Suspension internal viscosity

To calculate the characteristics of viscoelasticity in the framework of mesoscopic approach, one can start with the system of entangled macromolecules, considered as a dilute suspension of chains with internal viscoelasticity moving in viscoelastic medium, while the elastic and internal viscosity forces, according to equations (3.4)-(3.6) and (3.8), have the form... 

In the simplest case, at N = 1, the considered subchain model of a macromolecule reduces to the dumbbell model consisting of two Brownian particles connected with an elastic force. It can be called relaxator as well. The re-laxator is the simplest model of a macromolecule. Moreover, the dynamics of a macromolecule in normal co-ordinates is equivalent to the dynamics of a set of independent relaxators with various coefficients of elasticity and internal viscosity. In this way, one can consider a dilute solution of polymer as a suspension of independent relaxators which can be considered here to be identical for simplicity. The latter model is especially convenient for the qualitative analysis of the effects in polymer solutions under motion. 

We may note that, for a nonzero internal viscosity, the system of equations for the moments is found to be open the equations for the second-order moments contain the fourth-order moments, etc. This situation is encountered in the theory of the relaxation of the suspension of rigid particles (Pokrovskii 1978). Incidentally, for 7 —> 00, equation (F.28) becomes identical to the relaxation equation for the orientation of infinitely extended ellipsoids of rotation (Pokrovskii 1978, p. 58). 

Unlike a solid-in-liquid suspension, the viscosity of an emulsion may depend upon the viscosity of the dispersed phase. This dependence is especially true when internal circulation occurs within the dispersed droplets. The presence of internal circulation reduces the distortion of the flow field around the droplets (26), and consequently the overall viscosity of an emulsion is lower than that of a suspension at the same volume fraction. With the... 

If instead of solid particles the suspension contains drops of internal viscosity /If different from the viscosity /i of the ambient liquid (in this case we talk of emulsion rather than suspension), then the viscosity is determined by Taylor s formula [34] ... 

Because the regions of the alimentary tract vary widely ia pH and chemical composition, many different commercial formulations of barium sulfate are available. The final preparations of varyiag viscosity, density, and formulation stabiUty levels are controlled by the different size, shape, uniformity and concentration of barium sulfate particles and the presence of additives. The most important additives are suspending and dispersiag agents used to maintain the suspension stabiUty. Commercial preparations of barium sulfate iaclude bulk and unit-dose powders and suspensions and principal manufacturers are E-Z-EM (Westbury, New York), Lafayette-Pharmacol, Inc. (Lafayette, Indiana), and Picker International, Inc. (Cleveland, Ohio). 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

The above model assumes that both components are dynamically symmetric, that they have same viscosities and densities, and that the deformations of the phase matrix is much slower than the internal rheological time [164], However, for a large class of systems, such as polymer solutions, colloidal suspension, and so on, these assumptions are not valid. To describe the phase separation in dynamically asymmetric mixtures, the model should treat the motion of each component separately ( two-fluid models [98]). Let Vi (r, t) and v2(r, t) be the velocities of components 1 and 2, respectively. Then, the basic equations for a viscoelastic model are [164—166]... 

Accompanying the impeded particle rotation is the (kinematical) existence of an internal spin field 12 within the suspension, which is different from one-half the vorticity to = ( )V x v of the suspension. The disparity to — 2 between the latter two fields serves as a reference-frame invariant pseudovector in the constitutive relation T = ((to — 12), which defines the so-called vortex viscosity ( of the suspension. Expressions for (( ) as a function of the volume of suspended spheres are available (Brenner, 1984) over the entire particle concentration range and are derived from the prior calculations of Zuzovsky et ai (1983) for cubic, spatially-periodic suspension models. 

Belfort et al. (1994) proposed five stages of fouling. These are, (1) fast internal sorption of macromolecules, (2) build-up of a first sublayer, (3) build-up of multisublayers, (4) densification of sublayers, and (5) increase in bulk viscosity. The fifth stage can be neglected for dilute suspensions like surface water. The dependence on particle size can be described as... 

As with organic solvents, proteins are not soluble in most of the ionic Uquids when they are used as pure solvent (examples of the solubility of enzymes in ionic hquids can be found in S ection 8.4). As a result the enzyme is either applied as immobihzed enzyme coupled to a support or as a suspension in its native form. For production processes the majority of enzymes are used as immobilized catalysts in order to facilitate handling and to improve their operational stabihty [25-27]. As a support either inorganic materials, such as porous glass, or different organic polymers are used [28]. These heterogeneous catalyst particles are subject to internal and external mass transport limitations which are strongly influenced by the viscosity of the... 

A better criterion in defining a microemulsion could be its fluidity. In effect, the viscosity of (macro)emulsions and suspensions is known to increase as the fragment size decreases, and thus it is expected that an emulsion with extremely small drop size, an internal phase content greater than 20-30%, and a monodispersed distribution (as expected in a microemulsion) would be quite viscous. However, systems with such a high viscosity have been called gel emulsions or miniemulsions because the authors preferred to elude the label microemulsion in order to avoid confixsion with single-phase microemulsions [5-7]. 

This effect is not exclusive of monodispersed particles and has also been found in polydisperse, poly modal suspensions and emulsions (16.24). Figure 30 shows the viscosity of oil-in-waler emulsitnis having the same overall internal... 

The viscosity and rheological behavior of the continuous phase also modifies the behavior of emulsions and suspensions. In fact. Eqs. [50 -[53] establish that the larger the viscosity of the continuous phase (T) ), the larger the viscosity of the su.spension diJ. Furthermore, if the continuous phase is strongly viscoela,stic. die swelling and rod climbing may appear (26). Shear thickening has also been observed in concentrated emulsions of very viscous internal phase (27). 

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