Marrucci

For laminar non-Newtonian film flow, see Bird, Armstrong, and Hassager Dynamics of Polymciic Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977, p. 215, 217), Astarita, Marrucci, and Palumbo (Jnd. Eng. Chem. Fundam., 3, 333-339 [1964]) and Cheng (Jnd. Eng. Chem. Fundam., 13,394—395 [1974]). 

Astarita G, Marrucci G (1974) Principles of non-Newtonian fluid mechanics. McCrow-Hill... 

To evaluate the effect of holdup on bubble velocity, Marrucci (M3) used a spherical cell model of radius b such that... 

According to Levich (L3) Eq. (142) can approximate the convective dif-fusional flux even in the domain 1 < jVRc < 600. Hence the application of the Marrucci correction [Eq. (44)] to Eq. (38) before combining it with Eq. (142) gives... 

M4. Marrucci, G., Univ. of Napoli, Italy, Personal communication, 1966. 

Astarita. G. and Marrucci, G. Principles of Non-Newtonian Fluid Mechanics (McGraw-Hill, New York. 1974). 

Reasons have been advanced for both an increase and a decrease of the tube diameter with strain. A justification of the former view might be the retraction process itself [38]. If it acts in a similar way to the dynamic dilution and the effective concentration of entanglement network follows the retraction then Cgjy < E.u > so that a < E.u On the other hand one might guess that at large strains the tube deforms at constant tube volume La. The tube length must increase as < E.u >,so from this effect a < E.u > . Indeed, Marrucci has recently proposed that both these effects exist and remain unnoticed in step strain because they cancel [69] Of course this is far from idle speculation because there is another situation in which such effects would have important consequences. This is in conditions of continuous deformation, to which we now turn. 

If the ideas of Marrucci [69] are correct and the non-monotonic predictions of the simple Doi-Edwards theory need to be modified in the case of polymer melts (for a recent development see [78]), then an explanation will be required for the apparent difference at high shear rates between melts and wormlike micelle solutions. There is also evidence that ordinary entangled polymer solutions do exhibit non-monotonic shear-stress behaviour [79]. As in the field of linear deformations, it may be that a study of the apparently more complex branched polymers in strong flows may shed light on their deceptively simple linear cous-... 

Koide (1996) recommended that for air—water systems, if D 8 >2x10 4 m2, the flow can be considered to be in the heterogeneous regime. In this relationship, D is the column diameter and 8 the nozzle or hole diameter of the gas distributor. The transition region can be defined in terms of gas holdup by using Marrucci s and Akita-Yoshida equations as presented in Figure 3.28 (Koide, 1996). 

The Marrucci random tube model58) leads to the following expressions for the free energy and the elastic force at simple extension or compression for tubes with a circular cross section... 

It is desired to determine the distribution of segment orientations and we follow here the derivation offered by Marrucci and Grizzuti [87], At equilibrium, this distribution function is uniform and equal to... 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

G. Marrucci and N. Grizzuti, Predicted effect of polydispersity on rodlike polymer behaviour in concentrated solutions, J. Non-Newt. Fluid Mech., 14,103 (1984). 

D. S. Pearson, A. D. Kiss, L. J. Fetters, andM. Doi, Flow-induced birefringence of concentrated polyisoprene solutions, J. Rheol., 33, 517 (1989) D. S. Pearson, E. Herbolzheimer, N. Grizzuti, and G. Marrucci, Transient behavior of entangled polymers at high shear rates, J. Polym. Sci., Part B, 29,1589 (1991). 

M. Marrucci and P. L. Maffettone, Description of the liquid-crystalline phase of rodlike polymers at high shear rates, Macromolecules, 22,4076 (1989). 

J. C. Chang and M. M. Denn, Sensitivity of the Stability of Isothermal Melt Spinning to Rheological Constitutive Assumptions, in Rheology Applications, Vol. 3., G. Astarita, G. Marrucci, and L. Nicolais, Eds., Plenum Publishing, New York 1980, pp.9-13. 

D. Aciemo, F. P. La Mantia, G. Marrucci, and G. Titomanlio, A Non-linear Viscoelastic Model with Structure-dependent Relaxation Times I. Basic Formulation, J. Non-Newt. Fluid Meek, 1, 125-146 (1976). 

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