The Viscous Fluid

During the flow of a real Newtonian fluid, a certain quantity of the mechanical energy is converted or dissipated into heat or acoustic energy. The same is tme when a flow around a solid resistance (tubes, spheres, packing elements) takes place. Consider a plate with the area A which is moving with the velocity w on the surface of a fluid, see Fig. 3.1-2. The force F based on the area A or the shear stress T is proportional to the shear rate y = Aw/dy and the viscosity 77  

In the case of non-Newtonian liquids according to 77 = /(y) the shear stress is usually expressed by the relationship r = k- y) with k = rj and w = 1 valid for the special case of a Newtonian liquid. The symbol k is the eonsistency and 77 the fluidity (77 1 pseudoplastic and n dilatant). Such fluids are not discussed here. The fluid property viscosity quantifies the inner friction within a fluid or the friction between molecules and is zero for ideal fluids. Increasing temperatures lead to an increase of viscosity in gases but to a reduction of this property in liquids. 

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Figure 16 (145). For an elastic material (Fig. 16a), the resulting strain is instantaneous and constant until the stress is removed, at which time the material recovers and the strain immediately drops back to 2ero. In the case of the viscous fluid (Fig. 16b), the strain increases linearly with time. When the load is removed, the strain does not recover but remains constant. Deformation is permanent. The response of the viscoelastic material (Fig. 16c) draws from both kinds of behavior. An initial instantaneous (elastic) strain is followed by a time-dependent strain. When the stress is removed, the initial strain recovery is elastic, but full recovery is delayed to longer times by the viscous component.

When a load is applied to the system, shown diagrammatically, the spring will deform to a certain degree. The dashpot will first remain stationary under the applied load, but if the same load continues to be applied, the viscous fluid in the dashpot will slowly leak past the piston, causing the dashpot to move. Its movement corresponds to the strain or deformation of the plastic material. 

When a viscous fluid flows over a surface it is retarded and the overall flowrate is therefore reduced. A non-viscous fluid, however, would not be retarded and therefore a boundary layer would not form. The displacement thickness 8 is defined as the distance the surface would have to be moved in the 7-direction in order to obtain the same rate of flow with this non-viscous fluid as would be obtained for the viscous fluid with the surface retained at x = 0. 

How does the velocity v vary with the distance x from the electrode The velocity of the viscous fluid depends on x, as shown in Fig. 6.136. At x = 0, i.e., at the solid surface, the velocity is zero because the solid exerts forces on the fluid particles and does not allow them to slip past. This is equivalent to considering that the charges on the IHP and OHP are fixed and immobile. As one goes away from the electrode and from the OHP, the fluid velocity increases (assumed linear increase) and reaches a constant value. 

A good experimental method has yet to be devised to measure the temperature of highly viscous fluids flowing at high flow rates. Thermocouple measurements (16-18) have not been successful because they disrupt the flow field and become heated by the viscous fluid flowing past their surface. 

Ans. (a) The viscous fluid will be directed in the shell side. The higher the viscosity, the higher will be the pressure drop (i.e., resistance to flow), and if it is directed in the tube side, the pressure drop will be still larger, (b) The corrosive fluid will be directed in the tube side, and if any tube becomes corroded, it can be replaced. 

Hydrogenation was performed as described in Step 3. After filtration the solvents were removed by rotary evaporator, the residue diluted with brine and acidified with HCl until Congo Red indicator turned blue. The aqueous layer was decanted off, the mixture diluted with brine, and extracted with 500 ml EtOAc. The viscous fluid was purified by vacuum distillation or by chromatography on silica gel using CH2CI2. The solvent was removed, triturated with CH2Cl2/pentane, 1.0 50, and air dried to obtain 64% product. H-NMR data supplied. 

Viscosities of Reservoir Fluids (fio, fi ). The viscosity of a fluid, which is a measure of its resistance to flow, is defimed as the force in dynes on unit area of either of two horizontal planes unit distance apart, one of which is fixed while the other moves with unit velocity, the space between the planes being filled with the viscous fluid. 

Taylor, T.D., and Ndefo, D.E. (1971) Performance of the viscous fluid flow in the duct by means of a splintering method. In Proc. 2nd Int. Conference on numerical methods in fluid dynamics, Sept. 15-19, 1970, California, Berkeley. Berlin N.Y. Springer-Verlag. 

VISCOUS FLUIDS If mechanical cleaning is not required, higher heat transfer rates may be obtained by placing the viscous fluid on the shell side. Due to the flow pattern across the tube bank, turbulent flow may be maintained on the shell side at mass velocities which would yield laminar flow on the tube side. 

We seek the solution of the problem in the form of asymptotic expansions with respect to the small parameter e. The leading term of the expansion outside the drop is determined by the solution of the problem about the flow past a solid sphere. The leading term inside the drop corresponds to the viscous fluid... 

Flack and co-workers developed a complex model that included the effects of evaporation on the rheological properties of the viscous fluid. Their work established the idea that only fluid viscosity, angular speed, and evaporative effects are important in determining the final film thickness. Dispense volume, dispense rate, and other factors seem not to be particularly critical in determining the final film thickness as long as the wafer is spun for a sufficiently long time. Yet, in spite of evaporative effects, the final thickness /if of the fluid can be fairly well predicted with an inverse power law relationship [Eq. (11.13)], where C is a constant depending on the viscosity and contains the effects of viscous forces. 

In case of an incompressible fluid, the last term in (5.32) is equal to zero. Note also that for the viscous fluid O > 0. 

For dissolving polymer in solvent, the major problem is the small clumps of polymer formed in the viscous fluid. These clumps are difficult to break up. We need sufficient shear combined with axial flow in order to break the polymer quickly and immediately spread the polymer into the liquid for subsequent dissolution. Leave a small gap between the baffle and the tank wall in order to avoid the dead corner of undissolved polymer. If multiple impellers are used, then to save on power consumption, the bottom impeller might supply axial flow plus shear (as an open turbine) with the impeller above supplying axial flow. The Power number for the open turbine might be, for example, 1.2, whereas for axial flow the Power number value might be about 0.3. 

Zeta potential is an electric potential on this surface that is usually assumed as an electrical boundary condition at the walls of the microchannels. The interaction of an externally applied electric field and the ions of the EDL causes the net ion movement toward the oppositely charged electrode. It drags the viscous fluid and generates the bulk flow field in the channel, which is called the electrokinetic or the electroosmotic flow. 

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