Dynamic rheological behavior of DBS-induced poly(propylene glycol) physical gels

Physical gelation can be induced in various organic and silicone-based liquids, as well as in polymeric melts, upon addition of 1,3:2,4-dibenzylidene sorbitol (DBS). Such gels are stabilized by the formation of a percolated DBS network composed of highly interconnected nanofibrils. In this study, we explore several factors affecting the rheological properties of poly(propylene glycol) (PPG) gelled by DBS. To ascertain the effect of PPG molecular weight (M_PPG) on gel formation and rheology, we have investigated three series of DBS-induced PPG gels in which M_PPG varies from 425 g/mol to 4000 g/mol. Dynamic stress measurements reveal that the DBS concentration identifying the onset of PPG gelation decreases with increasing M_PPG. Since the solubility parameter (δ_s) of PPG decreases sharply as M_PPG increases over this M_PPG range, this observation suggests that DBS gelation is sensitive to δ_s of the matrix liquid, in agreement with previously reported data collected from DBS-gelled solvents. Moreover, the elastic modulus and yield stress are found to increase with increasing (i) DBS concentration for the three series of PPG/DBS gels examined here and (ii) recovery time after cessation of an introductory shear. Received: 22 February 2000 Accepted: 9 August 2000     

Characterization of polyacrylamide gels as an elastic model for food gels

Serving as an elastic model system for food gels, characteristics of polyacrylamide (PAAm) gels were investigated using small amplitude and large deformation rheological tests. The PAAm gels displayed elastic or viscoelastic behavior depending on network crosslink density. For elastic PAAm gels, the rheological properties obeyed the theory of rubber elasticity; whereas for viscoelastic PAAm gels, shear modulus depended on temperature. The elastic PAAm gel fracture parameters did not change with deformation rate (0.2–5.5 s^–1), indicating insignificant viscous flow during deformation. Fracture stress was correlated with gel monomer concentration, whereas the fracture strain remained constant regardless of the monomer concentration. In addition, the stress was linearly proportioned with strain up to fracture, indicating that PAAm gels did not experience finite network chain extensibility during large deformation. Consequently, the fracture of PAAm gels did not result from the extensional limitation of network chains, nor did gel fracture result from the nonlinear force–distance relationship between polymer connections. Purportedly, the fracture of PAAm gels was caused by external force overcoming the gel cohesive forces, and low strength of PAAm gels compared to rubbers caused fracture prior to experiencing nonlinear stress-strain deformation.Paper No. FSR04-20 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27695-7643. The use of trade names does not imply endorsement by the North Carolina Agricultural Research Service of products named, nor criticisms of similar ones not mentioned.     

An investigation of thermodynamic states during high-pressure fuel injection using equilibrium thermodynamics

A numerical investigation of mixing processes between an injected fuel (an n-alkane) and a chamber inert gas (nitrogen) was carried out for high-pressure fuel injection. The objective is to determine conditions for the coexistence of both liquid and gas phases under the typical ambient conditions encountered in diesel engines. A phenomenological investigation was built by coupling phase stability analysis with the energy conservation equation. Phase changes (including separation and combination) are predicted to occur so as to yield the lowest Gibbs free energy. It is also shown that predicted states without considering phase transitions can be very different from the corresponding thermodynamically correct states. By comparing four n-alkane/nitrogen mixtures it is shown that the lower limit of the two-phase region occurs at similar temperatures. However, heavy n-alkane/nitrogen mixtures have a larger upper limit, and phase separation occurs at higher temperatures. The present model predicts the existence of multiple phases locally in the dense spray jet under high temperature and pressure ambient conditions due to the significant reduction of the mixture temperature caused by vaporization and cooling.     

Physical gelation under shear for gelatin gels

Physical gelation is the process of crosslinking which reversibly transforms a solution of polymers into a gel. The crosslinks of the network have a physical origin (hydrogen bonding, Van der Waals forces... ) and therefore are sensitive to variations of temperature, pH, ionic content, etc. (non-permanent crosslinks). Physical and chemical gelation have been extensively studied in quiescent conditions, where rheology experiments have been performed to follow the network formation without disturbing the process. In this study we consider gelation of a well known physical, thermoreversible, gel (gelatin gel), which proceeds under flowing conditions. The gelling solution is submitted to a shearing, with imposed, permanent shear stresses or imposed, permanent, shear rates. Under flow, a competition arises between the formation of clusters by physical crosslinking and their disruption by the shear forces. This investigation defines the flowing conditions which either allow or impede gel formation. In particular, a critical shear rate , related to the gelation temperature and gelatin concentration, is identified which separates the two regimes. A microscopic model is proposed, based on the analysis of flow curves and dynamic measurements, which describes the structure of the gelling solution: microgel particles grow to a maximum size which depends on the flow. When the volume fraction of particles is high enough, percolation between particles occurs suddenly and a yield stress fluid is formed (particulate gel). The differences between gels made in quiescent conditions and gels made under flow are underlined.     

