Planar Elongation Research Articles

Revisit of crystal orientation in a vulcanizate of natural rubber under planar elongation

Revisit of crystal orientation in a vulcanizate of natural rubber under planar elongation

Influence of Deformation of Metal Matrix on the Mechanical Properties of Poly(Ethylene Terephthalate) Inside It

The influence of different types of deformation of the metal matrix on mechanical behavior of the amorphous PET film upon its transverse compression in the ductile metal matrix has been investigated. Three deformation modes have been probed. In the first case, a disc-shaped polymer specimen has been put between two 5 mm thick discs of the lead–tin alloy and squeezed in the press. In the second and the third cases, planar elongation has been performed in the so called “dead channel”, i.e., the channel with fixed side walls, the film being elongated due to decrease in the width or thickness, respectively. The plots of true yield stress at different draw ratios have formed a common master curve. At high total draw ratio Λ, the true yield stresses have been close for the considered three types of drawing in the metal. At the draw ratio Λ 2.6, the neck has not appeared, and the specimen has been deformed uniformly. When the film in the channel is elongated due to the decrease in thickness at constant width, the specimen width has been mainly decreased during subsequent elongation in the testing machine. When the film in the channel is elongated due to the decrease in width at constant thickness, further elongation has mainly led to the decrease in the specimen thickness. The true stress Σ has been expressed as Σ = Σ0 + KΛ3, with K being a constant. Deformation of the polymer in the channel occurred with the formation of shear bands. At the preliminary draw ratio Λ = 1.82, the bands have been oriented at the angle 21.5° with respect to the stretching axis. The planar elongation has led to abnormally strong deformation softening of the polymer. The drawing has been accompanied by an increase in the elasticity modulus of the polymer. The obtained results have suggested that the macromolecules orientation is the main reason for strain hardening of the polymer.

Deformation Response of Catenated DNA Networks in a Planar Elongational Field.

A kinetoplast is a complex catenated DNA network that bears resemblance to a two-dimensional polymeric system. In this work, we use single-molecule experiments to study the transient and steady-state deformation of kinetoplasts in a planar elongational field. We demonstrate that kinetoplasts deform in a stagewise manner and undergo transient deformation at large strains, due to conformational rearrangements from an intermediate metastable state. Kinetoplasts in an elongational field achieve a steady-state deformation that depends on strain rate, akin to the deformation of linear polymers. We do not observe an abrupt transition between the nondeformed and deformed states of a kinetoplast, in contrast to the coil-stretch transition for a linear polymer.

Simulations of Startup Planar Elongation of an Entangled Polymer Melt

Simulations of Startup Planar Elongation of an Entangled Polymer Melt

Dynamics and potential applications of a lunar space tethered system

Nonlinear dynamics and potential applications of a lunar space tether system, with one end connected to the Moon's surface and the other with a large floating counterweight, are investigated in the paper. Dynamical equations of the system with a massless viscoelastic tether considering the planar libration and elastic elongation within the elliptical Earth-Moon restricted three-body (EEMRTB) system are established. The equilibria and stability of the dynamical system are explored for the system at L1 side without considering small perturbations caused by eccentricity to facilitate the rough selection of the length and elastic coefficient of the tether. The potential applications including harvesting the Rayleigh Damping Dissipation power and accessible regions within the Earth-Moon system will be studied based on the dynamic analysis of the full nonlinear dynamics. The allowed parameter regions (the tether system will neither collide the Moon/Earth nor rotate about the Moon) are identified exactly using numerical analysis, moreover, the performance of the potential applications and other related references for building a tether system are explored at L1 and L2 numerically. It is suggested that one should design a space tether based energy harvester at L1 side, release an unpowered spacecraft with high mechanical energy at L2 side respectively. Some conclusions on selecting the parameters and evaluating the performance of the space tether based platform are obtained based on numerical calculations. The research will be useful for the Moon infrastructure constructions.

Concept of an Evaluation Technique for Planar Elongational Stress and Relaxation Time Using Hoop Stress in Swirling Flow

The paper reports a novel idea of an experimental approach to estimate the apparent planar elongational viscosity and the relaxation time of low viscosity fluids. A two-dimensional swirling contraction channel is designed to maintain a constant elongation rate to the flow direction. The hydrodynamic focusing creates a stable planar elongation flow field. The flow is injected into the center of the channel and a sheath flow is injected through both sides. The sample fluid is stretched in the flow field, and then forms the ribbon-shaped filament. In the swirling contraction part, a static force balance between the hoop force caused by the planar elongational stress and the centrifugal force determines the radial position of the filament. The distribution of the planar elongational stress can be estimated by observing this position, and then the apparent planar elongational viscosity was calculated using developed simplified expressions. On the other hand, when a channel with a constant width swirling part is used, the elongational stress generated in the straight contraction part gradually decreases passing through the constant width part. The sample filament position is then shifted based on the stress relaxation. The relaxation time can be evaluated by observing this variation.

Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows.

The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.

Resonant space tethered system for lunar orbital energy harvesting

Using a space tether system attached to the Moon's surface can in principle lead to energy harvesting from the mechanical damping of the tether as it experiences elongational motion due to time-varying tidal forces. It is shown that such a tether system can in principle provide electricity generation for lunar infrastructure, although the power generated is modest relative to the scale of engineering required. First, the dynamics of the coupled planar elongation and librational motion is established for a massless, elastic and damped tether with a large tip-mass in the frame of the elliptic Earth-moon restricted three-body (EEMRTB) system. Equilibria at the natural L2 point are obtained as reference positions to perform the analysis. The method of multiple scales is then used to obtain the steady state amplitude-frequency response by ordering key variables and parameters appropriately. The steady-state power output determined by the elasticity, length and damping of the tether is presented. Specific resonances for peaks of power output, together with corresponding resonance regions, are also investigated along with suggestions for tradeoffs among the key system parameters. Finally, the optimal damping for maximum power output is determined, together with the corresponding natural length and elasticity of the tether.

Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation.

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

Evaluation of planar elongation viscosity of low-viscosity liquids using annular abrupt contraction flow around a sliding disk-shaped bob

This paper proposes a mechanical measurement technique of the planar elongation viscosity of the low-viscosity liquids. A newly designed flow cell, which consists of a cylindrical cup and a disk-shaped bob with a knife-edged rim, generates the planar elongation flow. Three kinds of Newtonian fluids and an M1 fluid are used. A strain control rheometer pushed the bob into the cup filled with the test fluid and measured the resistant force. The planar elongation viscosity was evaluated using the following two assumptions: first, the resistant force is regarded as the sum of the buoyancy and the resultant forces caused by pressure drops in the planar elongation flow and the shear flow in the test section. Second, the hydraulic mean depth is used as a representative length. The relative errors of the Trouton ratio of the Newtonian fluids were less than 20% compared to the theoretical value of 4.

Measurement of planar elongation stress and viscosity in step planar elongation flow for mobile viscoelastic fluids

We propose a new technique which can treat low viscous viscoelastic fluids and which can measure the start-up and relaxation behavior of elongational stress in step elongation rate flow. This new device consists of two parts: the squeeze cell and the optical analyzer. The squeeze cell generates the planar squeeze flow and causes the step planar elongational flow at the stagnation point. The optical system measures the transient behavior of both birefringence and orientation angle in the start-up and relaxation region at the stagnation point. In this paper, we demonstrate the two-dimensionality of the flow in the planar squeeze cell. Next, we evaluated the planar elongational stress and viscosity from optical results for Maxwell fluid. These results show good agreement with Maxwell model. Finally, we clarify the measurement accuracy from the measurement results in channels of various sizes.

二次元対向噴流型伸張レオメーターを用いた機械的・光学的同時測定による平面伸張粘度評価手法

The technique to measure planar elongation viscosity from both mechanical and optical measurements by using two-dimensional opposing jets nozzle flow has been developed. This technique generates planar elongational flow between both nozzles and simultaneously measures reaction force acting on the nozzle and flow birefringence at the stagnation point. The correctness of elongational viscosity measured by this technique was verified from experimental results for Newtonian fluid and Maxwell fluid. Starch syrup aqueous solution and CTAB/NaSal surfactant solution are used for the Newtonian fluid and the Maxwell fluid respectively. As the results, transient behavior of nozzle reaction force and flow birefringence for Maxwell fluid show good agreement. It indicates that this technique can evaluate planar elongation viscosity for not only fluids that obey stress-optical rule but also fluids have flow birefringence property. In addition, Trouton ratio of optical results become 4 and it indicates the results from optical technique are accurate. On the other hand, the data from mechanical technique provide Trouton ratio with range 15 to 20. Trouton ratio of Newtonian fluid also shows 10 ~ 20 and these results conclude that mechanical data should be limited for qualitative evaluation. However, Trouton ratio of mechanical technique is independent from sample viscosity and elongaitonal rate. Therefore, it can provide quantitatively valuable result by using correction factor.

