PLANE SURFACE SUDDENLY SET IN MOTION IN A VISCOELASTIC FLUID WITH FRACTIONAL MAXWELL MODEL

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.

Study of Rheological Characterization of Fenugreek Gum with Modified Maxwell Model

Taking into account the viscoelasticity of the fenugreek gum, a modified Maxwell model in terms of fractional derivatives is developed. Using this model, it is observed that the fenugreek gums with at least two different concentrations obey the Cox-Merz rule.

Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model （Maxwell model） for two-phase porous materials is presented, serving an explicit thermo-physicM basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combi- nation of reduced effective heat flow area and elongated heat transfer distance （thermal tortuosity）.

Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.

Heat Transfer in MHD Flow of Maxwell Fluid via Fractional Cattaneo-Friedrich Model:A Finite Difference Approach

The idea of fractional derivatives is applied to several problems of viscoelastic fluid.However,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of these problems are linear.The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations.Most importantly,in the nonlinear problems,either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems(without developing the fractional model even using artificial replacement)are solved.These problems were mostly solved for steady-state fluid problems.In the present article,studied unsteady nonlinear non-Newtonian fluid problem(Cattaneo-Friedrich Maxwell(CFM)model)and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations;in other words,the artificial replacement of the classical derivatives with fractional derivatives is not done,but in details,the fractional problem is modeled from the fractional constitutive equations.More exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid(FMF)over an inclined plate with variable velocity and the temperature is studied.The Caputo time-fractional derivative model(CFM)is used in the governing equations.The proposed model is numerically solved via finite difference method(FDM)along with L1-scheme for discretization.The numerical results are presented in various figures.These results indicated that the fractional parameters significantly affect the temperature and velocity fields.It is noticed that the temperature field increased with an increase in the fractional parameter.Whereas,the effect of fractional parameters is opposite on the velocity field near the plate.However,this trend became like that of the temperature profile,away from the plate.Moreover,the velocity field retarded with strengthening in the magnetic parameter due to enhancement in Lorentz force.However,this effect reverses in the case of the temperature profile.

A Maxwell Demon Model Connecting Information and Thermodynamics

In the past decades several theoretical Maxwell＇s demon models have been proposed to exhibit effects such as refrigerating, doing work at the cost of information, and some experiments have been carried out to realize these effects. We propose a model with a two-level demon, information represented by a sequence of bits, and two heat reservoirs. The reservoir that the demon is interacting with depends on the bit. When the temperature difference between the two heat reservoirs is large enough, the information can be erased. On the other hand, when the information is pure enough, heat transfer from one reservoir to the other can happen, resulting in the effect of refrigeration. Genuine examples of such a system are discussed.

Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model

This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.

EXPERIMENTAL STUDY ON THE LOAD DECAY AND ITS EFFECT ON LEAK RATE OFO-RING

Experimental studies on load decay and leak rate of O-rings made of two kindsof silicone rubber are conducted. The results show that the characteristic of load decay isrelative to the material and temperature of O-rings; the rate of load decay increases with the riseof temperature; the effects of load decay on leak rate of O-rings are negligible at roomtemperature, but they are notable at high temperature, and they are related to the material ofO-rings. On the basis of study on the theory of load decay and analysis to the results ofexperiments, a theoretical model is developed to describe the load decay characteristic of O-rings,and it matches the experimental data very well. By the study of time-temperature equivalence of loaddecay, the interconvertting equation of test data of load decay at different temperatures isobtained.

Mechanism behind Time Dependent Elasticity of Crumb Rubber-Nano-Asphalt Hybrids Using Discrete Relaxation Spectrum

Crumb rubber powder is a successfully used renewable material obtained from waste tire rubber,which has been incorporated into paving asphalt since the 1930s due to its good resistance to deformation and fatigue as well as its eco-friendly performance.In this study,carbon nanotubes and nano silica were incorporated into the terminal blend crumb rubber modified asphalt technology to remedy the issues of excessive desulfurization and degradation of ground tyre rubber with this technology.The mechanism behind the high temperature delayed elastic properties of the crumb rubber-nano-asphalt hybrids was experimentally investigated based on discrete relaxation spectrum.Development of the discrete relaxation spectra was accomplished by fitting on the 60℃ storage modulus data tested by the dynamic shear rheometer using the generalized Maxwell model.Subsequently,the feasibility of characterizing delayed asphalt elasticity using main relaxation time was verified by test results from the 60℃ creep and recovery test.Results indicated that the crumb rubber-nano-asphalt hybrids exhibited arrheodictic behavior and the asphalt elasticity was strengthened by two nano agents.Moreover,the elasticity reinforcement with carbon nanotubes was greater than with nano silica.Additionally,a good correlation was observed between the 60℃ zero shear viscosity and main relaxation time,and greater 60℃ zero shear viscosity was correlated to longer main relaxation times.Furthermore,longer main relaxation time of the asphalt was related to greater average recovery rate in the creep and recovery test.This research is expected to shed some light on the mechanism behind time-dependent elasticity of crumb rubber modified asphalt from the perspective of polymer physics.

