Elasticity of liquids

The elasticity of liquid films that plays an important role in the stability of some foam films, is characterised quantitatively by the elasticity modulus... 

Small molecular mass liquid crystals do not respond to extension and shear stress. Liquid crystalline polymers may exhibit a high elastic state at some temperature due to the entanglements. However, the liquid crystalline network itself is an elastomer, showing rubber elasticity. In the presence of external stress, liquid crystalline networks deform remarkably and then relax back after the release of stress. The elasticity of liquid crystalline networks is more complicated than the conventional network, such as the stress induced phase transition, the discontinuous stress-strain relationship and the non-linear stress optical effect, etc. 

In continuous systems consisting of solid phases, the parameter G is the modulus of elasticity of rigid body. Its values may fall in the range between 109 and 10" N m 2. The elasticity modulus of common liquids under the conditions of uniform (hydrostatic) compression is also of the same order of magnitude. However, due to low viscosity, the shear elasticity of liquids may only be observed by rapid tests in which the time of stress action is close to the relaxation period. For this reason at typical times of mechanical action liquids with low r values behave as viscous media. 

This relation describes not only periodic deformations of a liquid surface. Using methods of integral transformations it is possible to show that the dynamic surface elasticity is a fundamental surface property and its value determines the system response to a small arbitrary surface dilation [161]. With this method it is also possible to determine the dynamic elasticity of liquid-liquid interfaces where the surfactant is soluble in both adjacent phases [133]. Moreover, similar transformations lead to an expression for the dynamic surface elasticity for the case when the mechanism of the slow step of micellisation is determined by scheme (5.185) or for frequencies corresponding to the fast step of micellisation [133,134]. However, as stated above, it is the slow process which mainly influences the adsorption kinetics from micellar solutions. 

W. Song, A.H. Windle, Size-dependence and elasticity of liquid-crystalline multiwalled carbon nanotubes. Adv. Mater. 20, 3149-3154 (2008)... 

In the last two centuries, a lot of attempts and discussion have been made on the elucidation and development of the various constitutive models of liquids. Some of the theoretical models that can be mentioned here are Boltzmann, Maxwell (UCM, LCM, COM, 1PM), Voight or Kelvin, Jeffrey, Reiner-Rivelin, Newton, Oldroyd, Giesekus, graded fluids, composite fluids, retarded fluids with a strong backbone and fading memory, and so on. Further and deeper knowledge related to the physical and mathematical consequences of the structural models of liquids and of the elasticity of liquids can be found in Ref. [6]. 

The bending elasticity of fluid membranes is closely related to the director field elasticity of liquid crystals. Of the three elastic deformations in nematics, which are splay, bend, and twist, only splay remains as it does in the case of smectics. In fact, a membrane is like an isolated smectic layer and this is why membrane curvature is sometimes expressed in terms of splay and saddle splay. 

Curvature Elasticity of Liquid Crystals in Three Dimensions... 

On the whole, it is possible to state that the currently available expmmental material does not yet permit drawing any definite conclusions concerning the roles of the chain structure of the macromolecules and the effect of the polymeric state of the liquid crystal on the elastic properties of the LC phase. The problem of the contribution of the conformational state of the main chains, their flexibility, and the length of the aliphatic spacer remains open. It is necessary to develop theoretical studies to clarify the question of the features of the elastic properties of the polym mesophases within the framework of the continuous theory of elasticity of liquid crystals. 

Stannarius R 1998 Elastic properties of nematic liquid crystals 1998 Handbook of Liquid Crystals Vol 2A. Low Molecular Weight Liquid Crystals led D Demus, J Goodby, G W Gray, Fl-W Speiss and V Vill (New York Wiley-VCH)... 

Successive reflections of the pressure wave between the pipe inlet and the closed valve result in alternating pressure increases and decreases, which are gradually attenuated by fluid friction and imperfect elasticity of the pipe. Periods of reduced pressure occur while the reflected pressure wave is travehng from inlet to valve. Degassing of the liquid may occur, as may vaporization if the pressure drops below the vapor pressure of the liquid. Gas and vapor bubbles decrease the wave velocity. Vaporization may lead to what is often called liquid column separation subsequent collapse of the vapor pocket can result in pipe rupture. 

P = pressure of liquid Vl = volume of hquid Ey = Young s modulus of elasticity V = Poisson s ratio... 

Neutron diffraction is one of the most widely used techniques for the study of liquid structure. In the experiment, neutrons are elastically scattered off the nuclei in the sample and are detected at different scattering angles, typically 3° to 40°, for the purpose of measuring intermolecular structure whilst minimizing inelasticity corrections. The resultant scattering profile is then analyzed to provide structural information. 

Among the causes producing irreversibility w7e may instance the forces depending on friction in solids, viscosity of liquids imperfect elasticity of solids inequalities of temperature (leading to heat conduction) set up by stresses in solids and fluids generation of heat by electric currents diffusion chemical and radio-active changes and absorption of radiant energy. 

Lower-density E-plastomers have found alternate use in cast film processes to make elastic film laminates with good breathability which contain laminates of liquid impermeable extensible polymeric films with extensible-thermoplastic-polymer-fiber nonwovens and nonwoven webs of polyethylene-elastomer fibers as the intermediate layers. The development relates to a breathable film including an E-plastomer and filler that contributes to pore formation after fabrication and distension of the film. The method and extent of distension is designed to produce a breathable film by stretching the film to form micropores by separation of the film of the E-plastomer from the particulate solids. This film is useful for manufacture of absorbent personal-care articles, such as disposable diapers and sanitary napkins and medical garments. In detail, these constructions comprise a liquid impermeable extensible film comprising polyolefins. The outer layer contains extensible-thermoplastic-polymer-fiber nonwovens, and an elastic intermediate layer contains nonwoven webs of fiber E-plastomers. The intermediate layer is bonded to the film layer and the outer... 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

As the two particles approach each other, the first contact will be made by the outer binder layers the liquid will subsequently be squeezed out from the space between the particles to the point where the two solid surfaces will touch. A solid rebound will occur based on the elasticity of the surface... 

---