Weakly elastic fluid

Y. Iso, D. L. Kuch, and C. Cohen, Orientation in Simple Shear Flow of Semi-dilute Fiber Suspensions 1. Weakly Elastic Fluids, J. Non-Newt. Fluid Mech., 62, 115-134 (1996). 

Finally we comment briefly on weakly elastic fluids. (See [26] and section 3.2.) We assume that the given Newtonian solution v satisfies ] v i < (ciRe), where Ci is some constant depending only on the domain of the flow this condition ensures that v is asymptotically Liapunov stable. (See e.g., [67].) Then, the viscoelastic solution (v ,Tt) close to (v, 0) is linearly (asymptotically) stable for c > 0 small enough. 

Y. Iso, D.L. Koch, C. Cohen. Orientation in simple shear flow of semi-dilute fiber suspensions 1. Weakly elastic fluids. /. Non-Newtonian Fluid Mech., 62 (2-3), 115-134,1996. 

In a weakly elastic polymeric fluid (Weissenberg number ]), experiments (Saffman 1956 ... 

In this respect, a theory that takes into account the deformation of one droplet (Doi and Ohta 1991) can be applied to describe the shear and normal stress transients. According to this model, blend morphology is characterized by a scalar (referring to a specific interfacial area) and a tensor (characterizing interface anisotropy). These parameters may be expressed in two equations—one describing the stresses of the interfacial structures and the other for the evaluation of the scalar and interface tensor. For immiscible blends with Newtonian or weakly viscoelastic fluids and an increase in shear, the droplets deform into fibrils while maintaining their initial diameter, d. In comparison, in a highly elastic matrix where droplet shape is... 

The term proportional to b in eq 4.3.1 incorporates a weak elastic memory into the constitutive equation. It can be shown under quite general conditions that a viscoelastic fluid will obey eq 4.3.1 if the flow is sufficiently slow and slowly varying, to ensure that... 

New mathematical techniques [22] revealed the structure of the theory and were helpful in several derivations to present the theory in a simple form. The assumption of small transient (elastic) strains and transient relative rotations, employed in the theory, seems to be appropriate for most LCPs, which usually display a small macromolecular flexibility. This assumption has been used in Ref [23] to simplify the theory to symmetric type of anisotropic fluid mechanical constitutive equations for describing the molecular elasticity effects in flows of LCPs. Along with viscoelastic and nematic kinematics, the theory nontrivially combines the de Gennes general form of weakly elastic thermodynamic potential and LEP dissipative type of constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank elasticity in liquid crystalline polymers. It should be mentioned that this theory is suitable only for monodomain molecular nematics. Nevertheless, effects of Frank (orientation) elasticity could also be included in the viscoelastic nematody-namic theory to describe the multidomain effects in flows of LCPs near equilibrium. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

In a recent series of papers, Kilian 9,50 52) proposed a new phenomenological approach to rubber elasticity and suggested a molecular network might be considered as a formelastic fluid the conformational abilities of which were adequately characterized by the model of a van der Waals conformational gas with weak interaction. The ideal network is treated as an ideal conformational gas. According to... 

Fig. 5. Schematic illustration of the fluid-to-gel transition observed for colloidal silica inks. The bottom graph is a plot of zeta potential as a function of pH for PEl-coated silica and bare silica microspheres suspended in water. The upper graph is a log-log plot of shear elastic modulus as a function of shear stress for concentrated silica gels of varying strength (o) denotes weak gel pH = 9.5 and ( ) denotes strong gel pH = 9.75 (Ref. 36).

Body itself is merely passive, and needed some other principle to move it and now that it is in motion, it needs some other principle for conserving that motion. By the tenacity of fluids, the attrition of their parts, and the weakness of elasticity in solids, the motion which we find in the world, is always dwindling and on the decay so that there arises a necessity of recruiting it by active principles Such are the cause of gravity (...) and such the cause of fermentation, by which the heart and blood of animals are kept in perpetual motion, the inward parts of the earth are constantly warm d, bodies bum and shine, mountains take fire, caverns blown up, c. For we see but little motion in the world, beside what is owing to these active principles And were it not for these, the bodies of the earth, planets, comets, sun, and all things in them, would grow cold, and freeze, and become unactive masses. ... 

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