Planar flow pattern

Regions in a liquid crystal having a specific cellular periodic flow-pattern in the form of long rolls induced by the application of an electric field perpendicular to a nematic layer with an initial planar alignment of the director. 

Fig. 6.18 Comparison of general flow patterns for planar and axisymmetric, finite-gap, stagnation flow.

Flow patterns in planar multi-layered stream mixers... 

However, there exists a way to employ the rigorous equations of continuum mechanics even for the cases, in which real phase boundaries cannot be exactly localized. This way is associated with the idea of hydrodynamic analogy between complex and simpler flow phenomena. More precisely, some particular similarities are meant between complex flow patterns encountered in industrial separations and geometrically simpler flows like planar films, cylindrical jets, spherical drops, etc., as well as their combinations (Kenig, 1997). These similarities are used in the hydrodynamic analogy approach by which the complex hydrodynamics established in a real column is replaced with an appropriate combination of simpler flow patterns. Such a replacement occurs on the basis of experimental observations which are very important for the successful... 

In planar flow situations, the qualitative agreement between computed stress fields and experimental flow birefiingence patterns is to be underlined. Concerning the constitutive differential equations iised to model the polymers, the mPTT model provides a better quantitative agreement, especially along the flow axis, than the GOB model. The mPTT model is able to capture the differences in stress patterns which are observed between LLDPE and LDPE. We think that this difference is mainly due to a poorer description of the relaxation times of the polymers in the GOB model. 

Fluid flow within the melt has a crucial effect on crystal quality. If the crystal is stationary, the dominant convection pattern is upward flow of material at the crucible walls and radial flow inward at the surface (type I). Rapid rotation of crystal causes material to be thrown radially outward at the surface, and opposes the thermal convective flow (type III). These flow patterns are shown in Figure 3. In the intermediate regime, where the two flows are of comparable rates, a more complex surface pattern is observed, labeled type II. The crystal-liquid interface is convex toward the melt in type I flow and planar in type II, a condition that is used for the growth of large crystals of gadolinium gallium garnet ... 

Chiba K, Sakatani T, Nakamura K (1990) Anomalous flow patterns in viscoelastic entry flow through a planar contraction. J Non-Newtonian Fluid Mech 36 193-203... 

MCFCs typically have a planar cell geometry, with areas ranging from bench scale 0.01 m to full scale up to 1 m [10]. The cell form is normally square or rectangular [11], but recently circular cells have also been proposed [12]. The flow pattern is cross-flow in most cases, but according to Kim et al. [13] the counter-flow pattern is associated with lower irreversible losses due to ohmic resistance and anode and cathode activation. Other workers [14] have found by numerical simulation that the co-flow configuration has a higher net output power in some cases. 

However, planar geometrical configurations will be the main focus here, as they are commonly found in microfluidic devices due to their ease of fabrication. Rodd et al. [4] have summarized the nonlinear flow phenomena in nricrofluidic channels in the De—Re space (see Fig. 1). Care should be taken when relating various phenomena from axisymmetric to planar geometries at similar De-Re regimes. For example, the formation and changes of the vortical flow pattern can be quahtatively different as a result of the difference in total strains and strain-rate histories experienced by the fluid elements in the two geometries [4,12]. 

Nigen S, Walters K (2002) Viscoelastic contractions flows comparison of axisymmetry and planar configurations. J Non-Newtonian Fluid Mech 102 343-359 13. Chiba K, Sakatani T, Nakamura K (1990) Anomalous flow patterns in viscoelastic entry flow through a planar contraction. J Non-Newtonian Fluid Mechn 36 193-203 Townsend P, Walters K (1994) Expansion flows of non-Newtonian liquids. Chemical Eng Sci 49 749-763 Hawa T, Rusak Z (2001) The dynamics of a laminar flow in a symmetric channel with a sudden expansion. J Fluid Mech 436 283-320... 

Figure 5-36 shows the flow pattern in the vertical plane of a vessel equipped with a helical ribbon. A fully structured hexahedral mesh with approximately 100 000 cells was used. The structured 3D mesh was created by extruding and twisting a 2D planar mesh. The fluid is viscous and the impeller Reynolds number is approximately 10. The velocity vectors show that the impeller pumps down at the wall and up in the center. Contours of velocity magnitude on the tank bottom show that there are low velocities in the center and higher velocities near the outside wall. Small circulation loops form between the impeller blades and the vessel wall, as discussed in the general literature. These indicate the need for an even larger D/T or the use of wall scrapers if optimum heat transfer is to be obtained. 

Fig. 5.5 Numerically computed nitrogen distribution (left) and flow pattern (right) during directional solidification of a silicon melt with dimension of 58 x 55 X 14 cm for a concave, planar and convex interface obtained by applying different thermal boundary...

The three strain fields, planar elongation, uniaxial elongation, and simple shear, are compared next to determine the flow pattern most favorable in terms of power consumption. High power consumption is unfavorable because of its high cost and requirements for specific equipment. Integration of the mechanical energy equation (Section 2.3) over the volume of the mixer shows that the specific power consumption (power consumption per unit volume), Pv, is equal to the viscous dissipation. 

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