An analytic solution describing the visco-elastic deformation of coal pillars in room and pillar mine

Coal pillar deformation is typically nonlinear and time-dependent. The accurate prediction of this defor- mation has a vital importance for the successful implementation of mining techniques. These methods have proven very important as a way to excavate coal resources from under buildings, railways, or water bodies. Elastic and visco-elastic theory are employed with a Maxwell model to formulate an analytic solution for displacement of coal pillars in room and pillar mine. These results show that the visco-elastic solution adequately predicts the coal pillar deformation over time. We conclude that the visco-elastic solution can predict the coal pillar and roadway displacement from the measured geological parameters of the conditions in situ. Furthermore, this method would be useful for mine design, coal pillar support optimization, ground subsidence prediction, and coal pillar stability analysis.

A revisit of strain-rate frequency superposition of dense colloidal suspensions under oscillatory shears

Strain-rate frequency superposition(SRFS) is often employed to probe the low-frequency behavior of soft solids under oscillatory shear in anticipated linear response. However, physical interpretation of an apparently well-overlapped master curve generated by SRFS has to combine with nonlinear analysis techniques such as Fourier transform rheology and stress decomposition method. The benefit of SRFS is discarded when some inconsistencies of the shifted master curves with the canonical linear response are observed. In this work, instead of evaluating the SRFS in full master curves, two criteria were proposed to decompose the original SRFS data and to delete the bad experimental data. Application to Carabopol suspensions indicates that good master curves could be constructed based upon the modified data and the high-frequency deviations often observed in original SRFS master curves are eliminated. The modified SRFS data also enable a better quantitative description and the evaluation of the apparent structural relaxation time by the two-mode fractional Maxwell model.

Fitting methods for relaxation modulus of viscoelastic materials

Based on viscoelastic theory, two new computational methods of solving linear equations and minimum value of the l-norm were put forward for transforming Kohlransch-William-Watts （KWW） function of viscoelastic materials to the generalized Maxwell model. The computational methods for the Maxwell model fitting were achieved in MATLAB software. It is found that fitting precision of the two methods is very high. The method of solving linear equations needs more fitting points and more numbers of Maxwell units. It makes the program of finite element analysis complex. While the method of solving minimum value of 1-norm can obtain very high precision only using less fitting points. These methods can fit not only experimental curve of KWW function, but also the experimental data directly.

Water Absorption and Degraded Stress Relaxation Behavior in Water-Borne Anticorrosive Urethane/Epoxy Coatings

The kinetics of water absorption in water-borne anticorrosive urethane/epoxy coatings, which were actually introduced in the industrial field, are studied. It is found that the high water affinity of a water-borne coating supports a higher saturated water content, Mχ, and helps to facilitate absorption D. The three parameters of stretched exponential function called the William-Watt equation, Eo, τ, and β, are determined to fit the degraded stress relaxation behavior in the water absorption process because this function quantitatively describes the relaxing ability and has been successfully used by a number of researchers. An increasing in the water content is shown to correlate strongly with a decrease in Eo and fl early in the absorption process between Mt/M（χ） = 0 and Mt/Mχ≈ 0.5. The adhesive characteristics of the coatings are correlated with water content, and shown to exhibit higher cohesive failure in coating epoxies under saturated conditions. This suggests that water interferes with the intermolecular bonding between polymer chains which degrades the bulk materials ability to diffuse stress concentrations and reduces its overall strength.

The GMMBS Method for Time-temperature Superposition of Viscoelastic Materials

Using the time-temperature superposition principle, the dynamic properties of viscoelastic materials can be shifted to obtain a master curve. A shifting method based on the Generalized Maxwell Model （ GMMBS ） , is proposed for the time-temperature superposition process of thermo-rheological simple, linear viscoelastic materials. Experimental data points under different temperatures are all considered as a whole and expressed with one unified representation by the GMMBS, which utilizes the feature that the Generalized Maxwell Model can describe a large class of viscoelastic materials with needed accuracy. Compared with traditional overlapping window based shifting methods, the proposed constitutive model based method needn＇t judge the size or existence of the overlapping window first, and computes shift factors with useful information contained in all experimental data points. The effectiveness of the proposed method is verified by simulated data, generated from published test results, with various experimental noise levels, densities of data points and sizes of overlapping windows. It has been shown that the GMMBS is robust and accurate.

