Tanner

The Art of Japanese Management Richard Tanner Pascale and Anthony G. Athos With an Introduction by Sir Peter Parker... 

As an example of the application of the method, Neumann and Tanner [54] followed the variation with time of the surface tension of aqueous sodium dode-cyl sulfate solutions. Their results are shown in Fig. 11-15, and it is seen that a slow but considerable change occurred. 

Heller E J, Sundberg R L and Tanner D J 1982 Simple aspects of Raman scattering J. Rhys. Chem. 86 1822-33... 

Tanner D J and Weeks D E 1993 Wave packet correlation function formulation of scattering theory—the quantum analog of classical S-matrix theory J. Chem. Phys. 98 3884... 

Phan-Thien, N. and Tanner, R.T., 1977. A new constitutive equation derived from network theory, Non-Newtonian Fluid Mech. 2, 353-365. 

Tanner, R.I., 1985. Engineering Rheology, Clarendon Press, Oxford. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

In this section the discretization of upper-convected Maxwell and Oldroyd-B models by a modified version of the Luo and Tanner scheme is outlined. This scheme uses the subdivision of elements suggested by Marchal and Crochet (1987) to generate smooth stress fields (Swarbrick and Nassehi, 1992a). 

For simplicity, we define T - and T (A iooTe/At). As explained by Luo and Tanner (1989), the decoupled method requires a suitable variable transfonna-tion in the governing equations (3.20) and (3.21). This is to ensure that the discrete momentum equations always contain the real viscous term required to recover the Newtonian velocity-pressure formulation when Ws approaches zero. This is achieved by decomposing the extra stress T as... 

In viscoelastic models in addition to the described conditions, stresses at the inlet should be given. As already mentioned there is no universal method to define such conditions, however, the following options may be considered (Tanner, 2000) ... 

Luo, X. L, and Tanner, R. L, 1989. A decoupled finite element streamline-upwind scheme for viscoelastic flow problems. J. Non-Newtonian Fluid Mech. 31, 143-162. 

Tanner, R.I. 2000. Engineering Rheology, 2nd edti, Oxford University Press, Oxford. Taylor, C., Ranee, J. and Medwell, J. O., 1985. A note on the imposition of traction boundary conditions when using FEM for solving incompressible flow problems. Comnmn. Appl. Numer. Methods 1, 113-121. 

The (CEF) model (see Chapter 1) provides a simple means for obtaining useful results for steady-state viscometric flow of polymeric fluids (Tanner, 1985). In this approach the extra stress in the equation of motion is replaced by explicit relationships in terms of rate of strain components. For example, assuming a zero second normal stress difference for veiy slow flow regimes such relationships arc written as (Mitsoulis et at., 1985)... 

Solution of the flow equations has been based on the application of the implicit 0 time-stepping/continuous penalty scheme (Chapter 4, Section 5) at a separate step from the constitutive equation. The constitutive model used in this example has been the Phan-Thien/Tanner equation for viscoelastic fluids given as Equation (1.27) in Chapter 1. Details of the finite element solution of this equation are published elsewhere and not repeated here (Hou and Nassehi, 2001). The predicted normal stress profiles along the line AB (see Figure 5.12) at five successive time steps are. shown in Figure 5.13. The predicted pattern is expected to be repeated throughout the entire domain. 

Figure 5,16. It is assumed that by using an exactly symmetric cone a shear rate distribution, which is very nearly uniform, within the equilibrium (i.e. steady state) flow held can be generated (Tanner, 1985). Therefore in this type of viscometry the applied torque required for the steady rotation of the cone is related to the uniform shearing stress on its surface by a simplihed theoretical equation given as...

Tanning of hides by any of the primitive methods was a dirty job withHttle assurance of success. The tanner was a speciaUst generating little respect in the community. In some parts of the world, this ancient prejudice against tanners exists even as of this writing (ca 1994). The tanner in primitive societies was limited to making leather using the hides or skins available locally. Tanning materials were also limited to those in local supply. Techniques were dependent on the climate as well as avadabihty of materials. The leather made was for local needs. 

Unha.iring, Unhairing can be done either by a hair save or a hair pulp system. The hair pulp system is preferred by most tanners for its speed and labor efficiency. In the hair pulp system the hides are treated with sodium sulfide (sulfhydrate) and lime (calcium hydroxide). The hair is quickly destroyed by the strong alkaline reducing conditions. 

For deliming, ammonium salts and acids are used. The proportion of ammonium salts to acids and the type of acids employed is a matter of the tanner s choice. The acid neutralizes the lime, Ca(OH)2, thereby adjusting the pH. The ammonium salts have two functions to buffer the solution to a pH required for bating, and to form calcium ammonium complexes. The acidity and the complex formation solubilize the calcium and serve to bring the hide to the desired pH. 

The usual procedure in the manufacture of chrome-tanned leathers is the use of a continuous bate, pickle, and tan method. The hides or skins remain in the dmm from the lime washing through the chrome tanning stages. The entire process usually takes about 22—24 hours. The bate, pickle, and tan can be done faster, but most tanners find that a one-day cycle fits well into production scheduling and results in a quaUty leather. 

American Association of Textile Chemists and Colorists P.O. Box 12215 Research Triangle Park, NC 27709 Inter-Society Color Council U.S. Army Natick R D Center Att STRNC-ITC Natick, Mass. 01760 Friction Materials Friction Materials Standards Institute E210, Route 4 Paramus, NJ 07652 Feather Tanners Council of America 2501 M Street, NW Washington, D.C. 20037... 

R. I. Tanner, Engineering Rheology Clarendon Press, Oxford, U.K., 1986. 

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