Dilational viscoelastic modulus

Many technologies and natural phenomena involve processes of fast expansion or compression of fluid interfaces covered with surfactant adsorption layers. The dynamic system properties depend on the mechanisms and rate of equilibrium restoration after a deformation. At small magnitudes of deformation the mechanical relaxation of an interface can be described by the complex dilational viscoelastic modulus [1,2]. For sinusoidal deformations it is deflned as the ratio of complex amplitudes of interfacial tension variation and the relative surface area variation f (I ty) = dy /din A being a function of frequency. This modulus may include... 

The viscoelasticity is a complex number determined by the dilatational elasticity and viscosity [19, 94, 95]. The viscoelasticity modulus (or surface dilatational modulus) incorporates a real and imaginary constituent, elasticity and viscosity, respectively. 

Figure 6 (a) Dynamic surface dilational moduli for pure gelatin and gelatin/[C -i-C im]Brj systems, (b) Static surface dilational viscoelasticity as a function of [C -5-C im]Brj concentrations, (c) Surface tension as a function of surfactant concentration for pure [C -5-C im]Brj and gelatin/[C -5-C im]Br2 systems, (d) A schematic illustration of the interaction between gelatin and imidazolium gemini surfactant on the air/solution surface. The surface dilational modulus. Reproduced from Ao et al. [94] with permission from the Royal Society of Chemistry. 

The sedimentation results obtained with the structured suspensions, are consistent with the predictions from rheological investigations. In the absence of any bentonite clay, the pesticidal suspension exhibits Newtonian behaviour with unmeasurable yield value, modulus or residual viscosity. In this case the particles are free to settle individually under gravity forming a dilatant sediment or clay. On the other hand, at bentonite concentrations above the gel point (> 30 g dm the non-Newtonian behaviour of the suspensions and in particular their viscoelastic behaviour results from the formation of a "three-dimensional" network, which elastically supports the total mass. After 21 weeks standing in 100 ml measuring cylinders, no separation was observed when the bentonite concentration was >37.5 g dm corresponding to a modulus > 60 Nm. Clearly the modulus value required to support the mass of the suspension depends on the density difference between particle and medium. 

Because protein-ba sed foams depend upon the intrinsic molecular properties (extent and nature of protein-protein interactions) of the protein, foaming properties (formation and stabilization) can vary immensely between different proteins. The intrinsic properties of the protein together with extrinsic factors (temperature, pH, salts, and viscosity of the continuous phase) determine the physical stability of the film. Films with enhanced mechanical strength (greater protein-protein interactions), and better rheological and viscoelastic properties (flexible residual tertiary structure) are more stable (12,15), and this is reflected in more stable foams/emulsions (14,33). Such films have better viscoelastic properties (dilatational modulus) ( ) and can adapt to physical perturbations without rupture. This is illustrated by -lactoglobulin which forms strong viscous films while casein films show limited viscosity due to diminished protein-protein (electrostatic) interactions and lack of bulky structure (steric effects) which apparently improves interactions at the interface (7,13 19). 

The main factors, which determine the foam formation ability and physical stability of the foams in mixed Lys-MR solutions, are surface activity and complex dilatation modulus. With increase of MR concentration in certain range a surface activity and complex dilatation modulus of interfacial layers increased and phase angle decreased. It means that viscoelasticity of interfacial layers became higher. In these conditions the foam volume and mutiplicity as well as stability of foams were growing. This effect may be used for creation of mixed protein-MR system foam type for pharmaceutical applications with improved physical stability and wide range of antibacterial actions. 

In solving viscoelastic stress analysis problems, assumptions on the material properties are often essential as gathering accurate time dependent data for viscoelastic properties is difficult and time consuming. Thus, one often only has properties for shear modulus, G(t) or Young s modulus, E(t), but not both. Yet of course for even the simplest assumption of a homogeneous, isotropic viscoelastic material, two independent material properties are required for solution of two or three dimensional stress analysis problems. Consequently, three assumptions relative to material properties are frequently encountered in viscoelastic stress analysis. These are incompressibility, elastic behavior in dilatation and synchronous shear and bulk moduli. Each of the common assumptions defines a particular value for either the bulk modulus or Poisson s ratio as follows. 

We have reported [66] a limited study of spread polymethyl methacrylates and polyethylene oxide. Figure 12.19 shows the variation in surface tension, shear viscosity and dilational modulus obtained from SQELS data as a function of surface concentration. The viscoelastic moduli both show maximum values at finite values of the surface concentration. As the capillary waves generate oscillatory stress and strain, these are related via the complex dynamic modulus of the surface... 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

To demonstrate that propellants are non-linear materials even at small strains, one need only check the superposition principle experimentally. In the range of small strains below detectable dewetting or volumetric dilatation [6,9-11], most propellants have a relaxation that is independent of strain and in general closely obey the scalar multiplication homogeneity rule. Yet this relaxation modulus cannot be used to accurately predict the response due to other isothermal, low rate, small strain inputs. To demonstrate the inadequacies of linear viscoelastic predictions on solid propellants, laboratory tests where superposition is applicable can be performed. Figure 6.1 illustrates the stress-strain-dilatational behavior of a typical composite propellant. The dilatation-strain behavior is caused by vacuole formation within the microstructure... 

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