Viscous dynamic viscosity

Other parameters that may be defined in dynamic shear rheology are the viscous dynamic viscosity, rj = G"/o, and the solid dynamic viscosity, tj" = G Ico. 

It IS the dynamic viscosity of the gas/fluid that determines its ability for free flow. Very viscous fluids require a large energy input to overcome the fric tional forces. 

Different types of liquid crystals exhibit different rheological properties [16,17]. With an increase in organization of the microstructure of the liquid crystal its consistency increases and the flow behavior becomes more viscous. The coefficient of dynamic viscosity r, although a criterion for the viscosity of ideal viscous flow behavior (Newtonian systems), is high for cubic and hexagonal liquid crystals but fairly low for lamellar ones. However, the flow characteristics are not Newtonian but plastic or pseudoplastic, respectively. 

A comparison with cross-linker 4a proves the underlying dynamics are controlled by metal-ligand dissociation. Ligand exchange kinetics for 4a are substantially faster than for 4b but the association thermodynamics are very similar, and the effect of those kinetics is dramatic. At 5% cross-linker, the dynamic viscosity of lOOmgmL 4a-PVP is only 6.7 Pa s, a factor of 80 less than that of the isostmctural network 4b PVP. Although the association constants are not identical, the effect of the thermodynamics would be to increase the viscosity of 4a PVP relative to 4b PVP, the opposite direction of that observed. The kinetics dominate even the extent of cross-linking 5% 4a PVP is less viscous by a factor of 5 than is 2% 4b PVP. 

The dissipation function, also called viscous dissipation, represents the irreversible conversion of kinetic energy into thermal energy. Since the dynamic viscosity p, is positive and all the terms are squared, the first two terms of the dissipation must be always positive. The bulk viscosity can be negative the Stokes hypothesis (Section 2.11) says that k = —2p/3. It turns out that the necessary condition for the dissipation function to be positive is that... 

From values of / and c, the diffusion coefficient (D) and dynamic viscosity (q) can be calculated (Examples 1.16-1.19). Estimation of the Knudsen (H d) and Reynold s numbers defines the nature of gas flow (viscous, molecular, intermediate) in vacuum systems (Examples 1.20-1.22). 

For viscoelastic fluids, the formalism of a viscous fluid and an elastic solid are mixed [31]. The equations for the effective viscosity, dynamic viscosity, and the creep compliance are given in Table 12.4 for a viscous fluid, an elastic solid, and a visco-elastic solid and fluid. For the viscoelastic fluid model the dynamic viscosity, >j (tu), and the elastic contribution, G (ti)), are plotted as a function of (w) in Figure 12.31. With one relaxation time, X, the breaks in the two curves occur at co. 

The principle rheological properties which reflect the polymer process dynamics are the loss modulus (C), storage modulus (G"), dynamic complex viscosity (n ), and tan delta parameters. In simplified form the loss modulus describes the viscous or fluid component of viscosity. That is, how easily the molecules can move past each other. The storage modulus describes the elastic or network entanglement structure of the polymers. It is, therefore, sensitive to cross linking, reaction formation and the elastomeric modifiers. The complex dynamic viscosity is the combined effect of both moduli discussed. It, therefore. 

Also based on the Goddard-Miller model. Bird et al. (1974) derived a relationship (Equation 3.115) between the apparent viscosity r]a and the dynamic viscosity t] = G"/o), where G" is the viscous modulus ... 

Viscous dissipation. The mixing efficiency of a viscous fluid is related to the viscous dissipation d> since = t D = 2r] D D where 17 is the dynamic viscosity. Maps of viscous dissipation can, therefore, be used to qualitatively predict the differences in mixing efficiency between different regions of the mantle, or between different models of mantle convection (Figure 10). 

The growth of bubbles is controlled by the rates at which volatiles in the melt can diffuse towards the bubbles, and the opposing viscous forces. Near a bubble, volatiles are depleted such that melt viscosity increases dramatically, and diffusivities drop, making it harder for volatiles to diffuse through and grow the bubble. These opposing factors are described by the nondimensional Peclet number (Pe), which is the ratio of the characteristic timescales of volatile diffusion (T(1 = r lD, where r is the bubble radius and D the diffusion coefficient of the volatile in the melt) and of viscous relaxation (t = 17/AP where 17 is the melt dynamic viscosity and AP the oversaturation pressure, i.e., Pe = Dingwell... 

Note that dynamic viscosity has replaced the binder amount and bowl volume of the Leuenberger s relevance list, thus making it applicable to viscous binders and allowing long-range particle interactions responsible for friction. 

Notice that the equation was evaluated by considering a particulate which moves through a fluid being pushed by the force resulting from impacts of many molecules of the (viscous) medium. In the same time, it experiences hydrodynamic resistance (friction). The dynamical viscosity of gases rather weakly depends on p and... 

Through use of classical network theories of macromolecules, G has been shown to be proportional to crosslink density by G = nKT -i- Gen, where n is the nnmber density of crosslinkers, K is the Boltzmann s constant, T is the absolnte temperature, and Gen is the contribution to the modulus because of polymer chain entanglement (Knoll and Prud Homme, 1987). The loss modulus (G") gives information abont the viscous properties of the fluid. The stress response for a viscous Newtonian fluid would be 90 degrees out-of-phase with the displacement but in-phase with the shear rate. So, for an elastic material, all the information is in the storage modulus, G, and for a viscous material, aU the information is in the loss modulus, G". Refer to Eigure 6.2, the dynamic viscosities p and iT are defined as... 

