Linear viscoelasticity of thermoassociative chitosan-g-poly(N-isopropylacrylamide) copolymer

Chitosan-g-poly(N-isopropylacrylamide) (chitosan-g-PNIPAM) was synthesized and characterized rheologically in aqueous solutions. The copolymer solution exhibits a thermoassociative behavior in which its elastic response dramatically increases when temperature is above the critical temperature or the association temperature, T _assoc. The copolymer at low concentration shows typical solution property. When the temperature is increased up to the critical temperature, the copolymer exhibits a gel-like characteristic due to the formation of physical cross-links between chitosan backbones through the self-aggregation of PNIPAM side chains. At high concentration, the system exhibits a weak elastic response due to the entanglement of the copolymer at 25°C. As temperature is raised above T _assoc, the system shows a strong elastic behavior due to the formation of additional physical cross-links via the aggregation of PNIPAM side chains. Chitosan-g-PNIPAM offers an attractive associating behavior in aqueous solution at temperature close to the body temperature, thus providing potential applications in pharmaceutical and medical industries.     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

A Simplified Model and Similarity Solutions for Interfacial Evolution of Two-Phase Flow in Porous Media

For two-phase flows of immiscible displacement processes in porous media, we proposed a simplified model to capture the interfacial fronts, which is given by explicit expressions and satisfies the continuity conditions of pressure and normal velocity across the interface. A new similarity solution for the interfacial evolution in the rectangular coordinate system was derived by postulating a first-order approximation of the velocity distribution in the region that the two-phase fluids co-exist. The interfacial evolution equation can be explicitly expressed as a linear function, where the slope of the interfacial equation is simply related to the mobility ratio of two-phase fluids in porous media. The application of the proposed solutions to predictions of interfacial evolutions in carbon dioxide injected into saline aquifers was illustrated under different mobility ratios and operational parameters. For the purpose of comparison, the numerical solutions obtained by level set method and the similarity solutions based on the Dupuit assumptions were presented. The results show that the proposed solution can give a better approximation of interfacial evolution than the currently available similarity solutions, especially in the situation that the mobility ratio is large. The proposed approximate solutions can provide physical insight into the interfacial phenomenon and be readily used for rapidly screening carbon dioxide storage capacity in subsurface formations and monitoring the migration of carbon dioxide plume.

     

On the influence of interfacial properties to the bending rigidity of layered structures

Layered structures are ubiquitous, from one-atom thick layers in two-dimensional materials, to nanoscale lipid bi-layers, and to micro and millimeter thick layers in composites. The mechanical behavior of layered structures heavily depends on the interfacial properties and is of great interest in engineering practice. In this work, we give an analytical solution of the bending rigidity of bilayered structures as a function of the interfacial shear strength. Our results show that while the critical bending stiffness when the interface starts to slide plastically is proportional to the interfacial shear strength, there is a strong nonlinearity between the rigidity and the applied bending after interfacial plastic shearing. We further give semi-analytical solutions to the bending of bilayers when both interfacial shearing and pre-existing crack are present in the interface of rectangular and circular bilayers. The analytical solutions are validated by using finite element simulations. Our analysis suggests that interfacial shearing resistance, interfacial stiffness and preexisting cracks dramatically influence the bending rigidity of bilayers. The results can be utilized to understand the significant stiffness difference in typical biostructures and novel materials, and may also be used for non-destructive detection of interfacial crack in composites when stiffness can be probed through vibration techniques.     

Structural and interfacial stability of multiple solutions for stratified flow

Prediction of the liquid level in stratified two-phase upwards flow shows that one may have multiple solutions. In this case it is necessary to determine which solutions will actually occur and whether hysteresis is possible, namely whether it is possible to have two or more solutions for the same operating conditions. In this work the stability of the solutions for stratified flow is considered using two types of stability analyses: (1) structural stability analysis; and (2) interfacial stability analysis (Kelvin—Helmholtz, K—H). For the K—H stability analysis we used two methods: an approximate simplified method suggested by Taitel & Dukler; and a more rigorous method suggested by Barnea, which is based on a combination of the viscous K—H and inviscid K—H analyses. The results show that whenever three solutions exist only the first, i.e. the solution with the thinnest liquid level, is stable. The middle solution is always structurally unstable (linearly), whereas the third solution is structurally unstable to large disturbances (non-linear stability). The third solution is usually also unstable to the K—H type of instability. As a result it is concluded that hysteresis is not possible and that only the thinnest solution will be observed practically.     