Limit thermodynamic model for compositional gas–liquid systems moving in a porous medium

It is shown that a multicomponent two-phase system moving through a porous medium may be described by a limit model in which the thermodynamic subsystem is totally separated from the hydrodynamics. The limit corresponds to a contrast phase mobility and a fast pressure relaxation process. The obtained limit thermodynamic model includes several differential thermodynamic equations and describes the equilibrium in an open system. The model is validated by comparing with the full compositional flow simulations. A numerical solution to the limit thermodynamic model is constructed. An application to the gas-condensate systems is compared to the full compositional model.     

A dynamic U-tube rheometer of novel design for the study of weak gels and foams

A novel rheometer based on the U-tube technique of Saunders and Ward has been developed to determine the shear moduli of very weak gels and foams. The instrument is fully automatic and operates in both static and oscillatory modes. The change of the shear modulus, with the time, was monitored in three series of samples to illustrate the performance of the instrument. The first series comprised gelatinized maize starch aqueous suspensions ranging in starch concentration from 6% to 12%. The second was a series of gelatine aqueous solutions ranging in gelatine content from 2% to 12%. The third was two commercial samples of shaving foam. The results indicated that the instrument is particularly suitable for the study of the gelation mechanism in very weak gels as well as for the study of the stability of foams in relation to time.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.     

Combustion with phase transition

The paper deals with a mathematical problem describing an exothermic chemical reaction in a diffusing substance possibly undergoing a change of phase. Global well-posedness in the classical sense is proved for the corresponding system of PDEs. Moreover, cases in which the phases are separated by sharp interphases or by transition regions are discussed. The limit case of negligible diffusion is also considered.

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Sommario Si studia il problema matematico che descrive una reazione chimica esotermica in una sostanza che diffonde e puo' subire cambiamenti di fase. Si dimostra esistenza globale in senso classico del relativo sistema di equazioni alle derivate parziali e si discute la possibilita' che le fasi siano separate da una regione di transizione e non da una netta superficie di interfase. Il caso limite di assenza di diffusione e' anche brevemente esaminato.

     

Phase field model for coupled displacive and diffusive microstructural processes under thermal loading

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible constitutive relationships and on the coupling of the numerous physical processes that are active. Phase changes are driven by temperature-dependent free-energy functions that become non-convex below a transition temperature. Higher-order spatial gradients are present in the model to account for phase boundary energy, and these terms necessitate the introduction of non-standard terms in the energy balance equation in order to satisfy the classical entropy inequality point-wise. To solve the resulting balance equations, a Galerkin finite element scheme is elaborated. To deal rigorously with the presence of high-order spatial derivatives associated with surface energies at phase boundaries in both the momentum and mass balance equations, some novel numerical approaches are used. Numerical examples are presented that consider boundary cooling of a domain at different rates, and these results demonstrate that the model can qualitatively reproduce the evolution of microstructural features that are observed in some alloys, especially steels. The proposed model opens a number of interesting possibilities for simulating and controlling microstructure pattern development under combinations of thermal and mechanical loading.     

A cellular automaton model for a bridge traffic bottleneck

A cellular automaton (CA) model is proposed in this paper to analyze a bridge traffic bottleneck. The simulation results with this model show that there are several phase transitions in the traffic average density, velocity and flow for each lane under a periodic boundary condition. An unstable phase in the traffic average density and velocity for the upstream and downstream lanes of the bridge is shown in a range of initial traffic densities. The critical points of the phase transitions and the phenomenon of the unstable phase found in the simulation are also explained with the mean-field theory.The project supported by the National Natural Science Foundation of China(70371067 and 10347001), the Key Project of Chinese Ministry of Education(02115) and the New Century Talent Plan of Guangxi Province in China(2001204).The English text was polished by Ron Marshall.     

Nucleation of Droplets in a Binary Mixture

We revisit the theory of condensation of a droplet in a vapour with the aim of finding the effect that the surface tension has on the phase diagram of a binary mixture. For that purpose we consider condensation under volume control and rederive the Gibbs phase rule. The Gibbs phase rule is equivalent to the common tangent construction for two free enthalpies corresponding to different pressures: in this case, the pressure in the vapour and the pressure in the droplet. Explicit results are calculated for a droplet mixed from incompressible liquids and for a vapour that is an ideal gas mixture. It turns out that in a certain range of volumes the equilibrium state of droplet and vapour has a higher free energy than the vapour alone. At the lower bound of that range of volumes a stable droplet of finite size will nucleate and consequently the vapour pressure will drop. The usual condensation line in a (p, X ₁)-phase diagram without surface tension is thus replaced by two lines: One for the incipient condensation and one for its completion; both lie above the condensation line without surface tension.     

