Liquid, Maxwell

Imagine a Maxwell liquid placed between two parallel plates and sheared by moving the upper plate in its own plane. However, instead of moving the plate at a constant velocity as discussed in Chapter 1, let the displacement of the plate vary sinusoidally with time, ie the plate undergoes simple harmonic motion. If the maximum displacement of the upper plate is X and the distance between the plates is h, then the amplitude A of the shear strain in the liquid is given by... 

Y. Renardy, Stability of the interface in two-layer Couette flow of upper-convected Maxwell liquids, J. Non-Newtonian Fluid Mech., 28 (1988) 99-115. 

Figure 10.3 Response of a Maxwell liquid to a shear step strain input.

Pharmaceutical materials are rarely described by simple mechanical equivalents such as the Kelvin (solid-like behavior) or the Maxwell (liquid-like behavior) model. 

Figure 2.4 depicts the growth rates predicted from (2.26) for two jets of the upper-convected Maxwell liquids, which are shown by curves 1 and 3. They correspond to different values of the relative gas velocity (U for curve 1 is higher... 

Fig. 2.5 The amplitude Y of the bending perturbations of a jet of the upper-convected Maxwell liquid is shown by curve 1 [1], The values of the dimensionless groups are IT] = 10 IT2 = 0.156 x 10, II3 = 0.64, 114 = 115 = 0. Curve 2 depicts the amplitude of the corresponding jet of Newtonian liquid (Hz = 0) (Courtesy of Pearson Education)...

Ata = -l,b = c = 0, equations [7.2.24] correspond to the Maxwell liquid with a discrete spectrum of relaxation times and the upper convective time derivative. For solution of polymer in a pure viscous liquid, it is convenient to represent this model in such a form that the solvent contribution into total stress tensor will be explicit ... 

It is rather complex to describe viscoelastic behaviors mathematically. We will only focus here the simple, but representative Maxwell model for viscoelastic liquids. A mechanical analogue of a Maxwell liquid model is obtained by a serial combination of a spring and a dashpot see Fig. lc(l). If the individual strain rates of the spring and the dashpot, respectively, are 4oiid liquid > then the total strain rate e is given by the sum of these two components ... 

Tandon GP, Weng GJ (1984) The effect of aspect ratio of inclusion on elastic properties of unidirectionally aligned composites. Polym Compos 5 327-333 Tanner RI (1960) Full-film lubrication theory for a Maxwell liquid. Int J Mech Sci 1 206-215 Tanner RI (1975) Stresses in dilute solutions of bead-nonlinear-spring macromolecules, ii. Unsteady flows and approximate constitutive relations, constitutive relations. J Rheol 19 37-65... 

MILNE, A.A. A theory of rheodynamlc lubrication for a Maxwell liquid, ibid. 66-71... 

Likewise, Moo-Young and Hirose (1972) used the perturbation approach to obtain the approximate stream function for bubble motion in a Maxwell liquid (Re l Wi l), which, in turn, was used to deduce the following expression for Xj ... 

Astarita, G., Spherical gas bubble motion through Maxwell liquids, Ind. Eng. Chem. Fundam. 5 548 (1966). 

Rheological measurements performed on highly concentrated W/0 emulsions (gel emulsions) showed that the equation proposed by Princen also holds for these systems. Measurements of the viscoelastic properties showed that these materials have a viscoelastic response that can be fitted to a Maxwell liquid element. The elastic and viscous terms of this model vary as a function of frequency as ... 

Concerning the relaxation time of the system, it was found that a simple model could account for the observed behaviour. The system is considered as a two-element body an elastic modulus produced by interfacial area increase and a viscous modulus produced by the loss caused by slippage of droplets against droplets. Putting these elements in series means that the systems behave as a Maxwell liquid and the value of the relaxation time can be calculated, taking into account the viscosity of the continuous phase and its participation in the global volume. ... 

Wc see that the system of Fig 13 exhibits features both of the Maxwell liquid (Fig. 14) and of the Kelvin body (Fig. 17). The permanent deformation als occurs in Fig 14, the elastic after-effect only in Fig. 17 ... 

---