Hydrodynamic slowing down

For symmetrical polymer blends (as well as weakly asymmetrical ones) the problem of hydrodynamical slowing down of long wavelength concentration fluctuations can be elegantly avoided by carrying out the simulation in the semi-grand-canonical ensemble rather than the canonical ensemble only the total number of chains n = is fixed, while the ratio... 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

Chemical considerations lead to two effects that influence the stability of reactive extrusion - the gel effect and the ceiling temperature. Gel effects increase the conversion by an autocatalytic behavior. If the gel effect occurs completely in the screws it stabilizes the process, but if it occurs near or in the die it may have a destabilizing effect. The occurrence of a ceiling temperature slows down the reaction and so has a direct, negative influence on hydrodynamic stability. 

The hydrodynamic adhesion force that expresses the resistance occurring when microparticles latch onto deposition elements. It is caused by the liquid that must be extracted out of the space between two particles when both microparticles adhere. This force allows the slowing down of microparticles adhesion and offers a possibility for drowning it in the flowing suspension. 

Some progress has been made in two-dimensional hydrodynamic models of a thick disk evolving under the action of a globally defined alpha viscosity, representing the effects of torques in a marginally gravitationally unstable disk (Yorke and Bodenheimer, 1999), but in these models the evolution eventually slows down and leaves behind a fairly massive protostellar disk after 10 Myr. 

The assumptions employed for the solutions mentioned above are not complied with in real systems. In view of the limited amount of melt, the diffusion distances are not quasi-infinite and thus both the difference in concentrations and the effective Dare changed in terms of time in the direction of slowing down the dissolution process. Nor can the hydrodynamic conditions be defined precisely because of the uncontrollable convection due to escaping gases and density convection taking place in the melt. 

This is the final asymptotic result relating the hydrodynamic force to the motion of the sphere toward the infinite plane wall. We can see from (5-118) that if the sphere were prescribed to move with a constant velocity (i.e., b = constant), the hydrodynamic force would blow up as h 1. This implies that the external force applied to the sphere would also be required to go to infinity as b x to maintain such a motion. Of course, the application of an infinite force is not possible, and for any lesser force the sphere will slow down as it approaches the wall. In the present case, the most straightforward assumption is that the external force on the sphere is a constant F in the — ez direction, as indicated in Fig. 5-9. 

In thermally non-homogeneous supercritical fluids, very intense convective motion can occur [Ij. Moreovei thermal transport measurements report a very fast heat transport although the heat diffusivity is extremely small. In 1985, experiments were performed in a sounding rocket in which the bulk temperature followed the wall temperature with a very short time delay [11]. This implies that instead of a critical slowing down of heat transport, an adiabatic critical speeding up was observed, although this was not interpreted as such at that time. In 1990 the thermo-compressive nature of this phenomenon was explained in a pure thermodynamic approach in which the phenomenon has been called adiabatic effect [12]. Based on a semi-hydrodynamic method [13] and numerically solved Navier-Stokes equations for a Van der Waals fluid [14], the speeding effect is called the piston effecf. The piston effect can be observed in the very close vicinity of the critical point and has some remarkable properties [1, 15] ... 

The ions in the same direction as the EOF are moved faster, while the movement against the EOF is slowed down. Neutral species move at the same rate as EOF. The important feature of EOF is that fluid is electrically driven and there is no pressure drop across the overall capillary. This is in contrast to the hydrodynamic flow using pressure-driven methods such as HPLC, which is shown in Fig. 2. The advantage is the occurrence of a flat profile plug with the same velocity driven by EOF regardless of their cross-sectional position in the capillary. This can give rise to a narrow zone and higher separation efficiency for CE method. 

The shear-driven fluidic approach is based on a radical modification of the fluidic channel concept. This recently developed technique for the transport of fluids in ultrathin channels based on the SDF [2] relies on a very basic hydrodynamic effect the viscous drag. This effect is present in every fluid flow, be it a liquid or a gas flow. In pressure-driven flows, the viscous drag manifests itself in an undesirable manner, as the stationary column and particle surfaces tend to slow down the fluid flow. In SDF, the viscous drag effect is... 

However, the movement of a charged particle is more complicated because of interference by the surrounding counterions. The counterions tend to move in the opposite direction. They drag the liquid along and this slows down the movement of the particle. This effect, which is of hydrodynamic origin, is known as electrophoretic... 

For large-seale equipment the effect of the ceiling temperature can be estimated by comparing it with the adiabatic temperature rise [Eq. (13.1)]. Apart from the negative effect on conversion, the occurrence of a ceiling temperature slows down the reaction and therefore enhances hydrodynamic instability. 

Consider a fluid moving through a pipe in the laminar flow regime. The wall of the pipe contains an electrode, located at a certain distance from the entry (Figure 4.26). The flow rate at the wall is zero. In the vicinity of the walls, viscous forces slow down the fluid as soon as it enters the pipe. Thus a gradient in flow rate is established across a layer referred to as the hydrodynamic boundary layer. Its thickness increases with the distance from the inlet. The boundary layers of opposing walls eventually meet after a distance L, called the hydrodynamic entrance length. From this point onward, the flow profile is observed to be parabolic. For a tube, Lh has a value of about 70 times its diameter. 

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