Effect of the finite extensibility of polymer chains and of the finite size of added electrolyte ions on polyelectrolyte brushes

1991 ◽  
Vol 95 (3) ◽  
pp. 2183-2192 ◽  
Author(s):  
Sanjay Misra ◽  
Sasidhar Varanasi
Keyword(s):  
Finite Size ◽  
Polymer Chains ◽  
Polyelectrolyte Brushes ◽  
Finite Extensibility

Finite-Size Networks from Cylindrical Polyelectrolyte Brushes and Porphyrins

2009 ◽  
Vol 42 (3) ◽  
pp. 830-840 ◽  
Author(s):  
Christian Ruthard ◽  
Michael Maskos ◽  
Ute Kolb ◽  
Franziska Gröhn
Keyword(s):  
Finite Size ◽  
Polyelectrolyte Brushes

Electroelasticity of dielectric elastomers based on molecular chain statistics

2018 ◽  
Vol 24 (3) ◽  
pp. 862-873 ◽  
Author(s):  
Mikhail Itskov ◽  
Vu Ngoc Khiêm ◽  
Sugeng Waluyo
Keyword(s):  
Constitutive Model ◽  
Polymer Chain ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Polymer Chains ◽  
Molecular Chain ◽  
Dielectric Elastomers ◽  
Finite Extensibility ◽  
Single Polymer Chain ◽  
Non Gaussian

The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.

The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow

2015 ◽  
Vol 777 ◽  
pp. 327-363 ◽  
Author(s):  
Jacob Page ◽  
Tamer A. Zaki
Keyword(s):  
Shear Flow ◽  
Polymer Chains ◽  
Mean Flow ◽  
Newtonian Flows ◽  
Polymer Relaxation ◽  
Finite Extensibility ◽  
Orr Mechanism ◽  
Amplification Mechanism ◽  
Spanwise Vorticity ◽  
Energy Amplification

The viscoelastic analogue to the Newtonian Orr amplification mechanism is examined using linear theory. A weak, two-dimensional Gaussian vortex is superposed onto a uniform viscoelastic shear flow. Whilst in the Newtonian solution the spanwise vorticity perturbations are simply advected, the viscoelastic behaviour is markedly different. When the polymer relaxation rate is much slower than the rate of deformation by the shear, the vortex splits into a new pair of co-rotating but counter-propagating vortices. Furthermore, the disturbance exhibits a significant amplification in its spanwise vorticity as it is tilted forward by the shear. Asymptotic solutions for an Oldroyd-B fluid in the limits of high and low elasticity isolate and explain these two effects. The splitting of the vortex is a manifestation of vorticity wave propagation along the tensioned mean-flow streamlines, while the spanwise vorticity growth is driven by the amplification of a polymer torque perturbation. The analysis explicitly demonstrates that the polymer torque amplifies as the disturbance becomes aligned with the shear. This behaviour is opposite to the Orr mechanism for energy amplification in Newtonian flows, and is therefore labelled a ‘reverse-Orr’ mechanism. Numerical evaluations of vortex evolutions using the more realistic FENE-P model, which takes into account the finite extensibility of the polymer chains, show the same qualitative behaviour. However, a new form of stress perturbation is established in regions where the polymer is significantly stretched, and results in an earlier onset of decay.

scholarly journals Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids

2013 ◽  
Vol 723 ◽  
pp. 232-263 ◽  
Author(s):  
Binh K. Lieu ◽  
Mihailo R. Jovanović ◽  
Satish Kumar
Keyword(s):  
Viscoelastic Fluids ◽  
Streamwise Velocity ◽  
Weissenberg Number ◽  
Channel Flows ◽  
Polymer Chains ◽  
Bypass Transition ◽  
Base Shear ◽  
Worst Case ◽  
Finite Extensibility ◽  
Spatio Temporal

AbstractAmplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analysing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations. In strongly elastic flows, we show that disturbances with large streamwise length scales may be significantly amplified even in the absence of inertia. For fluctuations without streamwise variations, we derive explicit analytical expressions for the dependence of the worst-case amplification (from different forcing to different velocity and polymer stress components) on the Weissenberg number ($\mathit{We}$), the maximum extensibility of the polymer chains ($L$), the viscosity ratio and the spanwise wavenumber. For the Oldroyd-B model, the amplification of the most energetic components of velocity and polymer stress fields scales as${\mathit{We}}^{2} $and${\mathit{We}}^{4} $. On the other hand, the finite extensibility of polymer molecules limits the largest achievable amplification even in flows with infinitely large Weissenberg numbers: in the presence of wall-normal and spanwise forces, the amplification of the streamwise velocity and polymer stress fluctuations is bounded by quadratic and quartic functions of$L$. This high amplification signals low robustness to modelling imperfections of inertialess channel flows of viscoelastic fluids. The underlying physical mechanism involves interactions of polymer stress fluctuations with a base shear, and it represents a close analogue of the lift-up mechanism that initiates a bypass transition in inertial flows of Newtonian fluids.

scholarly journals Poster: Elasto-inertial Turbulence in Dilute Viscoelastic Jets: Finite Extensibility of Polymer Chains Plays a Role

2021 ◽  
Author(s):  
Sami Yamanidouzisorkhabi ◽  
Yashasvi Raj ◽  
Gareth H. McKinley ◽  
Irmgard Bischofberger
Keyword(s):  
Polymer Chains ◽  
Finite Extensibility ◽  
Viscoelastic Jets

Efficiently amplified ultrasonic degradation of spherical polyelectrolyte brushes by a magnetic field

RSC Advances ◽  
2016 ◽  
Vol 6 (29) ◽  
pp. 24549-24556 ◽  
Author(s):  
Rui Zhang ◽  
Xiaoyan Hou ◽  
Yu Cang ◽  
Zhenchuan Yu ◽  
Zheqi Shen ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Polymer Chains ◽  
Green Method ◽  
Polyelectrolyte Brushes ◽  
Ultrasonic Degradation ◽  
Spherical Polyelectrolyte Brushes

This work describes a facile and green method about the ultrasonic degradation of polymer chains amplified by magnetic field.

Viscoelastic shear flow over a wavy surface

2016 ◽  
Vol 801 ◽  
pp. 392-429 ◽  
Author(s):  
Jacob Page ◽  
Tamer A. Zaki
Keyword(s):  
Polymer Chains ◽  
Critical Layer ◽  
Lower Wall ◽  
Fourier Synthesis ◽  
Channel Depth ◽  
Single Vortex ◽  
Flow Response ◽  
Finite Extensibility ◽  
Surface Protrusion ◽  
Sinusoidal Surface

A small-amplitude sinusoidal surface undulation on the lower wall of Couette flow induces a vorticity perturbation. Using linear analysis, this vorticity field is examined when the fluid is viscoelastic and contrasted to the Newtonian configuration. For strongly elastic Oldroyd-B fluids, the penetration of induced vorticity into the bulk can be classified using two dimensionless quantities: the ratios of (i) the channel depth and of (ii) the shear-waves’ critical layer depth to the wavelength of the surface roughness. In the shallow-elastic regime, where the roughness wavelength is larger than the channel depth and the critical layer is outside of the domain, the bulk flow response is a distortion of the tensioned streamlines to match the surface topography, and a constant perturbation vorticity fills the channel. This vorticity is significantly amplified in a thin solvent boundary layer at the upper wall. In the deep-elastic case, the critical layer is far from the wall and the perturbation vorticity decays exponentially with height. In the third, transcritical regime, the critical layer height is within a wavelength of the lower wall and a kinematic amplification mechanism generates vorticity in its vicinity. The analysis is extended to localized, Gaussian wall bumps using Fourier synthesis. The Newtonian flow response consists of a single vortex above the bump. In the shallow-elastic flow, a second vortex with opposite circulation is established upstream of the surface protrusion and is induced by the vorticity layer on the upper wall. In the deep transcritical case, the perturbation field consists of a pair of counter-rotating vortices centred on the large vorticity around the critical layer. The more realistic FENE-P model, which accounts for the finite extensibility of the polymer chains, shows the same qualitative behaviour.

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