Hydrodynamic amplification

Amplification, hydrodynamic 76 Amplification factor 71 Annealing 45,49 Arrhenius behavior 5, 40, 47, 58... 

It is important to note here that the presence of rigid filler clusters, with bonds in the virgin, unbroken state of the sample, gives rise to hydrodynamic reinforcement of the mbber matrix. This must be specified by the strain amplification factor X, which relates the external strain of the... 

In this connection, Fig. 2 provides a qualitative illustration for interpreting modulus change of an elastomer upon filler blending 9). A hydrodynamic or strain amplification effect, the existence of filler-elastomer bonds, and the structure of carbon black 10) all play a part in this modulus increase. 

Recent developments in ultrashort, high-peak-power laser systems, based on the chirped pulse amplification (CPA) technique, have opened up a new regime of laser-matter interactions [1,2]. The application of such laser pulses can currently yield laser peak intensities well above 1020 W cm 2 at high repetition rates [3]. One of the important features of such interactions is that the duration of the laser pulse is much shorter than the typical time scale of hydrodynamic plasma expansion, which allows isochoric heating of matter, i.e., the generation of hot plasmas at near-solid density [4], The heated region remains in this dense state for 1-2 ps before significant expansion occurs. 

Fig. 1 Schematic view of filler morphology in three concentration regimes. For reinforcement is due to hydrodynamic amplification by particles ( < 1) or clusters (cp> +) with eff= or cpeff= / A) respectively. For > reinforcement is due to the deformation of a flexible filler network...

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

The above interpretations of the Mullins effect of stress softening ignore the important results of Haarwood et al. [73, 74], who showed that a plot of stress in second extension vs ratio between strain and pre-strain of natural rubber filled with a variety of carbon blacks yields a single master curve [60, 73]. This demonstrates that stress softening is related to hydrodynamic strain amplification due to the presence of the filler. Based on this observation a micro-mechanical model of stress softening has been developed by referring to hydrodynamic reinforcement of the rubber matrix by rigid filler... 

In view of an illustration of the viscoelastic characteristics of the developed model, simulations of uniaxial stress-strain cycles in the small strain regime have been performed for various pre-strains, as depicted in Fig. 47b. Thereby, the material parameters obtained from the adaptation in Fig. 47a (Table 4, sample type C60) have been used. The dashed lines represent the polymer contributions, which include the pre-strain dependent hydrodynamic amplification of the polymer matrix. It becomes clear that in the small and medium strain regime a pronounced filler-induced hysteresis is predicted, due to the cyclic breakdown and re-aggregation of filler clusters. It can considered to be the main mechanism of energy dissipation of filler reinforced rubbers that appears even in the quasi-static limit. In addition, stress softening is present, also at small strains. It leads to the characteristic decline of the polymer contributions with rising pre-strain (dashed lines in... 

Hardness 115 Heat treatment 47-48 Hopping, thermally activated 40 Hydrodynamic amplification 76 Hysteresis 70 -, filler-induced 59, 76, 78... 

Under the long wavelength and quasistationary approximations and with the use of the linearized forms of the hydrodynamic and thermodynamic boundary conditions, first, we solve the Orr-Sommerfeld equation for the amplitude of perturbed part of the stream function from the Navier-Stokes equations. Second, we solve the equation for the amplitude of perturbed part of the temperature in the liquid film. The dispersion relation for the fluctuation of the solid-liquid interface is determined by the use of these solutions. From the real and imaginary part of this dispersion relation, we obtain the amplification rate cr and the phase velocity =-(7jk as follows ... 

The term amplification usually refers to a process whereby the power of a signal is increased without altering its basic information-carrying characteristics. The signal may be electronic, hydrodynamic, acoustic, or, in our case, chemical. 

A. Ajdari, L. Bocquet, Giant amplification of interfacially driven transport by hydrodynamic slip diffusio-osmosis and beyond, Phys. Rev. Lett.. 2006, 96,186102, 1-4. 

This set of parameter values fits well a liquid metal with 7 = 29.2, Ca = 0.2. The calculations of eigenvalues are completed for various values Ma, T, a. In Figure 10 typical curves for = Cr oi) and aci = aci a) are plotted. As amplification factor aci a) of various instability modes could differ to several orders, a normalized amplification factor f = maCi where m is appropriate scale is used in figures. One of these growing modes is easily identified as the hydrodynamic mode of the falling film with small wavenumber and is indeed the same when Ma = 0. The phase velocity Cr of this wave mode diminishes from Cr = 3 as a grows form a = 0, takes a minimum value, and then increases. Amplification factor aCi is positive in the interval 0 < o < a and has maximum value aci)m inside of this interval. Other growing modes, which are referred to as diffusion modes appear only at Ma 7 0. The term diffusion could be applied for any mode which disappears at... 

Figure 10. Phase velocities (a) and amplification factors (b) for hydrodynamic (solid curves 1, r and 1 connected with left axes) and diffusive modes (dashed curves 2 and 2 connected with right axes) at 7 = 29.4 1 — Ma = 0 l ,2 — Ma = 0.015 1 ,2 — Ma = 1.5.

Ma 0. Diffusion modes in the case under consideration exist as solutions of dispersion equation for high enough wavenumbers a > a, where a is to be determined by computations. The wave velocity of a diffusion mode is equal to 3/2 with great accuracy. Thus this wave moves with the velocity of liquid on the film surface. This mode which can be identified as a monotone instability mode on the liquid interface leads to patterned interface. The amplification factor aci of this diffusive mode is two to three orders lower that of hydrodynamic mode and tends to its maximum value as a grows. 

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