Viscosity ratio, definition

In SSF or Couette flow, it is not possible to break a drop if the viscosity ratio is greater than about 3. The deformed drop shape is stabilized by internal circulation. It has been concluded that extension is more effective than shear at breaking drops. With respect to practical flows, it is important not to interpret this statement too literally since in practical applications, a single steady shear gradient rarely exists. Bear in mind that the physical definitions of shear and extension depend on the environment seen by the drop along its trajectory, while the mathematical definitions are related to the choice of coordinate system. 

The second investigation concerns the influence of the viscosity ratio p. In the study, we change the values of solvent and polymer viscosity but keep the total viscosity and other parameter unchanged. The Deborah number is this study is De = 717.05. From the definition of the viscosity ratio, we know the larger the ratio, for a fixed total viscosity, the smaller portion of polymers in the fluid. 

To simulate the viscoelastic flow, the Oldroyd-B model has been implemented in the VOF-code. Stabilization approaches, such as the Positive Definiteness Preserving Scheme and the Log-Conformation Representation approach have been adapted and implemented in the code to stabilize the simulations at high Weissenberg numbers. The collision of viscoelastic droplets behaves as an oscillation process. The amplitude of the oscillation increases and the oscillation frequency decreases when the Deborah number becomes larger. The phenomenon can be explained with the dilute solution theory with Hookean dumbbell models. An increase of the fluid relaxation time yields a decrease of the stiffness of the spring in the dumbbell and restrains the deformation of the droplets. In addition, with larger the viscosity ratio the collision process is more similar to the Newtonian one since the fluid has less portion of polymers. 

How are Gp and tp related to experimental quantities We have repeatedly used the ratio of 77 to G as a definition of r in this chapter. The experimental viscosity is related to the products of the individual Gp and Tp values as follows ... 

This leads to a definition of apparent viscosity as the ratio of shear stress to apparent shear rate... 

The science that deals with the deformation and flow of matter is called rheology. An important rheological concept is the shear force, sometimes called the shear stress, or the force that causes a layer of a fluid material to flow over a layer of stationary material. The rate at which a layer of a fluid material flows over a layer of stationary material is called the shear rate. A fluid flowing through a tube, for example, would be the fluid material, while the tube wall would be the stationary material. An important rheological measurement that is closely related to the resistance to flow is called viscosity. The technical definition of viscosity is the ratio of shear stress to shear rate ... 

Solution It is apparent from the units of b] that solute concentration has been expressed in g/cm3. Dividing this concentration by the density of the unsolvated protein converts the concentration to dry volume fraction units. Since the concentration appears as a reciprocal in the definition of [17], we must multiply bl by p2 to obtain (lAA Mb/r/o) - 1]. For this protein the latter is given by (3.36)(1.34) = 4.50. If the particles were unsolvated, this quantity would equal 2.5 since the molecules are stated to be spherical. Hence the ratio 4.50/2.50 = 1.80 gives the volume expansion factor, which equals [1 + (mhb/m2)(p2/p )]. Therefore (m, tblm2) = 0.80(1.00/ 1.34) = 0.6O. The intrinsic viscosity reveals the solvation of these particles to be 0.60 g HaO per gram of protein. ... 

Phase diagrams from freezing point depressions show true compound formations for simpler amides—e.g., water-N-methylacetamide forms a compound at a mole ratio of 2 to 1, water-N,N-dimethylacetamide at 3 to 2 and 3 to 1, and water-N-methylpyrrolidone at 2 to 1. The heats of mixing and heat capacities at 25°C. of a number of water-amide systems were determined. All mixing curves were exothermic and possess maxima at definite mole ratios, while the heat capacities for the most part show distinct curvature changes at the characteristic mole ratios. Both experimental results point to the stability of the particular complexes even at room temperature. This is further supported by absolute viscosity studies over the whole concentration range where large maxima occur at these same mole ratios for disubsti-tuted amides and N-substituted pyrrolidones. 

