Mechanical Displacement Flow

We now analyze mechanical-displacement flow in a straight channel of constant cross-sectional area, as shown in Fig. 4.11 (with the upper plate at rest). A column of compacted solids of length L is compressed between two rams. The one on the left exerts a force Fo on the solids and it is opposed by a smaller force FL on the right. Thus, friction on the channel walls also opposes the applied resultant force. 

A differential force balance with the following assumptions (a) the compacted solids are either at a steady motion or in a state of incipient slip on the wall (friction at the wall is fully mobilized) (b) axial and radial stresses vary only with the axial distance x (c) the ratio of the radial-to-axial stresses is a constant K, independent of location (d) the coefficient of friction is constant and independent of compaction and (e) temperature effects in the case of steady motion are negligible, results in 

in dealing with steady motion of particulate solids, it is evident that the axial stress or pressure drops exponentially, whereas in the case of liquid flow, it drops linearly with distance. This difference stems, of course, from the fact that frictional forces on the wall are proportional to the absolute local value of normal stress or pressure. In liquids, only the pressure gradient and not the absolute value of the pressure affects the flow. Furthermore, Eq. 4.7.2 indicates that the pushing force increases exponentially with the coefficient of friction and with the geometric, dimensionless group CL/A, which for a tubular conduit becomes 4 L/D. 

Experimental support on the validity of Eq. 4.7-2 was presented by Spencer et al. (32), who also proposed a theoretical derivation based on considering a discrete number of contact points between solids and containing walls. They assumed isotropic stress distribution (K = 1) and obtained an expression identical to Eq. 4.7-2 

Example 4.1 Force Requirements of Ram Injection Molding Machines We consider a 

---

Steady Mechanical Displacement Flow Aided by Drag, 159... 

STEADY MECHANICAL DISPLACEMENT FLOW AIDED BY DRAG 159... 

Dry Test Meter Measures the total integrated volume of air sampled over a given time. The volume flow is measured by mechanical displacement of an internal bellows by the air flow. The displacement is recorded on a mechanical counter via a series of levers (accuracy 2-4%). 

These tests show that CC -foam is not equally effective in all porous media, and that the relative reduction of mobility caused by foam is much greater in the higher permeability rock. It seems that in more permeable sections of a heterogeneous rock, C02-foam acts like a more viscous liquid than it does in the less permeable sections. Also, we presume that the reduction of relative mobility is caused by an increased population of lamellae in the porous medium. The exact mechanism of the foam flow cannot be discussed further at this point due to the limitation of the current experimental set-up. Although the quantitative exploration of this effect cannot be considered complete on the basis of these tests alone, they are sufficient to raise two important, practical points. One is the hope that by this mechanism, displacement in heterogeneous rocks can be rendered even more uniform than could be expected by the decrease in mobility ratio alone. The second point is that because the effect is very non-linear, the magnitude of the ratio of relative mobility in different rocks cannot be expected to remain the same at all conditions. Further experiments of this type are therefore especially important in order to define the numerical bounds of the effect. 

The primary means of transfer of energy to the fluid that causes flow are gravity, displacement, centrifugal force, electromagnetic force, transfer of momentum, mechanical impulse, and a combination of these energy-transfer mechanisms. Displacement and centrifugal force are the most common energy-transfer mechanisms in use. 

First we want to gain some insight into the nature and mechanism of positive displacement flow. In the next two examples we examine the plunger-cylinder... 

Fig. 6.37 Schematic representation of four geometrical configurations utilizing external mechanical pressurization giving rise to positive displacement flow, (a) Axially moving plunger in a cylinder, (b) Squeezing disks, (c) Intermeshing gear pump, (d) Counterrotating intermeshing twin screws.

To inject the polymer melt into the mold, the melt must be pressurized. This is achieved by the forward thrust of the screw (a) or the piston (b), both of which act as rams. Hence we have static mechanical pressurization, as discussed in Section 6.7, which results in positive displacement flow. 

We use the word flow to describe all bulk fluid displacements, including direct mechanical displacement and the flow process itself. These are both nonselective forms of displacement initially described in Chapter 1. The treatment of flow in this section expands on a published approach interpreting the role of flow in separation processes [1]. 

When comparing the gas-drive processes GDS and GDW the presence of surfactant in the displaced liquid has a great effect on the displacement mechanisms and flow patterns. Figure 9 shows schematically the final extent of sweep for gas-drive of brine without surfactant (Frame a) and with surfactant (Frame b). In each case the gas appears to have preferentially flowed through a few large channels that zig-zag across the raicromodel however, in... 

Linear actuated devices control liquid movement by mechanical displacement (e.g. a plunger). Liquid control is mostly limited to a one-dimensional liquid flow (no branches or alternative paths) with the corresponding possibilities and limitations to assay implementation. The degree of integration is very high, with liquid calibrants and reaction buffers pre-stored in pouches. 

Peristaltic pumps are mechanical displacement pumps that induce flow in a fluid-fllled, flexible-walled conduit through peristalsis - transport due to traveling contraction waves. While macroscale peristaltic pumps appear in a variety of configurations, micropumps based on this principle almost exclusively use the sequenced contraction and expansion of a small number of discrete actuators - typically three - placed along the fluid channel. 

The examples described above of the successful use of SILP catalysis were aU gas-phase reactions under conditions where no condensation of substrates or products in the gas stream was possible. (Note that capillary condensation inside the porous network of a SILP catalyst might nonetheless occur under certain circumstances.) This is an important prerequisite for effective SILP catalysis as a continuous flow of liquid could remove the thin film of IL from the support (either by dissolution or mechanical displacement), rendering the catalyst inactive in most cases. In case of propene and 1-butene hydroformylation, the formation of the so-caUed heavies 18 and 19 via aldol condensation of the respective aldehyde products (see Scheme 15.3) was reported to reduce the catalyst activity over time, whereas the selectivity remained unchanged [15]. 

Coning and Quartering. A method of obtaining a random sample of a powder by pouring it out to form a cone, which is then divided into four by two diametral cuts . One quarter is selected, and the process may be repeated. Consistency. The flow or mechanical displacement properties of cements, mortars and refractory castables. See... 

---