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We study theoretically the steady viscoelastic flow in confined and symmetric hyperbolic channels considering slip along the walls. Under the lubrication approximation and a variety of constitutive models, a high-order perturbation solution with respect to the Deborah number is calculated. The solution for all the field variables (velocity, pressure, and extra-stress) is found analytically up to eighth order and is used along with proper acceleration techniques to achieve convergence up to order one Deborah number. We reveal that even in the presence of slip, the pressure drop decreases monotonically with increasing the fluid elasticity. We evaluate the influence of slip in terms arising from two different decompositions of the pressure drop obtained with the aid of the total force balance and the mechanical energy balance of the flow system. In contrast to the nonslip Newtonian flow, our analysis also showed that the fluid slip along the walls introduces variations in the strain rate at the midplane with the distance from the inlet. However, these are small, and an effective strain rate can be well-represented using a previously developed formula [Housiadas, K. D., and A. N. Beris, Phys. Fluids 36(2), 021702 (2024)]. We also show that when the solution for the midplane velocity is used in the general formula for the Trouton ratio, instead of the Newtonian lubrication solution, there are no appreciable changes, thus confirming the validity and accuracy of our previously reported results [Housiadas, K. D., and A. N. Beris, J. Rheol. 68(3), 327–339 (2024)]. [ABSTRACT FROM AUTHOR]

We study theoretically the elongational viscosity (or Trouton ratio, in dimensionless form) for steady viscoelastic flows in confined and symmetric hyperbolic tubes considering Navier-type slip along the wall(s). Both the planar and the cylindrical axisymmetric geometrical configurations are addressed. Under the classic lubrication approximation, and for a variety of constitutive models such as Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic with the Peterlin approximation models, the same general analytical formula for the Trouton ratio is derived as for the Oldroyd-B model, in terms of the velocity at the midplane/axis of symmetry and the Deborah number only. Assuming that the velocity field is approximated by the Newtonian lubrication profile, based on our previous study in the absence of slip, we show that a constant extensional strain rate can be achieved in the limits of zero or infinite slip. For finite slip, a slight modification of the geometry is required to achieve a constant strain rate. In these cases, the formula for the steady state Trouton ratio reduces to that for transient homogeneous elongation. We also provide analytical formulae for the modification (decrease) for both the extensional strain rate and the Hencky strain achieved in the confined geometries because of introducing wall slip. [ABSTRACT FROM AUTHOR]

We present new theoretical developments on the incompressible viscoelastic flow of an Oldroyd-B fluid in a hyperbolic contracting symmetric channel. We show uniformity of the effect of viscoelasticity in hyperbolic planar and cylindrical axisymmetric geometries by revealing a modified Deborah number according to which the lubrication solutions for the pressure drop and the Trouton ratio are simplified. We also develop an expression for the Trouton ratio in terms of the fluid velocity at the midplane only, valid beyond the lubrication limit. Using the Newtonian velocity as a first approximation, we show the enhancement of the Trouton ratio with increasing the fluid elasticity. [ABSTRACT FROM AUTHOR]

We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material. [ABSTRACT FROM AUTHOR]

We investigate theoretically the steady incompressible viscoelastic flow in a hyperbolic contracting channel. The fluid viscoelasticity is modeled using the upper convected Maxwell (UCM), Oldroyd-B, Phan-Thien and Tanner (PTT), Giesekus, and the finite elasticity non-linear elastic dumbbell with the Peterlin approximation (FENE-P) models. We first develop the general governing equations for flow within a non-deformable channel whose cross section varies with the distance from the inlet. We then exploit the classic lubrication approximation, assuming a small aspect ratio of the channel to simplify the original governing equations. The final equations, which we formulate in terms of the stream unction, are then solved analytically using a high-order asymptotic scheme in terms of the Deborah number, De, and the formulas for the average pressure drop are derived up to eight orders in De. The accuracy of the original perturbation solution is enhanced and extended over a wide range of parameters by implementing a convergence acceleration method for truncated series. Furthermore, convergence of the transformed solutions for the average pressure drop is demonstrated. The validity and accuracy of the theoretical results is independently confirmed through comparison with numerical results from simulations performed using high-order finite differences and pseudospectral methods. The results reveal the decrease in the average pressure drop with increasing the Deborah number, the polymer viscosity ratio, and the ratio of the inlet to the outlet height. We also show that the fundamental UCM and Oldroyd-B models can predict the major viscoelastic phenomena for this type of internal and confined lubrication flows, while the effect of the rheological parameters of the PTT, Giesekus, and FENE-P models on the results is minor. [ABSTRACT FROM AUTHOR]

