Shear flow, uniform

When droplets are initially not uniformly dispersed inside the flow cell, i.e. the emulsion is not homogeneous, the presence of a shear flow will induce mixing and the flow behavior of the system will be dependent on the spatial distribution of both phases. Therefore, in order to study the flow and mixing of an initially non-homogeneous emulsion it is necessary to obtain information on how both phases... 

Stroeve, P., and Varanasi, P. P., An experimental study of double emulsion drop breakup in uniform shear flow. J. Coll. Int. ScL 99,360-373 (1984). 

Varanasi, P. P., Ryan, M. E., and Stroeve, P., Experimental study on the breakup of model viscoelastic drops in uniform shear flow. I EC Research 33, 1858-1866 (1994). Verwey. E. J., and Overbeek, J. T. G., Theory of the Stability of Lyophobic Colloids. ... 

At present the development of more effective basic correlations of thermal and material transport in turbulent shear flow rests primarily upon an extension of the understanding of the mechanics of turbulence. Howarth and K rm n (Kl, K4) and Batchelor (B6) contributed materially to the knowledge of isotropic, homogeneous turbulence, but the prediction of the behavior in shear flow still must be based on experiment (L3) even for steady, uniform flow. The absence of a basic understanding of the growth and decay of turbulence (K5) prevents a microscopic analysis of thermal and material transport under nonuniform or unsteady conditions. 

Woods,M.E., Krieger,I.M. Rheological studies on dispersions of uniform colloidal spheres. I. Aqueous dispersions in steady shear flow. J. Colloid Sci. 34,91-99 (1970). 

For convenience, a mathematically simple arrangement is considered. It consists of a fluid layer of finite constant thickness, confined by two rigid parallel planes of infinite extension. Steady laminar shear flow is created in this layer by fixing one plane in space and moving the other one with constant speed in a direction parallel to both planes. In this way, a truly uniform and time independent shear rate q is created in the liquid. The magnitude of this shear rate is simply given by the ratio of the said speed to the mutual distance of the planes. Experimentally such an arrangement is approximated e.g. by the use of two coaxial cylinders. When the gap between the inner surfaces of these cylinders is made small compared with their radii, the above mentioned situation can be realized to a sufficient extent. 

The addition of water-soluble polymers such as polyethylene oxide (PEO) or polyvinyl alcohol (PVA) into the synthetic mixture of the C TMAX-HN03-TE0S-H20 system (n = 16 or 18 X = Br or Cl) under shear flow is found to promote uniformity and elongation of rope-like mesoporous silica. The millimeter-scaled mesoporous silica ropes are found to possess a three-level hierarchical structure. The addition of water-soluble polymer does not affect the physical properties of the silica ropes. Moreover, further hydrothermal treatment of the acid-made material under basic ammonia conditions effectively promotes reconstruction of the silica nanochannels while maintaining the rope-like morphology. As a result, a notable enhancement in both thermal and hydrothermal stability is found. 

Fiber motion — Jeffery orbits. The motion of ellipsoids in uniform, viscous shear flow of a Newtonian fluid was analyzed by Jeffery [32, 33] in 1922. For a prolate spheroid of aspect ratio a (defined as the ratio between the major axis and the minor axis) in simple shear flow, u°° = (zj), the angular motion of the spheroid is described... 

The Distribution of Interfacial Area Elements at High Strains in Simple Shear Flow Consider randomly distributed and equal-sized interfacial area elements placed in a Theologically uniform medium in simple shear flow. After a given strain, the interfacial area elements vary in size that is, a distribution of interfacial area elements evolves because of the flow, (a) Show that the variance of the distribution is... 

Erenburg VB, Pokrovskii VN (1981) Non-uniform shear flow of linear polymers. Inzh Fiz Zh 41(3) 449-456 (in Russian)... 

