Tensors for Physics

312 16 Constitutive Relations For zero pressure and at temperatures, where the fluctuation contributions to the elasticity coeff ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 313 withpλ=ελαβpαβ. The contributions to the entropy production(δδst)dvir ...

314 16 Constitutive Relations Positive entropy production requires that ηsymμνμ′ν′= 1 2 (ημνμ′ν′+ημ′ν′μν) is positive definite, ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 315 The 5 complex viscosity coefficientsη(m)have the propertiesη(m)=(η(−m ...

316 16 Constitutive Relations Its interrelation with the viscosity coefficients occurring in (16.47) can be inferred with the he ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 317 ∇μδP=−kμ= 2 ∇νημνμ′ν′∇μ′vν′. (16.55) For the geometry considered here ...

318 16 Constitutive Relations When the field points in the direction of the bisector between thex- andy-axes, viz. forh=(ex+ey)/ ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 319 ∂ ∂t pμν+ 2 p 0 ∇μvν+νppμν +νpa √ 2 p 0 aμν= 0 , (16.59) ∂ ∂t aμν−ωBH ...

320 16 Constitutive Relations Erlangen, Germany and, at about the same time independently by F.R. McCourt in his PhD work in Van ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 321 dJλ dt +τrot−^1 (Jλ−θωλ)= 0 ,τrot−^1 = 2 m ρθ ηrot, (16.65) with ther ...

322 16 Constitutive Relations direction such that〈Gxx〉is larger than〈Gyy〉, then the average rotational velocity is smaller than ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 323 is made. The term involving the vorticity describes the time change d ...

324 16 Constitutive Relations To study the effect of the vorticity on the flow birefringence, a plane Couette geometry is consid ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 325 exchanged. This means the relaxation time “matrix” formed by theτ..co ...

326 16 Constitutive Relations 16.3.7 Heat-Flow Birefringence Also a heat fluxqcan give rise to birefringence. By analogy to the ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 327 The pertaining complex shear modulusG(ω)is given by G(ω)=−iωτMη(ω)=G′ ...

328 16 Constitutive Relations viscosity coefficients are given by ηiso=ηNew ( 1 − τap^2 τaτp ) ,ηNew= ρ m kBTτp. (16.85) Similar ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 329 This type of nonlinearity is to be distinguished from the nonlinear f ...

330 16 Constitutive Relations the shear viscosity and the viscometric functions approach constant values at small shear rates. A ...

16.3 Viscosity and Non-equilibrium Alignment Phenomena 331 tensor∇νvμis symmetric traceless and one has ∇νvμ =ε [ 2 ezνezμ−(exνe ...