Chemically induced swelling of hydrogels

We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the model involves a supplemental interfacial equation imposing configurational force balance. We present a hybrid eXtended-Finite-Element/Level-Set Method for obtaining approximate solutions to the governing equations of the model. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued to engineer hydrogels with optimal response times.     

Experimental evaluation of Marangoni stress and surfactant concentration at interface of contaminated single spherical drop using spatiotemporal filter velocimetry

Spatiotemporal filter velocimetry (SFV) was extended to Lagrangian measurements with boundary-fitted measurement areas, and was applied to flows about single spherical drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions to examine its applicability to the estimation of the Marangoni stress and surfactant concentration at a moving interface. Effects of bulk concentration of surfactant on the velocity field, the Marangoni stress and the surface concentration of surfactant were discussed from the measured data. As a result, we confirmed that accurate velocity distribution in the vicinity of the interface measured by SFV enables us to evaluate interfacial velocity and interfacial shear stresses and to estimate the Marangoni stress, interfacial tension and surfactant concentration at the interface with the assumption of negligible surface viscosity. The flow inside the drop and the interfacial velocity become weak due to the Marangoni stress caused by the gradient of surfactant concentration at the interface as the bulk concentration of surfactant increases. These results demonstrate that SFV is of great use in experimental analysis of adsorption and desorption kinetics at a moving interface.     

Particle-induced bridging in immiscible polymer blends

Pickering emulsions are emulsions whose drops are stabilized against coalescence by particles adsorbed at their interface. Recent research on oil/water/particle systems shows that particles can sometimes adsorb at two oil/water interfaces. Such “bridging particles” can glue together drops of oil in water or vice versa. We hypothesize that the same effect should apply in immiscible polymer blends with droplet-matrix morphologies, viz., added particles should glue together drops and give rise to particle-bridged drop clusters. We test this hypothesis in PIB-in-PDMS blends [PIB, poly(isobutylene); PDMS, poly(dimethylsiloxane)] with fumed silica particles. Direct visualization shows that the particles can indeed induce clustering of the drops, and the blends appear to show gel-like behavior. Such gel-like behavior is confirmed by dynamic oscillatory experiments. However, we are unable to conclusively attribute the gel-like behavior to droplet clustering: Association of the fumed silica particles in the bulk, which itself causes gel-like behavior, confounds the results and prevents clear analysis of the gluing effect of the particles. We conclude that PIB/PDMS/fumed silica is not a good model system, for studying particle-containing polymer blends. We instead propose that spherical monodisperse silica particles can offer a far more convenient model system, and provide direct visual evidence of gluing of PIB drops in a PDMS matrix.     

Rheology and flow studies of drag-reducing gravel packing fluids

Viscoelastic additives are widely used as drag reducers in the oil and gas industry, and both polymeric additives and micellar surfactants are commonly used in well gravel packing applications. While the behaviour of polymeric additives such as the polysaccharide xanthan gum is well characterized in the literature, much less is known about how the rheology of the viscoelastic surfactants affects drag reduction, despite widespread use. In this study, we performed a number of rheological tests as well as flow loop experiments on solutions of a zwitterionic surfactant to understand the structural characteristics of the fluids in order to make better process predictions. Unlike xanthan, which displays typical viscoelastic liquid characteristics, zwitterionic surfactant-based fluids display elastic gel-like behaviour. The gel-like behaviour suggests long and relatively unbreakable chain lengths of the wormlike micelles in the viscoelastic surfactant solution at room temperature leading to gelation by entanglement. Also, a shear-thickening behaviour of viscoelastic surfactant samples at higher shear rates is observed, possibly as a result of shear-induced structures. Finally, we present a novel representation scheme to depict the flow loop results for drag in the laminar and turbulent regime, and relate this data to the rheological characterization.     