It is, therefore, not surprising that there exists a definite relationship between Aand the enthalpy of vaporization, Av H, the former constituting a fraction between 0.2 and 0.3 of the latter, as is readily obtained from the data in Tables 3.1 and 3.9. The pressure dependence of the viscosity is also closely related to the free volume of the solvent. The fluidity (O = l/r ) is proportional to the ratio between the free and the occupied volume, the former, as mentioned above, being the difference between the actual molar volume and the intrinsic molar volume (Tables 3.1 and 3. 4) (Hildebrand 1978). In fact, the logarithm of the viscosity of liquids was found (Marcus 1998) to be described well for some 300 liquids by the empirical relationship ... 

Viscosity and Plasticity—Viscosity and plasticity are closely related. Viscosity may be defined as the force required to move a unit-area of plane surface with unit-speed relative to another parallel plane surface, from which it is separated by a layer of the liquid of unit-thickness. Other definitions have been applied to viscosity, an equivalent one being the ratio of shearing stress to rate of shear. When a mud or slurry is moved in a pipe in more or less plastic condition the viscosity is not the same for all rates of shear, as in the case of ordinary fluids. A material may be called plastic if the apparent viscosity varies with the rate of shear. The physical behavior of muds and slurries is markedly affected by viscosity. However, consistency of muds and slurries is not necessarily the same as viscosity but is dependent upon a number of factors, many of which are not yet clearly understood. The viscosity of a plastic material cannot be measured in the manner used for liquids. The usual instrument consists of a cup in which the plastic material is placed and rotated at constant speed, causing the deflection of a torsional pendulum whose bob is immersed in the liquid. The Stormer viscosimeter, for example, consists of a fixed outer cylinder and an inner cylinder which is revolved by means of a weight or weights. 

Basically, all of these closely related problems occur because gas-flood injection fluids have very small viscosities at the temperatures and pressures at which they are used. For example, the viscosity of CO2 at 13.8 MPa (2,000 psi) and 38°C (100°F) is about 0.066 cp, whereas the viscosities of reservoir oils are at least an order of magnitude greater (16). This produces a ratio of the mobility of the CO2 to the mobility of the oil that is much greater than one. (The mobility of a fluid is defined as its relative permeability divided by its viscosity for the definition of relative permeability, see equations below.)... 

These figures have been compared with those obtained for rabbit acto-myosin and myosin (Hamoir, 1955). These last values differ notably from one author to another especially in the case of actomyosin, but they always remain lower than our determinations. The viscosity numbers determined by Kerekjarto (1952) for rabbit actomyosin and myosin at 15° C., which seem to be the most reliable, are, respectively, 0.32 and 0.17 ( 0.01). Both figures are definitely lower than our values carried out at higher temperature. In the case of actomyosin, this difference appears to be due to the structure of the solutions. Recent determinations (Hamoir, 1955) suggest that fish and rabbit actomyosins have approximately the same intrinsic viscosity at = 0. The axial ratio of these particles seems therefore not to differ notably. In view of this relationship, more accurate determinations are necessary in order to determine if the different viscosities observed in the presence of ATP are really due to a different shape of the particles. 

It is interesting to note the similarity between the definitions of the shear viscosity (Equation 13.1) and the shear modulus (Equation 13.2), which leads to a relationship (Equation 13.3) between r and G in terms of the ratio of the shear strain (y) divided by the shear rate (y). 

The intrinsic viscosity [77] is defined in Table 4.2 as a limit at zero concentration. Since the 77/770 ratios are obtained from Eq. (4.99) with measurements made at finite concentrations of the solution, it becomes necessary to extrapolate the data to zero concentration in order to satisfy this definition. There are a variety of ways to carry out this extrapolation. The variation in solution viscosity (77) with increasing concentration.(c) can be expressed as a power series in c. The equations usually used are the Huggins equation (Huggins, 1942) ... 

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