Viscosity instantaneous linear

Differences between solid-like and liquid-bke complex fluids show up in all three of the shearing measurements discussed thus far the shear start-up viscosity t), the steady-state viscosity rj(y), and the linear viscoelastic moduli G co) and G (o). The start-up stresses a = y/ +()>, t) of prototypical liquid-like and solid-like complex fluids are depicted in Fig. 1-6. For the liquid-like fluid the viscosity instantaneously reaches a steady-state value after inception of shear, while for the solid-like fluid the stress grows linearly with strain up to a critical shear strain, above which the material yields, or flows, at constant shear stress. 

For some materials the linear constitutive relation of Newtonian fluids is not accurate. Either stress depends on strain in a more complex way, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known collectively as non-Newtonian. Many different types of behavior have been observed, ranging from fluids for which the viscosity in the Navier-Stokes equation is a simple function of the shear rate to the so-called viscoelastic fluids, for which the constitutive equation is so different that the normal stresses can cause the fluid to flow in a manner opposite to that predicted for a Newtonian fluid. 

The rate of si hydrate formation for comparison is also indicated. As seen, the nucleation without LMGS is almost instantaneous however the rate is slower than TBME. The observed rates are generally linear in the first 30 minutes however they tend to slow down as soon as sufficient hydrate slurry is present in the suspension. This occurs when 10% of water has been converted into hydrate where the magnetic induced mixing cannot perform its job well. Hence better contacting mode may be required that implies higher power consumption required due to an increase in viscosity of the suspension. This is not encouraging because of the low conversion. 

Here, the sphere center is instantaneously situated at point 0 the sphere center translates with velocity U, while it rotates with angular velocity (a r is measured relative to 0 its magnitude r is denoted by r. Moreover, f = r/r is a unit radial vector. The latter solution is derivable in a variety of ways e.g., from Lamb s (1932) general solution (Brenner, 1970). [Equation (2.12) represents a superposition (Brenner, 1958) of three physically distinct solutions, corresponding, respectively, to (i) translation of a sphere through a fluid at rest at infinity (ii) rotation of a sphere in a fluid at rest at infinity (iii) motion of a neutrally buoyant sphere suspended in a linear shear flow. The latter was first obtained by Einstein (1906, 1911 cf. Einstein, 1956) in connection with his classic calculation of the viscosity of a dilute suspension of spheres, which formed part of his 1905 Ph.D. thesis.]... 

Exponential shear is therefore not a flow with constant stress history. The stress in this flow tends to grow without limit, even in an inelastic or linearly elastic fluid, and this makes the presentation of data an important issue. Doshi and Dealy [57] and Dealy [58] have argued that the results of an exponential shear experiment should be reported in terms of a time-dependent exponential viscosity rf that is defined in terms of the instantaneous shear rate ... 

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