Generalization of physical component boundary fitted co-ordinate (PCBFC) method for the analysis of free-surface flow

This paper presents a systematic and theoretically consistent approach for the analysis of free-surface flow, making use of a number of established ideas such as physical component, boundary-fitted co-ordinate (BFC) and Lagrangian front tracking. The approach extends, theoretically as well as numerically, the use of physical component to general non-orthogonal moving grids and provides a numerically stable BFC method with little labour of free-surface positioning, grid generation and grid renewal. The approach conserves mass even at the free surface and allows time step of the order of the Coulant number. The main body of the present paper starts with the definition of analytical space and Riemannian geometry intrinsic to the physical component by applying to it the theorems of differential geometry and manifold theory. Then the governing equations of flow and free surface for the physical component are defined in the general 3D form with the notation of the new Riemannian geometry. Numerical procedures and the fully discrete equations are also presented for the benefit of potential users. Finally, several 2D examples demonstrate the basic performance of the present method by showing the computability of complex free-surface motion.     

Experimental characterization and micromechanical modeling of superelastic response of a porous NiTi shape-memory alloy

Porous shape-memory alloys are usually brittle due to the presence of various nickel-titanium intermetallic compounds that are produced in the course of most commonly used synthesizing techniques. We consider here a porous NiTi shape-memory alloy (SMA), synthesized by spark-plasma sintering, that is ductile and displays full shape-memory effects over the entire appropriate range of strains. The porosity however is only 12% but the basic synthesizing technique has potential for producing shape-memory alloys with greater porosity that still are expected to display superelasticity and shape-memory effects. The current material has been characterized experimentally using quasi-static and dynamic tests at various initial temperatures, mostly within the superelastic strain range, but also into the plastic deformation regime of the stress-induced martensite phase. To obtain a relatively constant strain rate in the high strain-rate tests, a novel pulse-shaping technique is introduced. The results of the quasi-static experiments are compared with the predictions by a model that can be used to calculate the stress-strain response of porous NiTi shape-memory alloys during the austenite-to-martensite and reverse phase transformations in uniaxial quasi-static loading and unloading at constant temperatures. In the austenite-to-martensite transformation, the porous shape-memory alloy is modeled as a three-phase composite with the parent phase (austenite) as the matrix and the product phase (martensite) and the voids as the embedded inclusions, reversing the roles of austenite and martensite during the reverse transformation from fully martensite to fully austenite phase. The criterion of the stress-induced martensitic transformation and its reversal is based on equilibrium thermodynamics, balancing the thermodynamic driving force for the phase transformation, associated with the reduction of Gibbs’ free energy, with the resistive force corresponding to the required energy to create new interface surfaces and to overcome the energy barriers posed by various microstructural obstacles. The change in Gibbs’ free energy that produces the driving thermodynamic force for phase transformation is assumed to be due to the reduction of mechanical potential energy corresponding to the applied stress, and the reduction of the chemical energy corresponding to the imposed temperature. The energy required to overcome the resistance imposed by various nano- and subnano-scale defects and like barriers, is modeled empirically, involving three constitutive constants that are then fixed based on the experimental data. Reasonably good correlation is obtained between the experimental and model predictions.     

Effect of sodium hydroxide pretreatment on the relaxation spectrum of concentrated agar-agar gels

Summary Stress relaxation and ultrasonic absorption measurements were made for agar-agar pretreated by various concentrations of sodium hydroxide, in order to clarify the dominating factors in its rheological properties. Stress relaxation measurements were made up to 30 hours. Relaxation spectra were obtained by the reduced variable method. Gels prepared from agar-agar pretreated by concentrated sodium hydroxide show a larger relaxation modulus than those pretreated by dilute sodium hydroxide and those without alkaline pretreatment. It is suggested that hydrogen bonds are newly created as a result of desulfation in the molecule, and then, the microcrystalline structure is stabilised.With 13 figures and 2 tables     

A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels

An elastomeric gel is a cross-linked polymer network swollen with a solvent, and certain gels can undergo large reversible volume changes as they are cycled about a critical temperature. We have developed a continuum-level theory to describe the coupled mechanical deformation, fluid permeation, and heat transfer of such thermally responsive gels. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. We have numerically implemented our theory in a finite element program. We show that our theory is capable of simulating swelling, squeezing of fluid by applied mechanical forces, and thermally responsive swelling/de-swelling of such materials.     

Thermodynamic models of phase transformations and failure waves

Dynamics and quasi-statics of heterogeneous systems with sharp interfaces are analyzed. We dwell on two particular problems: dynamics of two-layered liquid incompressible planets with phase interfaces and failure fronts in brittle solids. In the former, the dynamics of the interfaces is controlled by the equality or jump in the scalar chemical potential. Similarly, in the latter example, it is controlled by the asymmetric tensorial chemical potential. We made several simplifying assumptions to reduce the system of partial differential equations to the systems of ordinary differential equations. We briefly touch on still existing obstacles.     

A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

Carbopol gels: Elastoviscoplastic and slippery glasses made of individual swollen sponges: Meso- and macroscopic properties,constitutive equations and scaling laws

This paper gives details of new data on neutralized Carbopol 940 dispersions. Appropriate techniques have been used to characterize the physical properties of the bulk gel and inter-phase slip at the wall. Previously published data are analysed and used wherever possible. Terminology and measurement difficulties are also addressed.