An improved population balance‐based rheological constitutive framework for polydisperse aggregating suspensions is derived by incorporating detailed models for orthokinetic and perikinetic aggregation and shear breakage processes. The framework accounts for critical properties such as dynamic arrest, viscoelasticity, kinematic hardening, thixotropy, and yield stress to generate a full range of thixotropic elasto‐viscoplastic (TEVP) response. Additionally, the model is thermodynamically consistent because the dynamics and timescales are completely determined by internal structural and kinetic variables. The model connects the rheological response to the structural descriptors such as the size distribution of agglomerates, mean sizes, fractal dimension, and agglomerate volume fraction. Predictions are compared against a wide range of shear rheology measurements data for model thixotropic suspensions of fumed silica and carbon black, including large amplitude oscillatory shear (LAOS), as well as ultra‐small angle neutron scattering under steady shear (Rheo‐uSANS). [ABSTRACT FROM AUTHOR]

This historical study deepens the rheologist’s understanding of the motto of The Society of Rheology, of its history, and of its many typographies. The motto “παντα ῥει̃” is not verbatim something written or said by the ancient Greek Ionian philosopher Heraclitus, ca. 540- 480 BCE. Rather it is first encountered much later, in the writings of the Roman Simplicius ca. 490- 560CE. Thus, although it is uniformly agreed by Greek scholars that it correctly and concisely distills Heraclitian philosophy, that of constant change, and although this is appropriately used as the motto of The Society of Rheology, there is little point in trying to rewrite it into another form (for example to capitalize it) in an effort to be more faithful to an ancient prototype. Rather, we suggest simply reinstating the two missing diacritical marks, and thus, to express it as “πάντα ῥει̃“ which is the form in which the motto was introduced in 1929. This is also consistent with current typography of ancient Greek writings, in use since the ninth century CE, following the byzantine scholars. We provide Table 1 to facilitate accurate typesetting of the motto.

Starting from a suspension of elastic dumbbells or chain-like particle aggregates as a simple model of a viscoelastic liquid, the rheological equation of state is inductively derived into which the concept of an "elastic strain component" (recoverable strain) is incorporated and can be understood as a nonlinear extension of the so-called "generalized Maxwell model." Here, the liquid is characterized by a sequence of nested continua, each associated with an elasticity law. The consideration of the directional dependence of the mobility of the structural elements requires that the behavior of the liquids represented in this way generally deviates from a Weissenberg liquid. [ABSTRACT FROM AUTHOR]

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes. [ABSTRACT FROM AUTHOR]

In the present work, the macroscopic governing equations governing the heat and mass transfer for a general multicomponent system are derived via a systematic nonequilibrium thermodynamics framework. In contrast to previous approaches, the relative (with respect to the mass average velocity) component mass fluxes (relative species momenta) and the heat flux are treated explicitly, in complete analogy with the momentum flux. The framework followed here, in addition to allowing for the description of relaxation phenomena in heat and mass transfer, establishes to the fullest the analogy between all transport processes, momentum, heat, and mass transfer, toward which R. B. Bird contributed so much with his work. The inclusion of heat flux-based momentum as an additional variable allows for the description of relaxation phenomena in heat transfer as well as of mixed (Soret and Dufour) effects, coupling heat and mass transfer. The resulting models are Galilean invariant, thereby resolving a conundrum in the field, and always respect the second law of thermodynamics, for appropriate selection of transport parameters. The general flux-based dynamic equations reduce to the traditional transport equations in the limit when mass species and heat relaxation effects are negligible and are fully consistent with the equations established from the application of kinetic theory in the limit of dilute gases. As an added benefit, for the particular example case of hyperbolic diffusion we illustrate the application of the proposed models as a method to allow the use of powerful numerical solvers normally not available for solving mass transfer models more generally. [ABSTRACT FROM AUTHOR]

