Elastic systems, characteristic ratio

Capillary forces in mixed fluid phase conditions are inversely proportional to the curvature of the interface. Therefore, menisci introduce elasticity to the mixed fluid, and mixtures of two Newtonian fluids exhibit global Maxwellian response. For more details see Alvarellos [1], his behavior is experimentally demonstrated with a capillary tube partially filled with a water droplet. The tube is tilted at an angle (3 smaller than the critical angle that causes unstable displacement. Then, a harmonic excitation is applied to the tube in the axial direction. For each frequency, the amplitude of the vibration is increased until the water droplet becomes unstable and flows in the capillary. Data in Figure 3 show a minimum required tube velocity between 40 and 50 Hz. This behavior indicates resonance of the visco-elastic system. The ratio of the relaxation time and characteristic time for pure viscous effect is larger than 11.64. 

Using Eq. (14), one can arrive at a convenient form for characterizing the elastic systems by introducing the characteristic ratio 7 "9)... 

In a recent study, Crosby et al. [31] have discussed the different possible initial failure mechanisms of a thin adhesive elastic layer in a probe test and have extracted two geometrical parameters which couple with the two material parameters, E and % . the degree of confinement of the adhesive layer (represented by the ratio of a lateral dimension over a thickness of the layer) and a characteristic ratio between the size of a preexisting internal flaw, ac, and a lateral dimension of the system, a. They distinguished among three main types of initial failure bulk cavitation, internal crack and external crack as shown in Fig. 6. 

Another possible choice for the reference state is the equilibrium swelling degree of the network. In that case the thermodynamic characteristics of the actual polymer-swelling solvent system would be taken into account. However this choice does not consider the conditions of network formation. Moreover when the gel is swollen to equilibrium, the elastic chains are extended with respect to the corresponding free chains, and the extension ratio is not easy to evaluate13. ... 

Numerical studies [167] of planar (d = 2) elastic random percolation networks have shown that if their linear dimension L < 0.2c (c is the correlation length), then Poisson s ratio for the system is negative, and if L > 0.2J , Poisson s ratio is positive In this case, if L/c —> oo, the limiting value of Poisson s ratio is vp = 0.08 0.04 and is a universal constant that is, it does not depend on the relative values of the local elastic characteristics If... 

Rheology is concerned with the flow and/or deformation of matter under the influence of externally imposed mechanical forces. Two limiting types of behaviour arc possible. The deformation may reverse spontaneously (relax) when the external force is removed this is called elastic behaviour and is exhibited by rigid solids. The energy used in causing the deformation is stored, and then recovered when the solid relaxes. At the other extreme, matter flows and the flow ceases (but is not reversed) when the force is removed this is called viscous behaviour and is characteristic of simple liquids. The energy needed to maintain the flow is dissipated as heat. Between the two extremes arc systems whose response to an applied force depends on the lime-scale involved. Thus pitch behaves as an elastic solid if struck but flows if left for years on a slope. Similarly, a ball of Funny Putty , a form of silicone rubber, bounces when dropped on a hard surface, when the contact time is a few milliseconds, but flows if deformed slowly on a time-scale of seconds or minutes. Systems of this kind are said to be visco-elastic. The precise nature of the observable phenomena depends on the ratio of the time it takes for the system to relax to the time taken to make an observation. This ratio is called the Deborah number (De) ... 

By varying several parameters such as the W/O ratio, one can induce an inversion from an O/W to a W/O microemulsion and vice versa. The type of structure in the inversion domain depends essentially on the bending constant a characteristic of the elasticity of the surfactant layer [7]. If Ke is on the order of kT (where k is the Boltzmann constant and T absolute temperature), the persistence length of the film (i.e., the distance over which the film is locally flat) is microscopically small. The interfacial film is flexible and is easily deformed under thermal fluctuations. The phase inversion occurs through a bicontinuous structure formed of water and oil domains randomly interconnected [8,9]. The system is characterized by an average curvature around zero, and the solubilization capacity is maximum. When K kT, is large and the layers are flat over macroscopic distances. The transition occurs through a lamellar phase. 

Figure 4.6 presents the distribution of internal stresses in the epoxy rubber coating determined by the lattice cell method. A feature of the calculation is the large ratio of the length to the width of the specimen, with a substantial difference of the elastic characteristics that characterize the system ...

The relative importance of elasticity in a flow is often described by the Deborah number, De, introduced by Reiner [13]. This number may be interpreted as the ratio of the magnitudes of the elastic forces to that of the viscous forces. It is defined as the ratio of a characteristic time (time scale) of the fluid A to a characteristic time of the flow system iflow [2]. 

This model utilizes two characteristic lengths for the spring, the displacement ° of the system at rest (F= 0), without application of a force, and the minimum displacement below which the spring cannot be compressed. The activity must be understood as the ratio between the basic quantity that is effectively available ( active ) for influencing some other poles and a reference quantity. For the force, a scaling force F is used its expression is written with the eigenvalue of the elastance operator, notated... 

The energy dissipated in a loading/unloading cycle divided by the total energy used to load the material. Its value must lie between 0 and 1 The constant of proportionality between the extension of a spring and the force applied to it Linear elastic fracture mechanics A system in which stress is proportional to strain A function of the temperature, strain rate, and strain level which varies from 1 to infinity as the hysteresis ratio varies from 0 to 1 A characteristic in the plot of log(peeling energy) vs. 

The relaxation period defines the behavior of the system, in accordance with the Maxwell model with respect to the timescale of the applied stress. If the time t during which stress is applied is greater than the relaxation period, that is, t > t the system has properties similar to those of a viscous liquid, while at t t the system behaves like an elastic solid. The flow of glaciers and other processes of strain development in mountains and cliffs are representative examples of such behavior. In rheology, the ratio of a material s characteristic relaxation time to the characteristic flow time is referred to as the Deborah number. This parameter plays an important role in describing the response of various materials to different stresses. 

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