Evolving Graphs by Singular Weighted Curvature

A new notion of solutions is introduced to study degenerate nonlinear parabolic equations in one space dimension whose diffusion effect is so strong at particular slopes of the unknowns that the equation is no longer a partial differential equation. By extending the theory of viscosity solutions, a comparison principle is established. For periodic continuous initial data a unique global continuous solution (periodic in space) is constructed. The theory applies to motion of interfacial curves by crystalline energy or more generally by anisotropic interfacial energy with corners when the curves are the graphs of functions. Even if the driving force term (homogeneous in space) exists, the initial-value problem is solvable for general nonadmissible continuous (periodic) initial data. (Accepted July 5, 1996)     

A generalized modified Kadomtsev-Petviashvili equation for interfacial wave propagation near the critical depth level

Propagation of interfacial waves near the critical depth level in a two-layer fluid system is investigated. We first present a generalized modified Kadomtsev-Petviashvili (gmKP) equation for weakly nonlinear and dispersive interfacial waves propagating predominantly in the longitudinal direction of a slowly rotating channel with gradually varying topography and sidewalls. For certain type of non-rotating channels, we find two families of periodic-wave solutions, which include solitarywave solutions and a shock-like solution as limiting cases, to the variable-coefficient gmKP equation. We also show that in this situation the gmKP equation has only unidirectional N-soliton solutions and does not allow soliton resonance to occur. In a rotating uniform channel, our small-time asymptotic analysis and numerical study of the gmKP equation show that, depending on the relative importance of the cubic nonlinearity to quadratic nonlinearity, the wavefront of a Kelvin solitary wave may curve either forward or backward, trailed by a small train of Poincaré waves. When these two nonlinearities almost balance each other, the wavefront becomes almost straight-crested across the channel, and the trailing Poincaré waves diminish.     

基于三维弹性杆模型的DNA拉伸响应的研究

通过Young-Laplace方程将界面张力引入Kirchhoff方程,并结合Gibbs与Langmuir吸附方程建立了受溶液浓度影响的三维DNA弹性杆模型。基于此模型,引入DNA端部的边界条件,运用打靶法来模拟计算溶液中的DNA链段受端部拉力作用下的几何构型。进一步分析了在界面能与弹性应变能的耦合作用下,DNA链段平衡构型的形状与尺寸的变化规律。     

The effect of parallel combined steady and oscillatory shear flows on blood and polymer solutions

Human blood at physiological volume concentration exhibits non-Newtonian and thixotropic properties. The blood flow in the microcirculation is pulsatile, initiated from the heart pulse and can be considered as superposition of two partial flows: a) a steady shear, and b) an oscillatory shear. Until now steady and viscoelastic behavior were separately investigated. Here we present the response to the combination of steady and oscillatory shear for human blood, a high molecular weight aqueous polymer solution (polyacrylamide AP 273E) and an aqueous xanthan gum solution. The polyacrylamide and xanthan solutions are fluids that model the rheological properties of human blood. In general, parameters describing blood viscoelasticity became less pronounced as superimposed steady shear increased, especially at low shear region and by elasticity, associated with reduction in RBC aggregation. The response of polymer solutions to superposition shows qualitative similarities with blood by elasticity, but their quantitative response differed from that of blood. By viscosity another behavior was observed. The superposition effect on viscous component was described by a modified Carreau equation and for the elastic component by an exponential equation.Paper in part presented at the Symposium on Rheology and Computational Fluid Mechanics dedicated to the memory of Prof. A. C. Papanastasiou, University of Cyprus, Nicosia, July 4–5, 1996     

Stability of multiple solutions in inclined gas/shear-thinning fluid stratified pipe flow

This work provides an investigation on multiple solutions in gas/shear-thinning fluid inclined stratified pipe flows. Multiple solution operative conditions are studied investigating the effect of the interfacial shear stress modeling and the rheology of the shear-thinning fluid. The modeling of the interfacial shear stress in counter-current has a strong influence of multiple solutions regions. The stability of multiple hold-up solutions is studied considering the structural stability, the interfacial stability, and the minimization of the dissipation approaches. The results of the three different approaches are commented both for concurrent and counter-current flows, giving the same conclusions only for upward inclined flows.     

Full field analysis of an anti-plane interface crack subjected to dynamic body forces

In this study, the transient full field response of an interface crack between two different media subjected to dynamic body force at one material is investigated. For time t < 0, the bimaterial medium is stress free and at rest. At t = 0, a concentrated anti-plane dynamic point loading is applied at the medium as shown in Fig. 1. The total wave field is due to the effect of this point loading and the scattering of the incident waves by the interface crack. An alternative methodology that is different from the conventional superposition method is used to construct the reflected, refracted and diffracted wave fields. A useful fundamental solution is proposed in this study and the full field solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying an exponentially distributed traction (in the Laplace transform domain) on the interfacial crack faces. The Cagniard–de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient closed form solutions for stresses and stress intensity factors are obtained. Numerical results for the time history of stresses and stress intensity factors during the transient process are discussed in detail.     

