The Dynamic Viscosity

The real or in-phase component n] of the complex dynamic viscosity is related to the loss modulus by the equation n] = G /(ji (equation 32 of Chapter 1). It is mostly useful for viscoelastic liquids because at low frequencies it approaches the steady-flow viscosity tjq. It is plotted with logarithmic scales in Fig. 2-5. 

As is obvious from the above relation, in regions where G is flat, r] is inversely proportional to frequency whereas when G rises steeply, on the left side of the maximum, -q may flatten out, as seen particularly in the cross-linked rubber. Example VI. But it decreases monotonically with increasing frequency and falls by many orders of magnitude. 

Real part of the complex dynamic viscosity, plotted logarithmically for the eight systems identified as in Fig. 2-1. 

An alternative frequency-dependent viscosity, which could also be called the dynamic viscosity, is the absolute value t = (t) -1- - (G - - 

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In Mehrotra s method, the dynamic viscosity is expressed as a function of temperature according to the relation ... 

The dynamic viscosity, or coefficient of viscosity, 77 of a Newtonian fluid is defined as the force per unit area necessary to maintain a unit velocity gradient at right angles to the direction of flow between two parallel planes a unit distance apart. The SI unit is pascal-second or newton-second per meter squared [N s m ]. The c.g.s. unit of viscosity is the poise [P] 1 cP = 1 mN s m . The dynamic viscosity decreases with the temperature approximately according to the equation log rj = A + BIT. Values of A and B for a large number of liquids are given by Barrer, Trans. Faraday Soc. 39 48 (1943). 

Kinematic viscosity v is the ratio of the dynamic viscosity to the density of a fluid. The SI unit is meter squared per second [m s ]. The c.g.s. units are called stokes [cm -s l] poises = stokes X density. 

The dynamic viscosity is related to the loss component of the shear modulus through the result 77= G"/co As co 0, the dynamic viscosity approaches the zero shear viscosity of an ordinary Uquid, 77 -... 

A viscoelastic material also possesses a complex dynamic viscosity, rj = rj - - iv( and it can be shown that r = G jiuj-, rj = G juj and rj = G ju), where CO is the angular frequency. The parameter Tj is useful for many viscoelastic fluids in that a plot of its absolute value Tj vs angular frequency in radians/s is often numerically similar to a plot of shear viscosity Tj vs shear rate. This correspondence is known as the Cox-Merz empirical relationship. The parameter Tj is called the dynamic viscosity and is related to G the loss modulus the parameter Tj does not deal with viscosity, but is a measure of elasticity. 

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

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. 

The proportionality factor /i, is the dynamic viscosity of the fluid, its units being force X time/length and is expressed as N s rrr or Pa s. 

The kinematic viscosity v is the ratio of the dynamic viscosity /x and density p ... 

In old literature the cgs system is found, in which the dynamic viscosity is measured in centipoise = 0.1 poise = 0,001 dyne s cm - ... 

V is the kinematic viscosity 7 is the dynamic viscosity in the mass flow... 

A pump lifts water from a lake. At the pump suction entry a foot valve is fitted. Determine the maximum static delivery height the water can be raised without cavitation taking place. The saturation pressure of water is 1.23 kPa at 10 °C and the dynamic viscosity is 1.3 x 10" kg m s T The suction pipe water velocity is 2.0 m s , the internal pipe diameter is 100 mm, and the pipe roughness is 0.03 mm. The resistance of the foot valve is 4.5. 

H is the height of the plates in the heat exchanger (assuming the plates are in a vertical position, which is normal), and is the number of gaps between the plates, p. in Eq. (9.37) is the dynamic viscosity of the gas. 

The term g in Equation 2-56 is the dynamic viscosity of the fluid. The dynamic viscosity is the ratio of the shear stress to the shear rate. It has units of (force x time)/(area). The most common unit of viscosity is the centipoise (1 centipoise = 0.01 g/cm - s). Dynamic viscosity may be a function of temperature, pressure, and shear rate. 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

To describe laminar flow of a fluid, the unit shear stress x is some function of the dynamic viscosity l(lb/ft ), and the velocity difference dV(ft/sec) between adjacent laminae that are separated by the distance dy(ft). Develop a relationship for x in terms of the variables l, dV and dy. 

For non-Newtonian drilling fluids, the concept of an effective viscosity can be used to replace the dynamic viscosity in Equation 4-89. 

Pisarzhevski-Walden equation to measured values of the dynamic viscosity. However, use of this relation is only correct for solutions in the limit of zero concentration and no change in solution mechanism. 

The relationship of isoviscosity calculated by Eq (5) and a distance apart from the solid surface is shown in Fig. 7. For different kinds of solid materials with different surface energy, the isoviscosity becomes very large as the film thickness becomes thinner. It increases about several to more than ten times that of bulk fluid when it is close to the solid surface. In the thick film region, the isoviscosity remains a constant, which is approximately equal to the dynamic viscosity of bulk liquid. Therefore, the isoviscosity of lubricant smoothly... 

Here, is the average effective radius of pore, is surface tension between liquid and vapor, 0 is the contact angle, rj is the dynamic viscosity of the electrolyte, and h is the height elevation of the electrolyte within pore at time r. In the experiment, the amount of electrol he wetted within the anode electrode, m, expressed as h = m/pAP, was measured instead of the height, h. Integrated Eq. (l)for t becomes Eq. (2). 

In these expressions, ju is the dynamic viscosity, L the length of the channel segment, w and e their width and depth and a correction factor accounting for the non-circularity of the channels. Clearly, the above equations rely on the assumption of a hydrodynamicaUy developed flow. 

Kinematic viscosity is the ratio of dynamic viscosity and density, and can be obtained by dividing the dynamic viscosity of a fluid with its mass density, as shown by Equation 18.2 ... 

The dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane with respect to the other at a unit velocity when maintained at a unit distance apart by the fluid. The readers are referred to Equations 18.1 and 18.2 for the dynamic viscosity. 

The zero-shear viscosity and the dynamic viscosity (at low frequencies) diverge at high concentration, while they are constant at low concentration [99,100,102-105],... 

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