channel dimension is not very large compared to the mean free path of the gas. When the mean free path is comparable to the channel dimension, flow is dominated by collisions of molecules with the wall, rather than by colhsions between molecules. An approximate expression based on Brown, et al. J. Appl. Phys., 17, 802-813 [1946]) for the mean free path is... 

The Knudsen number Kn is the ratio of the mean free path to the channel dimension. For pipe flow, Kn = X/D. Molecular flow is characterized by Kn > 1.0 continuum viscous (laminar or turbulent) flow is characterized by Kn < 0.01. Transition or slip flow applies over the range 0.01 < Kn < 1.0. 

As seen from Fig. 1, characteristics of gas-containing polymer melts reduced to channel dimensions can be divided into three areas depending on the type of extrudate obtained. 

An interesting and practically valuable result was obtained in [21] for PE + N2 melts, and in [43] for PS + N2 melts. The authors classified upper critical volumetric flow rate and pressure with reference to channel dimensions x Pfrerim y Qf"im-Depending on volume gas content

channel entrance (pressure of 1 stm., experimental temperature), x and y fall, in accordance with Eq. (24), to tp 0.85. At cp 0.80, in a very narrow interval of gas concentrations, x and y fall by several orders. The area of bubble flow is removed entirely. It appears that at this concentration of free gas, a phase reversal takes place as the polymer melt ceases to be a continuous phase (fails to form a continuous cluster , in flow theory terminology). The theoretical value of the critical concentration at which the continuous cluster is formed equals 16 vol. % (cf., for instance, Table 9.1 in [79] and [80]). An important practical conclusion ensues it is impossible to obtain extrudate with over 80 % of cells without special techniques. In other words, technology should be based on a volume con-... 

These methods rely on temperature changes, alternation of channel dimensions and flow rates, to produce foamed articles of a required structure, which is important for manufacturing foamed and foam-filled articles made of plastics, as well as for equipment design in this sphere. 

The design question is given the heat rate Q, the length L, and width W, select a working fluid with mass flow rate m, channel dimension d, channel spacing Sxd (for 5" is a number >1), number of channels n, and material and thickness of the block H. We will be particularly interested in the pumping power P. 

In experiments related to flow and heat transfer in micro-channels, some parameters, such as the flow rate and channel dimensions are difficult to measure accurately because they are very small. For a single-phase flow in micro-channels the uncertainty of ARe is (Guo and Li 2002,2003)... 

Table 1.2 Calculated heats of adsorption and adsorption constants for various hydrocarbons in zeolites with different channel dimensions.

Scale-up of microchannel reactors is based on using the optimal channel dimensions rather than seeking the smallest or the largest microchannel. In some cases, the channels may range from 100 pm in hydrauhc diameter to a few millimeters. The classification of a rigorous size range to designate a reactor as microchannel is not necessary. 

Figure 11.1 Scale-up versus numbering up for microchannels. All critical channel dimensions remain constant in a microchannel system independent of the overall process capacity.

On shrinking the size of micro-channel reactors by reducing the channel dimensions, a number of characteristic quantities such as pressure drop and the degree of chemical conversion are affected. In order to permit a meaningful comparison of the reactor geometry with a scaled geometry, it is important to keep one or a few... 

The comparison given above shows that a reduction in channel dimensions offers some substantial benefits in cases where surface reactions are involved or efficient heat and mass transfer are needed. One important conclusion to be drawn is that a decrease in the channel diameter at fixed efficiency does not necessarily mean an increase in pressure drop. Rather, the pressrue drop can be kept constant... 

Figure 3.10 Calculated heat transfer coefficient depending on micro-channel dimensions and water flow rate. Experimental data are given in [47].

Referring to highly parallel synthesis, the smallness of the micro-channel dimensions enables one to combine several micro imit operations on one chip [23]. By using multi-layered chip architecture complicated fluidic circuits with nx m combinations of fluid streams can be made. By this means, truly combinatorial parallel processing can be achieved. 

OS 43] [R 14] [P 32] Using a three-liquid layer (water/oil/water) flow instead of a two-liquid layer flow at constant channel dimensions decreases the liquid lamellae width and doubles the absolute value of the organic/aqueous interface. As a consequence, mass transport is facilitated compared with the two-flow configuration. Hence it was found that a much higher yield was obtained for the three-liquid layer flow when performing experiments of both flow configurations imder the same experimental conditions (210 s, 0.2 pi min room temperature, 300 W, > 300 nm... 

Figure 16 Schematic layout of microchip designs for (a) PCRD1 and (b) PCRD2 dimensions in mm. Letters are referred to in the text and identify the solution introduction reservoirs and points where potentials were applied. Indicated channels dimensions are for 10-pm-deep devices, and are not repeated in (b) except where differing from those in (a). (From Ref. 107, with permission.)...

The axial pressure and temperature distributions for the molten resin in the melt-conveying channel are calculated using the control volume method outlined in Section 7.7.5. For this method, the change in pressure and temperature are calculated using the local channel dimensions, HJ z) and FK (z), and the mass flow rate in the channel using Eq. 7.54 for flow and the methods in Section 7.7.5.1 for energy dissipation and temperature. The amount of mass added to the melt chan-... 

Table 11.4 Screw Channel Dimensions for an 88.9 mm Diameter, 33 L/D Barrier Screw for Running an LDPE Resin...

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