A new constitutive equation derived from network theory
TL;DR: In this paper, a constitutive equation is derived from a Lodge-Yamamoto type of network theory for polymeric fluids, where the network junctions are not assumed to move strictly as points of the continuum but allowed a certain "effective slip".
Abstract: A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.
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AT&T1
TL;DR: In this article, the authors present a review of the latest developments as well as earlier work in this area, organized into the following categories: Taylor-Couette flows, instabilities in cone and plate-and-plate flows, parallel shear flows, extrudate distortions and fracture, Instabilities in shear flow with interfaces, extensional flows, and thermohydrodynamic instabilities.
Abstract: Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.
883 citations
01 Nov 2011
TL;DR: In this paper, the authors introduce colloid science and rheology, and present an overview of colloid physics and its applications in viscoelastic media. But they do not discuss the role of non-spherical particles.
Abstract: 1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.
792 citations
TL;DR: It is demonstrated that viscoelasticity can reduce turbulence and suppress cavitation, and subsequently increase the injector’s volumetric efficiency.
Abstract: We identify the physical mechanism through which newly developed quaternary ammonium salt (QAS) deposit control additives (DCAs) affect the rheological properties of cavitating turbulent flows, resulting in an increase in the volumetric efficiency of clean injectors fuelled with diesel or biodiesel fuels. Quaternary ammonium surfactants with appropriate counterions can be very effective in reducing the turbulent drag in aqueous solutions, however, less is known about the effect of such surfactants in oil-based solvents or in cavitating flow conditions. Small-angle neutron scattering (SANS) investigations show that in traditional DCA fuel compositions only reverse spherical micelles form, whereas reverse cylindrical micelles are detected by blending the fuel with the QAS additive. Moreover, experiments utilising X-ray micro computed tomography (micro-CT) in nozzle replicas, quantify that in cavitation regions the liquid fraction is increased in the presence of the QAS additive. Furthermore, high-flux X-ray phase contrast imaging (XPCI) measurements identify a flow stabilization effect in the region of vortex cavitation by the QAS additive. The effect of the formation of cylindrical micelles is reproduced with computational fluid dynamics (CFD) simulations by including viscoelastic characteristics for the flow. It is demonstrated that viscoelasticity can reduce turbulence and suppress cavitation, and subsequently increase the injector’s volumetric efficiency.
704 citations
TL;DR: In this article, a new mixed finite element method for computing viscoelastic flows is presented based on the introduction of the rate of deformation tensor as an additional unknown.
Abstract: A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the rate of deformation tensor as an additional unknown. Contrary to the popular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. Non-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is performed into the constitutive equation. Hence, the described method can be used to compute solutions of rheological models where the EVSS method does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm. The stability and the robustness of the method are investigated on two benchmark problems: the 4:1 contraction flow problem and the stick-slip flow problem. Numerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Newtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheology, 33 (1989) 207] models show that our method is remarkably stable and cheap in computer time and memory.
461 citations
TL;DR: In this article, a complete rheological equation of state for dilute polymer solutions is obtained by modelling the polymer molecules as bead-spring chains, in which the springs are finitely extensible.
Abstract: A complete rheological equation of state for dilute polymer solutions is obtained by modelling the polymer molecules as bead—spring chains, in which the springs are finitely extensible. Hydrodynamic interactions among the beads are accounted for approximately by using the equilibrium-averaged Oseen tensor as in the Zimm theory. The rheological equation of state thus obtained may be regarded as an extension of the Lodge—Wu equation. Consequently, it incorporates all the good features of the Zimm theory, but it can describe nonlinear viscoelastic phenomena as well, such as monotone decreasing shear-rate-dependent viscosity. Comparisons with experimental data on shear flows are encouraging.
393 citations
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TL;DR: In this article, the authors derived the stress-strain-time (S − S − T )relation at each instance of macroscopic observations by using the statistical mechanical considerations of equilibrium states.
Abstract: Many kinds of amorphous high polymer substances show the non-ideal rheological behaviours even in the “static” observations. In this paper, the general stress-strain-time relation and energy of dissipation of these systems are treated by adopting the modified rubber-like network model in which the junctions connecting the polymer chains break up and reform continually. The probability of the breakage of the junction, namely the breakage of the chain, per unit time is not a constant but a functions of both the number of segments which construct the chain and the end-to-end distance of the chain. It is assumed that the velocities of deformation of the system and of the change of the situation of network structure are extremely slower than those of the micro-Brownian movements of polymer segments. Therefore the statistical mechanical considerations of equilibrium states may be used to derive the stress-strain-time ( S – S – T )relation at each “instance” of macroscopic observations. From our general expressi...
272 citations
TL;DR: In this article, constitutive equations based on the network models of Yamamoto, Lodge, and Kaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum.
Abstract: In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by alternative assumptions concerning the creation and loss of network segments, and the theory is extended to non-Gaussian networks.Kayes theory is extended to allow for the presence of entanglement junctions of different complexities.
211 citations
TL;DR: In this paper, the authors used the continuum theory of anisotropic fluids, as developed by Ericksen and others, to formulate an expression for the time derivative of the end-to-end vector of a linear macromolecule when used in conjunction with the equation describing the distribution function for a dilute solution of dumbbell elements.
Abstract: The continuum theory of anisotropic fluids, as developed by Ericksen and others, has been used to formulate an expression for the time derivative of the end‐to‐end vector of a linear macromolecule When this expression is used in conjunction with the equation describing the distribution function for a dilute solution of dumbbell elements, the results exhibit important differences from the usual dumbbell theory Presence of an additional term in the differential equation for the distribution function leads to the prediction of both a non‐Newtonian viscosity and nonzero first and second normal stress differences in simple shearing flow The normal stress differences are found to be of opposite sign, the secondary normal stress difference being negative In small‐amplitude oscillatory shear flow, and in pure deformational flow, the results are equivalent to those of the dumbbell theory Expressions are presented for both stress and optical properties in an arbitrary homogeneous shear field
155 citations