ANALYSIS OF A SCREW DISLOCATION INSIDE A CIRCULAR INCLUSION WITH INTERFACIAL CRACKS IN PIEZOELECTRIC COMPOSITES

IntroductionPiezoelectric materials have potentials for use in many modern devices and compositestructures. The presence of various defects, such as inclusions, holes, dislocations andcracks, can greatly influence their characteristics and coupled behavio…     

Coupled mixed-mode cohesive zone modeling of interfacial debonding in simply supported plated beams

The development of predictive models for plate end debonding failures in beams strengthened with thin soffit plates is a topic of great practical relevance. After the early stress-based formulations, fracture mechanics approaches have become increasingly established. More recently, the cohesive zone (CZ) model has been successfully adopted as a bridge between the stress- and fracture mechanics-based treatments. However, the few studies of this nature propose complex formulations which can only be implemented numerically. To date, the only available analytical solution based on CZ modeling for the prediction of interfacial stresses/debonding in plated beams is limited to the determination of interfacial shear stresses and thus neglects the mixed-mode effects generated by the presence of interfacial normal stresses at the plate end. This paper presents a new analytical formulation based on the CZ modeling approach for the prediction of plate end debonding in plated beams. A key enhancement with respect to the previous solution is the use of a coupled mixed-mode CZ model, which enables a full account of mixed-mode effects at the plate end. The model describes the evolution of the interface after the end of the elastic regime, and predicts the value of the load at incipient debonding. The achievement of a closed-form solution for this quite complex case entails the introduction of a crucial simplifying assumption, as well as the ad hoc modeling of an effective cohesive interfacial response. The paper presents the analytical theory and compares its predictions with numerical and experimental results.     

Energetic versus maximally-dissipative local solutions of a quasi-static rate-independent mixed-mode delamination model

A quasi-static rate-independent model of delamination of linearly elastic bodies at small strains, sensitive to mode of delamination, using interfacial damage and interfacial plasticity as two internal parameters, is further developed with the aim to extract representations typically employed in engineering interface-models, i.e. fracture envelope and fracture energy dependence on the mode mixity, which are suitable for the model fitting to experimental data. Moreover, two concepts of solutions are implemented: globally stable energy-conserving solutions or stress-driven maximally-dissipative local solutions, arising by the fully implicit or by a semi-implicit time-stepping procedures, respectively, both yielding numerically stable and convergent time-discretizations. Spatial discretization is performed by the symmetric Galerkin boundary-element method (SGBEM). Alternating quadratic programming is implemented to cope with, respectively, global or local, energy-minimizations in the computation of the time-discretized solutions. Sample 2D numerical examples document applicability of the model as well as efficiency of the SGBEM numerical implementation and facilitate comparison of the two mentioned solution concepts.     

A Dynamic Pore Network Model for Oil Displacement by Wettability-Altering Surfactant Solution

A dynamic pore network model, capable of predicting the displacement of oil from a porous medium by a wettability-altering and interfacial tension reducing surfactant solution, is presented. The key ingredients of the model are (1) a dynamic network model for the displacement of oil by aqueous phase taking account of capillary and viscous effects, (2) a simulation of the transport of surfactant through the network by advection and diffusion taking account of adsorption on the solid surface, and (3) the coupling of these two by linking the contact angle and interfacial tension appearing in the dynamic network simulation to the local concentration of surfactant computed in the transport simulation. The coupling is two-way: The flow field used to advect the surfactant concentration is that associated with the displacement of oil by the injected aqueous phase, and the surfactant concentration influences the flow field through its effect on the capillarity parameters. We present results obtained using the model to validate that it reproduces the displacement patterns observed by other authors in two-dimensional networks as capillary number and mobility ratio are varied, and to illustrate the effects of surfactant on displacement patterns. A mechanism is demonstrated whereby in an initially mixed-wet medium, surfactant-induced wettability alteration can lead to stabilization of displacement fronts.