By G. Böhme
This quantity is to be used in technical universities, and for training engineers who're concerned with move difficulties of non-Newtonian fluids. The therapy of the topic is predicated all through on continuum mechanics version innovations and strategies. simply because in Non-Newtonian fluids the fabric houses working count seriously at the kinematics of the movement, particular consciousness is paid to the derivation and clarification of the sufficient constitutive equations used. The e-book might be learn irrespective of different assets. It starts via contemplating a few basic rules of continuum mechanics, experiences uncomplicated motions (steady and unsteady shear flows) and proceeds through levels to kinematically extra complicated motions. difficulties of varied levels of hassle on the finish of every bankruptcy invite energetic participation via the reader. a number of stimulating themes from the literature are thought of within the booklet.
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Additional resources for Non-Newtonian Fluid Mechanics
55)· Because time independent laminar flows are steady in material coordinates (D/Dt = 0 ) , the first term on the right-hand side of equation ( 1 . 5 5 ) vanishes. a = 2 Using ( 1 . 7 6 ) and ( 1 . 78) 0 0 0 0 2? 79) 26 1 Principles of continuum mechanics After A^ all higher Rivlin-Ericksen tensors vanish, A = 0 for η > 3 . This property is characteristic of all steady shear flows. n two principal invariants A. and A are zero in both cases. 2 vanishing invariants are related in a simple way toy : ^(A^) = - γ , I^Ag) = 2γ .
In actual applications it is expedient to fix ρ over the boundary conditions for the stresses. For compressible fluids on the other hand ρ signifies the thermodynamic pressure. e. 110) One therefore requires six scalar quantities for the description of the stress condition in a continuum, and these represent the components of a symmetrical tensor. 9 τ (x,y,z,t), etc. 105) to be represented in the form / / S n d A , that is the resultant surface force A acting on an arbitrarily chosen part of the moving fluid.
The memory of the past therefore consists of a single bit of information, the quantity γ which is constant for each fluid particle, so viscometric flows are special flows with a constant stretch history. 2 Poiseuille flow The shearing surfaces in this flow are coaxial circular section cylind rical surfaces which move in the axial direction. The velocity of the individual shearing surfaces depends only on the distance r from the axis of the cylinder. polar coordinates It is expedient here to use cylindrical r, φ,ζ, instead of Cartesian coordinates, so that the common axis of the shearing surfaces is identical with the z-axis (Fig.