Slow flow

The (CEF) model (see Chapter 1) provides a simple means for obtaining useful results for steady-state viscometric flow of polymeric fluids (Tanner, 1985). In this approach the extra stress in the equation of motion is replaced by explicit relationships in terms of rate of strain components. For example, assuming a zero second normal stress difference for veiy slow flow regimes such relationships arc written as (Mitsoulis et at., 1985)... 

The windows in some medieval cathedrals show greater thickness at the bottom than at the top, owing to the slow flow of the glass under the influence of gravity. 

For non-Newtonian fluids in slow flow, friclion loss across a square-woven or fuU-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to the average minimal opening between achacent wires, and length twice the diameter, without entrance effects (Carley and Smith, Polym. Eng. Set., 18, 408-415 [1978]). For screen stacks, the losses of individual screens should be summed. 

Process Flow The schematic in Fig. 22-56 may imply that the feed rates to the concentrate and diluate compartments are equal. If they are, and the diluate is essentially desalted, the concentrate would leave the process with twice the salt concentration of the feed. A higher ratio is usually desired, so the flow rates of feed for concentrate and feed for diluate can be independently controlled. Since sharply differing flow rates lead to pressure imbalances within the stack, the usual procedure is to recirculate the brine stream using a feed-and-bleed technique This is usually true for ED reversal plants. Some nonreversal plants use slow flow on the brine side avoiding the recirculating pumps.. Diluate production rates are often 10X brine-production rates. 

To apply these data and equations to the problem of ground resistance, the maximum anticipated current must first be estimated. For practical industrial situations, Iq varies in the range 0.01-100/rA. The upper value represents extreme cases such as microfiltration and the lower value to slow flow in pipe. Typical charging currents for tank tmck loading are of the order 1 /rA (5-3.1.1). As an example, consider a system such as a tank with a capacitance less than 1000 pF. First, consider the minimum ignition voltages in Table A-4-1.3b. From Eq. (2), f L = In the case of hydrogen the mini-... 

Solvent conversion of columns designed for aqueous size exclusion chromatography is rarely a problem. However, it should always be carried out at slow flow rates. For Ultrahydrogel columns, the recommended flow rate for a solvent conversion is below 0.3 ml/min. One should typically use 0.1 ml/min for most solvent conversion procedures. 

The sodium borohydride solution is added dropwise to the stirred boron trifluoride etherate-diglyme solution resulting in the formation of diborane. The gas is swept into the olefin-TH F solution (held at 20°) by maintaining a slow flow of dry nitrogen through the generator. 

Laminar Versus Turbulent Flames. Premixed and diffusion flames can be either laminar or turbulent gaseous flames. Laminar flames are those in which the gas flow is well behaved in the sense that the flow is unchanging in time at a given point (steady) and smooth without sudden disturbances. Laminar flow is often associated with slow flow from small diameter tubular burners. Turbulent flames are associated with highly time dependent flow patterns, often random, and are often associated with high velocity flows from large diameter tubular burners. Either type of flow—laminar or turbulent—can occur with both premixed and diffusion flames. 

Fig. 5 Decrease of surface water and the effects on the longitudinal distribution of riverine habitats. During high flow (a) surface habitats, i.e. riffle (fast flowing sections) and pools (slow flowing sections), are available. Drying first affects the surface waters (b), causing fragmentation and the formation of remaining pools (c). During this phase the hyporheic compartment is also restricted to the pool habitats. Finally, both the superficial and hyporheic compartments dry completely up, and potential refuge for the aquatic biota disappear...

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

Figure 132. Two-dimensional net of knots to simulate a heat storage including knots for the heat transfer fluid and also the environment. For slow flow (left) and fast flow (right) of the heat transfer fluid, the phase front will move differently...

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

Fig. 27.2. Concentration of dissolved silica and the quartz dissolution rate along a quartz sand aquifer being recharged at left by rainwater, for the scenario considered in Figure 27.1. Results were calculated assuming a range of flow velocities rapid flow corresponds to a Damkohler number Da less than one, whereas Da is greater than one for slow flow.

Since laminar flow itself occurs at low values of Re( = Dupl/x), the most likely situations are those characterized by low velocity (u) or high viscosity (p,), such as those involving the slow flow of polymers in extrusion reactors, or of blood in certain organs in animals. Even if not a close approximation in some cases, the predictable performance of an LFR may serve as a limiting model for actual performance. 

For laminar conditions of slow flow, as in candle flames, the heat transfer between a fluid and a surface is predominately conductive. In general, conduction always prevails, but in the unsteadiness of turbulent flow, the time-averaged conductive heat flux between a fluid and a stationary surface is called convection. Convection depends on the flow field that is responsible for the fluid temperature gradient near the surface. This dependence is contained in the convection heat transfer coefficient hc defined by... 

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