Viscosity is the resistance presented by a liquid to external forces subjecting it to flow. Laminar flow only is considered in polysaccharide rheology - as the name implies, the velocity in laminar flow increases monotonically with distance away from the edge of the vessel, pipe, etc. (in turbulent flow the flow rate will have local maxima and minima) (Figure 4.26). Imagine two hypothetical plates parallel to the direction of flow and the sides of the container, separated vertically by a distance 5x. One plate will be moving faster than the plate below it and will experience a force F because of viscous forces. This force will be in proportional to the area of the plane, so we can define a sheer stress of FjA, where A is the area of the plate. The force will bring about a difference of velocity 8v between two adjacent plates separated by 8x and we can define a sheer strain rate, usually denoted y, as 8v/8x, in the limit dv/dx (with dimensions of Kinetic or dynamic viscosity, t, is defined by eqn. (4.10) and... 

The static and dynamic properties of DNA have been studied by the temperature-dependent Stokes shift of the intercalated dye acridine orange [192] and by molecular dynamic simulation [193]. A large part of the Stokes shift of the intercalated dye in DNA is found to be frozen out at low temperature, as in the solution. Thus, the interior of DNA is found to have the diffusive and viscous dynamic characteristics of a fluid rather than the purely vibrational characteristics of a crystal. The results suggest that the probe dye molecule senses the movement of DNA and at high viscosity the rate of DNA motion is limited by the rate of solvent motion. 

Kinematic viscosity Viscosity is a fluid s internal resistance to flow, or its thickness. Kinematic viscosity is a measure of the ratio of the viscous force to the inertial force of the fluid or v = p/p, where p is the dynamic viscosity (in centipoise [cP]), p is the density (in grams per cubic centimeter), and v is the kinematic viscosity (in centistokes [cSt]). 

The dynamic interaction between flow and drops and bubbles floating in the flow may deform or even destroy them. This phenomenon is important for chemical technological processes since it may change the interfacial area and the relative velocity of phases and cause transient effects. In this case, the viscous and inertial forces are perturbing actions, and the capillary forces are obstructing actions. The bubble shape depends on the Reynolds number Re = aeU,p/p and the Weber number We = aeU2p/cr, where p, and p are the dynamic viscosity and the density of the continuous phase, a is the surface tension coefficient, and ae is the radius of the sphere volume-equivalent to the bubble. 

This part of the chapter deals with the effects of viscosity on an electrolyte flowing in the electrochemical reactor in two dimensions. The boundary layers appear on the surface of bodies in viscous flow because the fluid seems to stick to the electrocatalyst s surface. As we have described above, right at the surface, the flow has zero speed, and this fluid transfers a linear momentum to the adjacent layers through the action of dynamic viscosity. Therefore, a thin fluid... 

In this lecture, a variety of results for convective heat transfer in microtubes and microchannels in the slip flow regime under different conditions have been presented. Both constant wall temperature and constant wall heat flux cases have been analyzed in microtubes, including the effects of rarefaction, axial conduction, and viscous dissipation. In rough microchannels the abovementioned effects have also been investigated for the constant wall temperature boundary condition. Then, temperature-variable dynamic viscosity and thermal conductivity of the fluid were considered, and the results were compared with constant property results for microchannels, with the effects of rarefaction and viscous dissipation. 

Drainage kinetics laws are usually dependent upon the interfacial viscous stresses, which exist in the film and at the film interfaces,16 and also of the dynamic viscosity of the liquid. 

As with other physical properties, viscosity is affected by temperature, with a lower temperature giving a higher viscosity. For most oils, the viscosity varies as the logarithm of the temperature, which is a very significant variation. Oils that flow readily at high temperature can become a slow moving, viscous mass at low temperature. In terms of oil spill cleanup, viscous oils do not spread rapidly, do not penetrate soils rapidly, and affect the ability of pumps and skimmers to handle the oil. The dynamic viscosity of oil (in mPa s) is conveniently measured by a viscometer using a variety of cup-and-spindle sensors at very strictly controlled temperatures. 

Newtonian fluids are characterised by pure linear viscous behaviour. When a load is applied they display a linear change in shear over time, and there is a linear relationship between shear rate and stress, i.e. dynamic viscosity is independent of shear rate. When the load is removed, the shear remains completely preserved. 

Fluid flow around a hair in an array depends on the relative importance of inertial and viscous forces, as represented by the Reynolds number (Re = ulp/p), where u is velocity, 1 is hair diameter, p is fluid density, and p is the dynamic viscosity of the fluid (viscosity is the resistance of the fluid to being sheared a fluid is sheared when neighboring layers of fluid move at different velocities). We humans are big (high 1), rapidly moving (large u) organisms who experience high Re turbulent flow dominated by inertia. In contrast, very small (low 1) structures such as aesthetascs operate at low Re, where fluid motion is smooth and laminar because viscous forces damp out disturbances to the flow. 

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