Many of the comments in the previous chapter about the selection of grade, additives and mixing before moulding apply equally in preparation for extrusion. It is important of course that the material should be appropriate for the purpose, uniform, dry, and free from contamination. It should be tested for flow and while many tests have been devised for this it is convenient to classify them as either for low or high rates of shear. The main terms used in such testing ( viscosity , shear rate , shear strain , etc.) are defined in words and expressed as formulae in ISO 472, and it is not necessary to repeat them here. Viscosity may be regarded as the resistance to flow or the internal friction in a polymer melt and often will be measured by means of a capillary rheometer, in which shear flow occurs with flow of this type—one of the most important with polymer melts—when shearing force is applied one layer of melt flows over another in a sense that could be described as the relationship between two variables—shear rate and shear stress.1 In the capillary rheometer the relationship between the measurements is true only if certain assumptions are made, the most important of which are ... 

In retrospect, the effect of the change of variables has been to deform the velocity field from axisymmetric stagnation flow over a sphere to linear shear flow along a flat plate. The main advantage of the new coordinates is that the coefficients of the derivatives in (32) are independent of X, and consequently Duhamel s theorem can be applied. Thus, the following procedure can be used (1) solve equation (32) subject to a uniform surface concentration (2) extend this solution to one valid for an arbitrary, nonuniform surface concentration by applying Duhamel s theorem (3) select the surface concentration which satisfies (33a). 

The long-range, purely hydrodynamic interaction between two suspended spheres in a shear flow was first calculated by Guth and Simha (1936), yielding a value of kx = 14.1 via a reflection method. Saito (1950,1952) proposed two alternative modifications, obtaining kt = 12.6 and 2.5, respectively the latter value is obtained upon supposing a spatially uniform distribution of particles. 

While the experiments under quiescent conditions show the effect of diffusion control, the study by Agarwal and Khakhar [32] of polymerization of PPDT in a coaxial cylinder reactor with a uniform shear flow, most clearly illustrate the role of shearing and orientation on the polymerization. Figure 2 shows the... 

Under uniform shear flow, Smoluchowski (06, S27) derived... 

Consider the shear flow geometry in Fig. 1, with three different anchoring conditions on the top and bottom planes. The initial condition is a uniform n field consistent with the wall anchoring. Cases (a) and (b) are similar in which n lies initially in the y-z plane. In both cases, the LE theory predicts an in-plane tumbling instability and an out-of-plane twist instability. ... 

The tests were also performed on computer-generated data in which additional uniform or non-uniform motion was added, to study how far the CG algorithm could be pushed beyond its original design parameters. For uniform motion, CG tracking was as successful as in the quiescent case for small drifts but failed for drifts of the order of half the particle-particle separation. For non-uniform (linear shear) flows with small strains between frames the identification worked correctly, but large non-uniform displacements caused major tracking errors. 

Rigid spheres sometimes experience a lift force perpendicular to the direction of the flow or motion. For many years it was believed that only two mechanisms could cause such a lift. The first one described is the so-called Magnus force which is caused by forced rotation of a sphere in a uniform flow field. This force may also be caused by forced rotation of a sphere in a quiescent fluid. The second mechanism is the Saffman lift. This causes a particle in a shear flow to move across the flow field. This force is not caused by forced rotation of the particle, as particles that are not forced to rotate also experience this lift (i.e., these particles may also rotate, but then by an angular velocity induced by the flow field itself). 

Particles in a uniform, laminar shear flow collide because of their relative motion (Fig. 7.4a). The streamlines are assumed to be straight, and the panicle motion is assumed to be... 

Reeks, M. W. 2005b On probability density function equations for particle dispersion in a uniform shear flow. Journal of Fluid Mechanics 522, 263-302. 

Figure 7-2. Illustration of the decomposition of the problem of a freely rotating sphere in a simple shear flow as the sum of three simpler problems (a) a sphere rotating in a fluid that is stationary at infinity, (b) a sphere held stationary in a uniform flow, and (c) a nonrotating sphere in a simple shear flow that is zero at the center of the sphere. The angular velocity Cl in (a) is the same as the angular velocity of the sphere in the original problem. The translation velocity in (b) is equal to the undisturbed fluid velocity evaluated at the position of the center of the sphere. The shear rate in (c) is equal to the shear rate in the original problem.

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