Hydrodynamics viscosity

I I I I I (j) = 0.45, N = 27 Total Viscosity n,-A Hydrodynamic Viscosity ° Brownian Viscosity yy Figure 6.8 Stokesian dynamics simulation results for the steady shear viscosity at 0 = 0.45 also shown are, the separate contributions of the Brownian and hydrodynamic stresses. (From... 

In these equations, v is the hydrodynamic viscosity of the solution, w the angular rotation rate. The Prandtl number is usually of the order of 1000 - that is, the diffusion layer at a rde is only about 1/5 the thickness of the hydrodynamic layer. An excellent work on the significance of Pr in electrochemistry is that of Vielstich (1953). 

For rod-shaped molecules, pi = 1, for spheres, pi = (1/3), whereas for flexible chtdns, pi = (1/2). The radius of gyration is proportional to the hydrodynamic viscosity based radius ri, determined from the intrinsic viscosity of the macrosolute via the hydrodynamic volume V), (Ladisch, 2001, pp. 557-561) ... 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

Other SFA studies complicate the picture. Chan and Horn [107] and Horn and Israelachvili [108] could explain anomalous viscosities in thin layers if the first layer or two of molecules were immobile and the remaining intervening liquid were of normal viscosity. Other inteipretations are possible and the hydrodynamics not clear, since as Granick points out [109] the measurements average over a wide range of surface separations, thus confusing the definition of a layer thickness. McKenna and co-workers [110] point out that compliance effects can introduce serious corrections in constrained geometry systems. 

TWo limiting conditions exist where lubrication is used. In the first case, the oil film is thick enough so that the surface regions are essentially independent of each other, and the coefficient of friction depends on the hydrodynamic properties, especially the viscosity, of the oil. Amontons law is not involved in this situation, nor is the specific nature of the solid surfaces. 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

A hydrodynamic injection is made by applying a pressure difference of 2.5 X 10 Pa (approximately 0.02 atm) for 2 s to a 75-cm long capillary tube with an internal diameter of 50 Jtm. Assuming that the buffer solution s viscosity is 10 kg m s what volume of sample is injected ... 

An alternative point of view assumes that each repeat unit of the polymer chain offers hydrodynamic resistance to the flow such that f-the friction factor per repeat unit-is applicable to each of the n units. This situation is called the free-draining coil. The free-draining coil is the model upon which the Debye viscosity equation is based in Chap. 2. Accordingly, we use Eq. (2.53) to give the contribution of a single polymer chain to the rate of energy dissipation ... 

The intrinsic viscosity of poly(7-benzyl-L-glutamate) (Mq = 219) shows such a strong molecular weight dependence in dimethyl formamide that the polymer was suspected to exist as a helix which approximates a prolate ellipsoid of revolution in its hydrodynamic behaviorf ... 

When normal hydrodynamic and squeeze-film action gives inadequate load support, the fluid may be pressurized externally before being introduced into the bearing film in the manner of Figure 2b and c. Such a procedure is common for starting and slow speeds with heavy machines, or with low viscosity fluids. 

Wide range of viscosity ia commercial petroleum oils is illustrated by the representative types listed ia Table 3. Despite this range, the largest proportion of oils are ia the 25-75 mm /s at 40°C viscosity range. Oils ia this range combine generally adequate hydrodynamic load capacity with low power loss, low volatiUty, and satisfactory low temperature properties. 

Liquid metal selection is usually limited to the lower melting point metals in Table 15. Figure 17 shows that Hquid metal viscosity generally is similar to water at room temperature and approaches the viscosities of gases at high temperature. Hydrodynamic load capacity with both Hquid metals and water in a bearing is about 1/10 of that with oil, as indicated in Table 2. 

Because of the low viscosities of cryogenic Hquids, rolling element bearings seem better suited than hydrodynamic bearings for turbo pumps. AISI 440C stainless balls and rings generally are preferred for their corrosion resistance over the more commonly used AISI 52100 steel. 

A general flow map of different hydrodynamic conditions (Fig. 23) consists of regions of flooding, dispersion, and recirculation on a plot of N vs for a Rushton turbine. For a low viscosity aqueous/air system, the gas flow numbers for the three conditions are given hy FI = 30Fr[D/TY for flooding, = 0.2Fr° (F/r)° for complete dispersion, and =13FF D/TY for recirculation. 

The presence of inorganic salts in solutions of poly(ethylene oxide) also can reduce the hydrodynamic volume of the polymer, with attendant reduction in intrinsic viscosity this effect is shown in Figure 7. 

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