J. L. Tevaarwerk

Bio: J. L. Tevaarwerk is an academic researcher from University of Cambridge. The author has contributed to research in topics: Constitutive equation & Linear elasticity. The author has an hindex of 2, co-authored 2 publications receiving 477 citations.

Shear behaviour of elastohydrodynamic oil films

Abstract: A simple constitutive equation is proposed for the isothermal shear of lubricant films in rolling/sliding contacts. The model may be described as nonlinear Maxwell, since it comprises nonlinear viscous flow superimposed on linear elastic strain. The nonlinear viscous function can take any convenient form. It has been found that an Eyring 'sinh law' fits the measurements on five different fluids, although the higher viscosity fluids at high pressure are well described by the elastic/perfectly plastic equations of Prandtl-Reuss. The proposed equation covers the complete range of isothermal behaviour: linear and nonlinear viscous, linear viscoelastic, nonlinear viscoelastic and elastic/plastic under any strain history. Experiments in support of the equations are described. The nonlinear Maxwell constitutive equation is expressed in terms of three independent fluid parameters: the shear modulus $G$, the zero-rate viscosity $\eta $ and a reference stress $\tau _{0}$. The variations of these parameters with pressure and temperature, deduced from the experiments, are found to be in broad agreement with the Eyring theory of fluid flow.

Shear behaviour of elastohydrodynamic oil films

Abstract: A simple constitutive equation is proposed for the isothermal shear of lubricant films in rolling/sliding contacts. The model may be described as nonlinear Maxwell, since it comprises nonlinear viscous flow superimposed on linear elastic strain. The nonlinear viscous function can take any convenient form. It has been found that an Eyring 'sinh law' fits the measurements on five different fluids, although the higher viscosity fluids at high pressure are well described by the elastic/perfectly plastic equations of Prandtl-Reuss. The proposed equation covers the complete range of isothermal behaviour: linear and nonlinear viscous, linear viscoelastic, nonlinear viscoelastic and elastic/plastic under any strain history. Experiments in support of the equations are described. The nonlinear Maxwell constitutive equation is expressed in terms of three independent fluid parameters: the shear modulus $G$, the zero-rate viscosity $\eta $ and a reference stress $\tau _{0}$. The variations of these parameters with pressure and temperature, deduced from the experiments, are found to be in broad agreement with the Eyring theory of fluid flow.

On a hierarchy of approximate models for flows of incompressible fluids through porous solids

Abstract: The celebrated equations due to Fick and Darcy are approximations that can be obtained systematically on the basis of numerous assumptions within the context of mixture theory; the equations however not having been developed in such a manner by Fick or Darcy. Relaxing the assumptions made in deriving these equations via mixture theory selectively leads to a hierarchy of mathematical models and it can be shown that popular models due to Brinkman, Biot and many others can be obtained via various approximations. It is shown that a variety of other generalizations are possible in addition to those that are currently in favor, and these might be appropriate for describing interesting technological applications.

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Abstract: Viscosities η and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TVγ, where the exponent γ is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of γ for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing γ in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) wi...

The Rheological Properties of Elastohydrodynamic Lubricants

Abstract: The methods of measuring the rheological properties of EHD lubricants are reviewed, but for pressures in excess of 1.0 GPa there is currently no simple alternative to the disc machine. A technique has been developed which enables disc machine traction tests to be carried out at constant mean film temperature. Isothermal tests provide further evidence for the existence of a limiting shear stress τc at which the fluid shears in the manner of a plastic solid. At stresses below this limit the experimental data are found to be in very good accord with the non-linear Maxwell rheological model based on the Eyring theory of fluid flow proposed by Johnson and Tevaarwerk and by Hirst and Moore. The model incorporates three fluid properties: shear modulus G, viscosity τ and Eyring stress τ0. Disc machine measurements of τ, τ0 and the limiting shear stress τc for three fluids—a mineral oil HVI 650, a synthetic polyphenyl ether 5P4E and a traction fluid Santotrac 50—are presented for a range of pressures (0.6–2.5 GPa)...