In Ref. [1], there was an error in the second integral of Eq. (14) due to an erroneous application of Eq. (A3) in Appendix A of that paper. Correction of the above error requires consideration of a more general expression for the gradient of the chemical potential HT ht (obtained from a general equilibrium thermodynamics reference, such as Refs. Note that only when this error is corrected, the (correct) equation for the time evolution for the entropy density, Eq. (29) of Ref. [1], can be derived. [Extracted from the article]

The effect of a spatially dependent viscosity in the unbounded flow around a rigid spherical particle that translates with constant velocity is investigated theoretically. The variable viscosity emulates the effect of a variable concentration of an additive material in a simple solvent. The analysis is performed utilizing a smooth function for the viscosity of the additive material, which can describe qualitatively both depletion and accumulation phenomena around the particle. Assuming steady state, creeping and isothermal conditions, and no external forces and torques, the momentum and mass balances are a generalization of the classical Stokes equations for which the linearity is preserved. Manipulating suitably the governing partial differential equations, a single ordinary integrodifferential equation for the radial part of the radial velocity component is derived. This equation is solved either numerically using a Chebyshev pseudospectral method or analytically using an asymptotic technique. A decrease in the total drag on the particle as the additive material increases is predicted in the depletion case. In the accumulation case, the total drag may increase or decrease in comparison to the simple Newtonian fluid. Analysis of the total drag to its individual contributions reveals that the friction drag (due to viscous forces) is affected substantially by the change of the viscosity, while the form drag (due to pressure) varies much smoother and milder. Finally, we investigate under which conditions the variable viscosity fluid can be approximated as a constant viscosity fluid with Navier type slip at the wall. [ABSTRACT FROM AUTHOR]

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n1,e and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction φ; both n1,e and φ enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z≤2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z=2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z≤2l, continuum for distances z>2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical. [ABSTRACT FROM AUTHOR]

Explores the Poissonian character of the reversible part of the nonequilibrium dynamics to determine a dynamically consistent expression of a reptation model without the independent alignment assumption. Illustration of the compatibility of such a model with the generic formalism of nonequilibrium thermodynamics; Demonstrations of irreversibility effects.

Part II. Reports on the application to a neutral surface of a hierarchical model for surface effects on chain conformation and rheology of polymer solutions. Background on the governing equations; Static equilibrium profiles; Non-equilibrium profiles; Shear stress' enhancement of the depletion phenomena near the wall.

New in vitro measurements from two human donors for both steady and transient hemorheology are presented that are particularly suited for testing thixotropic and viscoelastic models for human blood and are made available to the community along with the relevant blood physiology. This more complete data set is analyzed within the context of recent thixo-elasto-visco-plastic models, and we improve upon the Horner-Armstrong-Wagner-Beris (HAWB) model to better model transient hemorheology. The improved model features an additional viscoelastic equation for the red blood cell rouleaux within blood, along with simplifications to the structure kinetics equation. The resulting model is fit to additional experimental data on human whole blood for a step shear change and steady shear experiments, and the corresponding parameter values are used to predict oscillatory shear moduli, transient large amplitude oscillatory shear, and unidirectional large amplitude oscillatory shear data. The modified HAWB model shows significant improvement in fitting and predicting the experimental data. Specifically, a significant overshoot is captured in step shear changes from a low shear rate to a moderate shear rate, and a plateau for the storage modulus is observed at low frequencies. Highly nonlinear behavior is observed for the third harmonic in unidirectional large amplitude oscillatory shear in the form of multiple extremum separated widely in frequency, which can be identified with the two dominant mechanisms for generating viscoelasticity in human blood, namely, rouleaux structuring and red blood cell deformation. We also discuss the potential applications and difficulties associated with the constitutive modeling of transient blood rheology and provide insight into microstructural sources of the stress contributions to the bulk flow behavior. [ABSTRACT FROM AUTHOR]