Flow nonuniform viscous

The effects of flow nonuniformities, in particular, can be severe in gas systems when the ratio of bed-to-particle diameters is small in liquid systems when viscous fingering occurs as a result of large viscosity gradients in the adsorption bed when very small particles (<50 Im) are used, such as in high performance liqmd chromatography systems and in large-diameter beds. A lower bound of the axial... 

The effects of flow nonuniformities, in particular, can be severe in gas systems when the ratio of bed-to-particle diameters is small in liquid systems when viscous fingering occurs as a result of large... 

VELOCITY PROFILE ANALYTIC SOLUTION FOR NONUNIFORM VISCOUS FLOW (A Method Derived by R. L. Turner and E. D. Wohlsen)... 

Such expressions can be extended to permit the evaluation of the distribution of concentration throughout laminar flows. Variations in concentration at constant temperature often result in significant variation in viscosity as a function of position in the stream. Thus it is necessary to solve the basic expressions for viscous flow (LI) and to determine the velocity as a function of the spatial coordinates of the system. In the case of small variation in concentration throughout the system it is often convenient and satisfactory to neglect the effect of material transport upon the molecular properties of the phase. Under these circumstances the analysis of boundary layer as reviewed by Schlichting (S4) can be used to evaluate the velocity as a function of position in nonuniform boundary flows. Such analyses permit the determination of material transport from spheres, cylinders, and other objects where the local flow is nonuniform. In such situations it is not practical at the present state of knowledge to take into account the influence of variation in the level of turbulence in the main stream. 

Atoms are transported by viscous flow by differences in the capillary pressure at nonuniformly curved surfaces. 

Example 9.3 Nonisothermal Drag Flow of a Power Law Model Fluid Insight into the effect of nonisothermal conditions, on the velocity profile and drag flow rate, can he obtained by analyzing a relatively simple case of parallel-plate nonisothermal drag flow with the two plates at different temperatures. The nonisothermicity originates from viscous dissipation and nonuniform plate temperatures. In this example we focus on the latter. 

One of the assumptions made in solving the flow in the fully developed region of the capillary was that of constant fluid temperature throughout the flow region. This is not a valid assumption for the flow of very viscous fluids at high rates of shear in which a nonuniform temperature field is created. As we have already mentioned in connection with the thermal-energy balance (Section 2.2), the rate of viscous heating per unit volume ev is... 

The influence of the polymer concentration is well known in SEC. Theoretically, SEC assumes independence of the elution volume with regard to the concentration of the molecular species. Practically, it is well known that a high concentration of the sample solution leads to distortion of the polymer peak and dependence of the elution volume on the concentration of the sample. The concentration effect [3] depends on the difference in molecular mobility between the pure solvent and the viscous polymeric solution. This difference causes nonuniform flow, often called viscous fingering, and, as a result, multiple peaks. In addition, it is... 

On the map of mechanical states in region I, elastic and anelastic (shaded areas) deformations take place. In the region II, the inhomogeneous plastic deformation with the formation of shear bands takes place. The horizontal broken line corresponds to the theoretical yield stress of LRC. In the region III, the homogeneous diffusional-viscous flow takes place and, in the region IV, the mixed viscous flow is realized. Curves 1,2, 3 show the temperature dependence of the stress at different constant strain rates. The continuations of these curves in regions IV and II correspond to the mixed nonuniform plastic deformation. 

By neglecting inertia terms. Orchard (Ol) analyzed recently the two-dimensional flow of thin layers of viscous liquids and gels and obtained an expression for the rate of decay of surface irregularities. In Orchard s work, surface-tension forces varied from point to point as a result of the nonuniformity of the surface curvature. 

When the viscous heat generation is important, high melt temperature regions form in the center of the channel. This is due to the thermal convection caused by the recirculating flow pattern in the screw channel. Thus, the melt temperature nonuniformities that form are inherent to the flow in single screw extruders. 

The smallest viscosity ratio simulated, (pa/Pb = 0-1). demonstrates that the smaller viscosity material is starting to flow around the higher viscosity material producing a nonuniform layer thickness-a phenomenon called viscous encapsulation. The effect of the flow rate ratio (Qa/Qb) on the interface between the two polymers is... 

Metrology plays a cmcial role in enabling any type of CMP process control, and can be implemented in different ways based on the measurement techniques used, its location in the process flow, and the type and amount of data generated. During the CMP cycle, pad characteristics such as the thickness, the Young s modulus, and viscous properties of the pad tend to be dynamic. Therefore measurement of these properties is very important towards understanding polishing nonuniformity and the maintenance of acceptable WIWNU and wafer-to-wafer nonuniformity. 

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