The importance of flow history in mixed shear and extensional flows

Many complex fluid flows of industrial and academic interest exhibit mixed kinematics with localized regions of shear and elongation. Examples include converging flows (e.g. through planar hyperbolic contractions in microfluidic devices), flows through porous media, and polymer processing flows past submerged obstacles (e.g. ‘spiders’ and mandrels). For polymer solutions, characterization of 2D flow as locally shear or extensional in character is particularly important for analysis, as these ‘weak’ and ‘strong’ flows, respectively, orient and deform polymer chains in very different ways. Through the introduction of a ‘flow-type parameter’ α which varies between 0 in simple shear to 1 in planar elongation, the local velocity fields of all such mixed two-dimensional flows can be concisely characterized. We determine an analytic expression for the stress field of an Oldroyd-B fluid for two different flow histories: (i) constant strain rate and constant (but arbitrary 0 ≤ α ≤ 1) flow-type parameter, and (ii) constant strain rate and time varying flow-type parameter (0 ≤ α(t) ≤ 1). We demonstrate that both the flow strength and kinematic sequencing (i.e. whether the flow is initialized in shear or elongation) are critical for determining the local dynamical response of material elements as a result of the fluid’s fading memory of the entire deformation history, and can only be ignored in the limit of infinitely slow variations. Finally, we consider the flow of an Oldroyd-B fluid around a circular cylinder, and show that by treating the instantaneous polar angle θ(t) as the flow type parameter, the elastic and viscous contributions to the stress field can be analyzed in a similar manner.

円板ボブの押し込みによる環状急縮小流れ場を用いた平面伸張粘度測定手法の検討

円板ボブの押し込みによる環状急縮小流れ場を用いた平面伸張粘度測定手法の検討

砲弾ボブの押し込み反力による平面伸張粘度の機械的測定手法の開発

砲弾ボブの押し込み反力による平面伸張粘度の機械的測定手法の開発

Alignment of Copolymer Morphology by Planar Step Elongation during Spinodal Self-Assembly.

Using simulation and numerical self-consistent field theory of an unentangled diblock copolymer melt, we study the interplay between relaxation of molecular conformations from a highly stretched, nonequilibrium state and structure formation of the local, conserved density during self-assembly from a disordered state. We observe that the planar elongation of molecular conformations in the initial, disordered state results in an alignment of lamella normals perpendicular to the stretch direction during the subsequent self-assembly. Although thermodynamically the parallel orientation is favored, the alignment of the lamella normal perpendicular to the stretch direction is characterized by the larger growth rate of composition fluctuations during the spinodal ordering process.

Stretching of capsules in an elongation flow, a route to constitutive law

AbstractSoft bio-microcapsules are drops bounded by a thin elastic shell made of cross-linked proteins. Their shapes and their dynamics in flow depend on their membrane constitutive law characterized by shearing and area-dilatation resistance. The deformations of such capsules are investigated experimentally in planar elongation flows and compared with numerical simulations for three bidimensional models: Skalak, neo-Hookean and generalized Hooke. An original cross-flow microfluidic set-up allows the visualization of the deformed shape in the two perpendicular main fields of view. Whatever the elongation rate, the three semi-axis lengths of the ellipsoid fitting the experimental shape are measured up to 180 % of stretching of the largest axis. The geometrical analysis in the two views is sufficient to determine the constitutive law and the Poisson ratio of the membrane without a preliminary knowledge of the shear elastic modulus$G_{s}$. We conclude that the membrane of human serum albumin capsules obeys the generalized Hooke law with a Poisson ratio of 0.4. The shear elastic modulus is then determined by the combination of numerical and experimental variations of the Taylor parameter with the capillary number.

Reversed planar elongation of soft polymeric networks

The newly developed planar elongation fixture, designed as an add-on to the filament stretch rheometer, is used to measure reversible large amplitude planar elongation on soft elastomers. The concept of this new fixture is to elongate an annulus, by keeping the perimeter constant. The deformation on the cylindrical probe is measured using digital imaging, and it is found that the diameter only changes a few percent compared with the initial diameter. Additionally, it is found that a time-strain separable K-BKZ model based on a Doi–Edwards (DE) network strain (without independent alignment) captures the experimental data well. In particular, it is observed that it reproduces the deformation on the cylindrical probe, and this observation confirms our previous statement that the deformation on the cylindrical probe is highly sensitive towards the choice of strain tensor. The stress itself is well described by both the modified Lodge and the DE network strain. The amount of work needed during the deformation is calculated, and it is illustrated how the sample itself contributes with work upon flow reversal. As the stress is time-strain separable the energy loss originates from linear viscoelastic relaxation even in the nonlinear regime, and the loss can be determined solely from linear viscoelastic measurements.

Evaluation of a tube-based constitutive equation using conventional and planar elongation flow optical rheometers

The predictions of the Marrucci and Ianniruberto model (2003) have been studied in various rheometric flows as well as a planar elongation flow using the ‘optical elongational rheometer’ technique proposed by Schuberth and Münstedt (Rheol Acta 47:111–119, 2008). This combination of techniques extended the range of pertinence of the model to high-extensional rates. Relevance of the identified parameters with respect to tube theory was then discussed.