L.F. del Castillo

The role of viscous flow in theories of membrane transport

Abstract The effects of viscous flow on membrane transport have recently been consistently included in both a macroscopic thermodynamic theory and a statistical-mechanical theory. These two theories are here shown to be essentially equivalent, and applicable to gases as well as to liquids. The results apply to both isothermal and non-isothermal transport, but the thermal gradient terms play no essential role and are included only for completeness. Several consequences of the proper inclusion of viscous flow are explored. One is that viscous flow terms can either be written explicitly in the transport equations, or else the viscosity coefficient can be concealed in diffusion-like transport coefficients. A more surprising consequence is related to semipermeability and Onsager reciprocity. If nonseparative viscous flow is assumed, then semipermeable behavior cannot be attained by simple manipulation of transport coefficients, because the viscous flow channel provides a permanent leak for all species. But if the idea of separative viscous flow is introduced to remedy this apparent defect, then Onsager reciprocity is lost. In fact, Onsager reciprocity will usually be lost whenever the structure or behavior of a membrane system is sufficiently complex to require extra parameters for the description of transport. Such extra parameters require the breaking of the symmetry of the transport coefficients.

Generalization of membrane reflection coefficients for nonideal, nonisothermal, multicomponent systems with external forces and viscous flow

Abstract The notion of reflection coefficients is generalized from dilute ideal solutions to apply to virtually any kind of solution and any kind of membrane whose properties are not affected by the solution. The crucial points in the generalization are the selection of a suitable definition of partial osmotic pressure and the inclusion of separative viscous flow as a transport mechanism (necessary to obtain the correct semipermeability limit). The latter can lead to loss or concealment of Onsager reciprocity, so that the reflection coefficients for volume flow and for solute fluxes are not necessarily equal. Two choices of reference state are presented: the traditional choice of zero reflection coefficient for solvent volume flow, and a more symmetric choice of an average reflection coefficient equal to zero. Several examples are worked out for binary and ternary solutions and compared with results from experiments and from model calculations. Thermal gradients are included for completeness, but play no essential role in the reflection coefficients. The development is given entirely in terms of differential equations of transport, and problems and inconsistencies associated with the use of finite-difference equations are briefly discussed.

Nonequilibrium chemical potential and shear-induced migration of polymers in dilute solutions

We consider the contribution of a nonequilibrium chemical potential depending on the shear rate on shear-induced polymer migration. It is seen that this nonequilibrium contribution strongly enhances, above a threshold of polymer concentration and of shear rate, the migration of the polymer towards the regions with lower stress. This enhancement may explain why the migration rate experimentally observed is much higher than that predicted by constitutive laws where the nonequilibrium effects on the chemical potential are ignored.

Shear induced polymer migration: analysis of the evolution of concentration profiles

In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient. From this model of coupling between diffusion and viscous pressure, together with the mass balance equation, we derive some general features of the concentration profile, the temporal behavior of the polymer concentration near the apex of the cone and some relevant trends of the dynamical process of polymer migration.

Potential of particle and fibre reinforcement of tyre tread elastomers

Abstract In an attempt to increase resilience and reduce energy losses in tyre materials, glass and carbon fibres, as well as granular material (sand), were studied as possible reinforcements for treads. The matrix was either natural or synthetic rubber with either carbon black or silica. It was found that beach sand is an effective promoter of resilience, particularly in the case of a natural rubber matrix with either carbon black or silica. The best result was obtained with carbon black and 6% sand impregnated with an adhesive. Tests were carried out to determine Youngs modulus in tension and compression. The three reinforcing materials increased both moduli, as well as Shore hardness. Tests were also performed to determine friction coefficients against dry pavement and also to obtain a rough estimate of wear resistance.

Fluids with internal degrees of freedom. I. Extended thermodynamics approach

Extended irreversible thermodynamics (EIT) is used to derive a complete set of time evolution equations for the state variables describing a general polyatomic fluid. The internal degrees of freedom of the fluid are represented by suitable nonconserved variables. In particular, these time evolution equations are shown to resemble relaxation‐type equations. The sign of the unknown coefficients included in such equations is undetermined. However, when a comparison is made with the results obtained from the moment solution method of a kinetic equation for a dilute polyatomic fluid, several of the general features of the phenomenological results are clarified. Indeed, the predictions of kinetic theory fully agree with the basic equations of EIT. This provides a mesoscopic foundation for the theory. The sign of the unknown coefficients appearing in the relaxation‐type equations for the nonconserved variables is such that the corresponding relaxation times are positive definite. Therefore, such equations are in...

Linear viscoelasticity and irreversible thermodynamics

The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.

A thermodynamic model for shear-induced concentration banding and macromolecular separation

We present a simple thermodynamic model for shear-induced concentration banding in polymer solutions, based on a nonequilibrium chemical potential depending on the shear rate. This dependence provides a coupling between diffusion and shear, besides the more classical coupling provided by the divergence of the viscous pressure tensor. When both couplings are taken into account, shear-induced concentration banding appears in a natural way. If the initial homogeneous concentration is higher than a threshold value, shear banding appears for sufficiently high value of the shear rate γ; if the initial concentration is lower, the steady-state concentration profile under shear is smooth. The banding profile depends on the polymer molecular mass and therefore it provides a basis for the chromatographic separation of polymers of different molecular mass.

Dielectric relaxation in polar and viscoelastic fluids with internal rotation

Using the formalism of extended irreversible thermodynamics we derive the generalized constitutive equations for the polarization vector and the symmetric and antisymmetric parts of the total stress tensors (the sum of the Maxwell and viscous stress tensors) of a viscoelastic polar fluid. The analysis of these equations shows several interesting features for a permanent dipolar system. The diffusive transport of polarization charge and the diffusion of the transverse polarization component are two elementary physical processes in terms of which complex cases of dielectric relaxation can be described, taking into account both translational and rotational motions of the dipolar particles in a viscoelastic fluid. The calculations for several cases of the complex dielectric susceptibility are presented. In these results, the coupling between polarization and hydrodynamics predicts several modes of dielectric energy dissipation. These various channels are due to the intimate coupling between different degrees ...

Dielectric relaxation in polar and viscoelastic fluids

The generalized evolution equations for the polarization vector and the total stress tensor (viscous plus Maxwell’s electric stress tensors) are obtained in the framework of extended irreversible thermodynamics. The coupling of these equations represents the mutual influence between mechanical and dielectric properties of a viscoelastic and dielectric fluid. The dipolar memory and the associated correlation functions are discussed in order to give an understanding in the current way of thinking based on linear response theory. A comparison with studies of polarization charge diffusion is included as a particular result obtained from the generalized constitutive equations. Calculations of the complex electric susceptibility and the complex viscosity for the linear and incompressible case are presented.