Extended Fractional-Order Jeffreys Model of Viscoelastic Hydraulic Cylinder

Novel modeling approach for viscoelastic hydraulic cylinders with negligible inertial forces is proposed based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. The comparison between the measured and computed frequency response functions and time domain transient response argue in favor of the proposed four-parameters fractional-order model.

Viscoelasticity of biomolecular condensates conforms to the Jeffreys model

ABSTRACTBiomolecular condensates, largely by virtue of their material properties, are revolutionizing biology, and yet physical understanding of these properties is lagging. Here I show that the viscoelasticity of condensates can be captured by a simple model, comprising a component where shear relaxation is an exponential function of time and a component that is purely viscous (corresponding to instantaneous shear relaxation). Modulation of intermolecular interactions, e.g., by adding salt, can disparately affect the two components, such that the exponentially-relaxing component may dominate at low salt whereas the purely viscous component may dominate at high salt. Condensates have a tendency to fuse, with the dynamics accelerated by surface tension and impeded by viscosity. For fast-fusion condensates, shear relaxation may become rate-limiting. These insights help narrow the gap in understanding between the biology and physics of biomolecular condensates.

Modeling the initial mechanical response and yielding behavior of gelled crude oil

The initial mechanical response and yielding behavior of gelled crude oil under constant shear rate conditions were investigated. By putting the Maxwell mechanical analog and a special dashpot in parallel, a quasi-Jeffreys model was obtained. The kinetic equation of the structural parameter in the Houska model was simplified reasonably so that a simplified constitutive equation of the special dashpot was expressed. By introducing a damage factor into the constitutive equation of the special dashpot and the Maxwell mechanical analog, we established a constitutive equation of the quasi-Jeffreys model. Rheological tests of gelled crude oil were conducted by imposing constant shear rates and the relationship between the shear stress and shear strain under different shear rates was plotted. It is found that the constitutive equation can fit the experimental data well under a wide range of shear rates. Based on the fitted parameters in the quasi-Jeffreys model, the shear stress changing rules of the Maxwell mechanical analog and the special dashpot were calculated and analyzed. It is found that the critical yield strain and the corresponding shear strain where shear stress of the Maxwell analog is the maximum change slightly under different shear rates. And then a critical damage softening strain which is irrelevant to the shearing conditions was put forward to describe the yielding behavior of gelled crude oil.

A Numerical Approach on New Constitutive Model for Thixotropic Substances

The thixotropic substances can be found in different industrial sectors, such as chemical, biomedical, manufacturing and oil. These substances show a rheological time-dependent behavior, dependent of their structural level. Generally, a constitutive model for the thixotropic substances is composed by a pair of coupled equations: the constitutive equation (based on viscoelastic models) and the rate equation (that describes the structural evolution). In many works presented in the specialized literature, the shear modulus and viscosity dependencies with the structural nature are not formally considered in the dynamical principles from that the constitutive equation is originated. In the present work, a new, thermodynamically consistent, constitutive model for thixotropic substances, where such dependences are considered, is presented and some rheological tests are analyzed in a numerical simulation point of view (code developed in MATLAB). The constitutive model is based on Jeffreys’ model and the coagulation theory of Smoluchowsky.

Linear shape oscillations and polymeric time scales of viscoelastic drops

We study small-amplitude axisymmetric shape oscillations of viscoelastic drops in a gas. The Jeffreys model is used as the rheological constitutive equation of the liquid, which represents a liquid with a frequency-dependent dynamic viscosity. The analysis of the time-dependent deformations caused by the oscillations yields the characteristic equation for the complex frequency, which describes the oscillation frequency and damping rate dependence on the viscous liquid behaviour and the stress relaxation and deformation retardation time scales ${\lambda }_{1} $ and ${\lambda }_{2} $ involved in the viscoelastic material law. The aim of this study is to quantify the influences of the two time scales on the oscillation behaviour of the drop and to propose an experimental method to determine one of the time scales by measuring damped oscillations of a drop. A proof-of-concept experiment is presented to show the potential and limitations of the method. Results show that values of ${\lambda }_{2} / {\lambda }_{1} $ from these measurements are orders of magnitude smaller than typical values used in simulations of viscoelastic flows.