The elasticity of liquids

Because of its molecular mobility a liquid cannot sustain a shear stress and the only modulus of elasticity that can be defined for a liquid is the bulk modulus K. 

Values for K for simple liquids at constant temperature are about two orders of magnitude less than those for solids and are rather more dependent on pressure. For water at 15°C, and pressures in the range 1-25 atmospheres, K is 2.05 X 10 Pa, while for mercury at 20 °C, and pressures in the range 8-37 atmospheres, is 26.2 X 10 Pa. 

Solids are almost incompressible and liquids only slightly less so. This is in accord with the simple description given in Chapter 1, in which the molecules in both solids and liquids are effectively in contact, but the molecules in a liquid have a high mobility because of their somewhat smaller number of near neighbours. 

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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 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]. 

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. 

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... 

The value of C in equation 10.39 depends on the way in which the pipe is restrained but for practical purposes a value of unity is adequate. In this equation, E is Young s modulus of elasticity of the pipe, d, the internal diameter of the pipe and tw its wall thickness. The value of E for steel is about 2 x 10s MPa and K for water is about 2 x 103 MPa thus K/E is about 10-2. It will be seen that the elasticity of the pipe has a negligible effect with thick-wall pipes but with thin-wall ones (say djtw > 40) the propagation speed a will typically be reduced to about 70 per cent of the speed of sound c in the liquid. 

The surface molecules are under a different force field from the molecules in the bulk phase or the gas phase. These forces are called surface forces. A liquid surface behaves like a stretched elastic membrane in that it tends to contract. This action arises from the observation that, when one empties a beaker with a liquid, the liquid breaks up into spherical drops. This phenomenon indicates that drops are being created under some forces that must be present at the surface of the newly formed interface. These surface forces become even more important when a liquid is in contact with a solid (such as ground-water oil reservoir). The flow of liquid (e.g., water or oil) through small pores underground is mainly governed by capillary forces. Capillary forces are found to play a very dominant role in many systems, which will be described later. Thus, the interaction between liquid and any solid will form curved surface that, being different from a planar fluid surface, initiates the capillary forces. 

As is known, if one blows air bubbles in pure water, no foam is formed. On the other hand, if a detergent or protein (amphiphile) is present in the system, adsorbed surfactant molecules at the interface produce foam or soap bubble. Foam can be characterized as a coarse dispersion of a gas in a liquid, where the gas is the major phase volume. The foam, or the lamina of liquid, will tend to contract due to its surface tension, and a low surface tension would thus be expected to be a necessary requirement for good foam-forming property. Furthermore, in order to be able to stabilize the lamina, it should be able to maintain slight differences of tension in its different regions. Therefore, it is also clear that a pure liquid, which has constant surface tension, cannot meet this requirement. The stability of such foams or bubbles has been related to monomolecular film structures and stability. For instance, foam stability has been shown to be related to surface elasticity or surface viscosity, qs, besides other interfacial forces. 

THE SURFACE OF LIQUID WATER BEHAVES LIKE AN ELASTIC FILM... 

The structure of an elastomer comprises a network of chains, meaning that there are gaps between adjacent chains. Indeed the elasticity of rubber relies on substantial thermal motion of the chains, which would not be possible if the chains were closely packed. The free volume available in the rubber means that some liquids can enter the rubber and cause swelling - sometimes very large amounts of swelling. For example the ability of oil to swell natural rubber is well known. 

Abstract In this contribution, the coupled flow of liquids and gases in capillary thermoelastic porous materials is investigated by using a continuum mechanical model based on the Theory of Porous Media. The movement of the phases is influenced by the capillarity forces, the relative permeability, the temperature and the given boundary conditions. In the examined porous body, the capillary effect is caused by the intermolecular forces of cohesion and adhesion of the constituents involved. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force. Moreover, the friction interaction forces caused by the motion of the constituents are included in the mechanical model. The relative permeability depends on the saturation of the porous body which is considered in the mechanical model. In order to describe the thermo-elastic behaviour, the balance equation of energy for the mixture must be taken into account. The aim of this investigation is to provide with a numerical simulation of the behavior of liquid and gas phases in a thermo-elastic porous body. 

Nascent surface Explain the difference in the concept of liquid lubrication mechanism in (a) hydrodynamic, (b) elastohydrodynamic and (c) boundary lubrication. Which of the following characterize (a), (b), and (c) lubrication regime continuous fluid film, negligible deformation, complete separation of the surfaces, elastic and plastic deformation, no wear takes place, no contact between the sliding surfaces, involving surface topography, physical and chemical adsorption, catalysis and reaction kinetics, and tribochemical film formation ... 

Polymers differ from other substances by the size of their molecules which, appropriately enough, are referred to as macromolecules, since they consist of thousands or tens of thousands of atoms (molecular weight up to 106 or more) and have a macroscopic rectilinear length (up to 10 4 cm). The atoms of a macromolecule are firmly held together by valence bonds, forming a single entity. In polymeric substances, the weaker van der Waals forces have an effect on the components of the macromolecules which form the system. The structure of polymeric systems is more complicated than that of low-molecular solids or liquids, but there are some common features the atoms within a given macromolecule are ordered, but the centres of mass of the individual macromolecules and parts of them are distributed randomly. Remarkably, the mechanical response of polymeric systems combines the elasticity of a solid with the fluidity of a liquid. Indeed, their behaviour is described as viscoelastic, which is closely connected with slow (relaxation time to 1 sec or more) relaxation processes in systems. 

In the case of solids it is evident that deformation is either linear elastic - like a Hookean solid (most solids including steel and rubber) - or non-linear elastic or viscoelastic. In the case of liquids, fluids differ between those without yield stress and those with yield stress (so-called plastic materials). Fluids without yield stress will flow if subjected to even slight shear stresses, while fluids with yield stress start to flow only above a material-specific shear stress which is indicated by o0. 

Chandrasekhar, 1977). This cooperative behavior results in weak elastic properties. Then, the application of an electric field can easily change the molecular orientation, which is initially fixed by the mechanical boundary conditions. The concomitant changes in the optical properties form the basis of liquid crystal displays (LCD). 

A note with Southern s initials acknowledges Dalton s claim that the difference of the temperature of two vapours of the same elastic force, raised from two different liquids , is a constant quantity.57 In his further account of experiments on the elasticity of steam, Watt once again acknowledged Dalton s experiments (as reported in Manchester Memoirs) and also those of Mr De Betancourt (in Prony s Nouvelle Architecture Hydraulique), and of a Mr Schmidt. After recounting his own experiments of 1764-5 and 1774, Watt noted that he had asked Southern to repeat them, with the assistance of Mr Creighton and considered the results (presented in Southern s letter to Watt in the Appendix) as very reliable.58... 

On removal of the electric field, the ionic movement decreases dramatically and the initial alignment is recreated by elastic forces propagated from the surface boundary layers as well as by conduction. Therefore, switch-off times, /off, are an order of magnitude longer ( 20-100 ms) due to the high degree of disorder caused by the flow of liquid crystal and the absence of a restoring field effect. 

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