Enhanced dielectric and optical properties of nanoscale barium hexaferrites for optoelectronics and high frequency application

M-type barium hexaferrites with chemical composition Ba1-xDyxFe12-yCryO19(x = 0.0, 0.1, 0.2, and y =0.0, 0.4, 0.5) were synthesized via sol–gel auto-combustion method. The samples were pre-sintered at 400℃ for 3 h and sintered at 950℃ for 5 h. The changes in the structural, dielectric, and optical properties were studied after the substitution of Dy3+and Cr3+ions. X-ray diffraction(XRD) analysis confirms the formation of single phase hexaferrites with the absence of secondary phase. FTIR analysis gives an idea of the formation of hexaferrites with the appearance of two peaks at 438 cm-1and 589 cm-1. The field emission scanning electron micrographs(FESEM) show a combination of crystallites with large shapes close to hexagonal platelet-like shape and others with rice or rod-like shapes, whereas EDX and elemental analysis confirm the stoichiometry of prepared samples. The calculated band gap from UV-vis NIR spectroscopy spectra was found to decreases with increase in Dy3+–Cr3+substitution. The dielectric properties were explained on the basis of Maxwell–Wagner model. Enhancement of dielectric constant at higher frequencies was observed in all the samples. Low dielectric loss is also observed in all the samples and Cole–Cole plot shows that grain boundary resistance(Rgb) contribute most to the dielectric properties. The prepared samples exhibit properties that could be useful for optoelectronics and high frequency application.

Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation

Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large class of exist-ing mixed conformingfinite elements for elasticity in the spatial discretization.In the fully discrete scheme,a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables.Error estimates of the semi-discrete and fully discrete schemes,as well as an unconditional stability result for the fully discrete scheme,are derived.Numerical experiments are provided to verify the theoretical results.

Viscoelastic modeling of the stress relaxation behavior for the bionic extracellular matrix polymer scaffold

Viscoelasticity of the extracellular matrix(ECM)plays a critical part in controlling cell behavior.However,the structure-related viscoelasticity of the synthetic ECM and its mechanism are rarely reported.Due to its high tissue similarity,synthetic ECM with structural anisotropy and viscoelasticity holds a great promise for structure and function correlation studies.Here,we reported a series of synthetic composite hydrogel-based ECM with different levels of anisotropic orientation and viscoelastic properties through recently developed post-treatment procedures(the confined pre-strain stretching and drying procedure,the soaking salt solution procedure,and the synergetic sequences of two procedures).Further,by establishing a multimode Maxwell viscoelastic mechanic model,the stress relaxation behavior of the bionic ECM with different levels of anisotropic orientation and viscoelastic properties was simulated successfully.The characteristic viscoelastic parameters of the bionic ECM could also be calculated exactly.This study presented a novel viscoelastic mechanic model for mimicking the key ECM features of the synthetic ECM with anisotropic structure and viscoelasticity properties.

Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study

Mathematical model for Maxwell fluid flow in rotating frame induced by an isothermal stretching wall is explored numerically. Scale analysis based boundary layer approximations are applied to simplify the conservation relations which are later converted to similar forms via appropriate substitutions. A numerical approach is utilized to derive similarity solutions for broad range of Deborah number. The results predict that velocity distributions are inversely proportional to the stress relaxation time. This outcome is different from that observed for the elastic parameter of second grade fluid. Unlike non-rotating frame, the solution curves are oscillatory decaying functions of similarity variable. As angular velocity enlarges, temperature rises and significant drop in the heat transfer coefficient occurs. We note that the wall slope of temperature has an asymptotically decaying profile against the wall to ambient ratio parameter. From the qualitative view point, temperature ratio parameter and radiation parameter have similar effect on the thermal boundary layer. Furthermore, radiation parameter has a definite role in improving the cooling process of the stretching boundary.A comparative study of current numerical computations and those from the existing studies is also presented in a limiting case. To our knowledge, the phenomenon of non-linear radiation in rotating viscoelastic flow due to linearly stretched plate is just modeled here.

FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell （UCM） fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method （FVM） in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number （We）, further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweeo efficiency.