Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts

Soft Matter ◽  
2020 ◽  
Vol 16 (28) ◽  
pp. 6468-6483 ◽  
Author(s):  
Mahdi Boudaghi-Khajehnobar ◽  
Brian J. Edwards ◽  
Bamin Khomami
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Shear Flow ◽  
Chain Length ◽  
Simple Shear ◽  
Polymer Melts ◽  
Shear Banding ◽  
Simple Shear Flow ◽  
Polydisperse Polymer ◽  
Transient And Steady State

Transient and steady-state shear banding are demonstrated for polydisperse polymer melts as functions of applied shear rate.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Effects of shear rate on rouleau formation in simple shear flow

Biorheology ◽  
1988 ◽  
Vol 25 (1-2) ◽  
pp. 113-122 ◽  
Author(s):  
T. Murata ◽  
T.W. Secomb
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Rouleau Formation

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

1998 ◽  
Vol 361 ◽  
pp. 117-143 ◽  
Author(s):  
S. RAMANUJAN ◽  
C. POZRIKIDIS
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Large Deformations ◽  
Viscosity Ratio ◽  
Curvilinear Coordinates ◽  
Triangular Element ◽  
Elastic Membrane ◽  
Simple Shear Flow ◽  
Liquid Drops

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Reynolds numbers using a boundary-element method. The surface of the capsule is discretized into quadratic triangular elements that form an evolving unstructured grid. The elastic membrane tensions are expressed in terms of the surface deformation gradient, which is evaluated from the position of the grid points. Compared to an earlier formulation that uses global curvilinear coordinates, the triangular-element formulation suppresses numerical instabilities due to uneven discretization and thus enables the study of large deformations and the investigation of the effect of fluid viscosities. Computations are performed for capsules with spherical, spheroidal, and discoidal unstressed shapes over an extended range of the dimensionless shear rate and for a broad range of the ratio of the internal to surrounding fluid viscosities. Results for small deformations of spherical capsules are in quantitative agreement with the predictions of perturbation theories. Results for large deformations of spherical capsules and deformations of non-spherical capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially spherical capsules deform into steady elongated shapes whose aspect ratios increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed for any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymmetric capsules subject to a stagnation-point flow. When the shear rate is sufficiently high and the viscosity ratio is sufficiently low, liquid drops exhibit continuous elongation leading to breakup. Axisymmetric capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of capsules in shear flow, large elastic tensions develop at large deformations and prevent continued elongation, stressing the importance of the vorticity of the incident flow. The long-time behaviour of deformed capsules depends strongly on the unstressed shape. Oblate capsules exhibit unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sphericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinning behaviour.

Flow of Granular Materials Modeled as a Generalized Reiner-Rivlin Type Fluid

2012 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
Mehrdad Massoudi
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Constitutive Model ◽  
Granular Materials ◽  
Simple Shear ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Lower Plate ◽  
Simple Shear Flow ◽  
Rate Dependent

In this paper we use a non-linear constitutive model for flowing granular materials developed by Massoudi [1] which not only considers the effect of volume fraction but also has a viscosity which is shear rate dependent. This model is a generalization of Reiner’s model [2] derived for wet sand. Specifically we study the simple shear flow of granular materials between two horizontal plates, with the lower plate fixed and the upper plate moving at a constant speed. Numerical solutions are presented for various dimensionless parameters.

Long slender drops in a simple shear flow

1980 ◽  
Vol 98 (2) ◽  
pp. 305-328 ◽  
Author(s):  
E. J. Hinch ◽  
A. Acrivos
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Equilibrium Shape ◽  
Simple Shear Flow ◽  
Critical Shear Rate ◽  
Shear Rates ◽  
Low Viscosity ◽  
Stable Equilibria ◽  
Small Disturbances

We study theoretically the slow viscous motion of a long slender drop placed in a simple shear flow, the drop having a low viscosity compared with that of the suspending fluid. As a simplifying approximation, the cross-section of the drop is taken to be circular. An equilibrium shape with the drop nearly aligned with the flow is found for all shear rates, although the equilibrium is only stable to small disturbances for shear rates below some critical value. The stable equilibria just below the critical shear rate are found to be accessible only if the shear rate is increased slowly.

An orientational order transition in a sheared suspension of anisotropic particles

2016 ◽  
Vol 811 ◽  
Author(s):  
Navaneeth K. Marath ◽  
Ruchir Dwivedi ◽  
Ganesh Subramanian
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Orientational Order ◽  
Thermal Fluctuations ◽  
Simple Shear Flow ◽  
Two Phase ◽  
Physics Literature ◽  
Dilute Suspension ◽  
Neutrally Buoyant

Under Stokesian conditions, a neutrally buoyant non-Brownian spheroid in simple shear flow rotates indefinitely in any of a one-parameter family of closed (Jeffery) orbits characterized by an orbit constant $C$. The limiting values, $C=0$ and $C=\infty$, correspond to spinning and tumbling modes respectively. Hydrodynamics alone does not determine the distribution of spheroid orientations across Jeffery orbits in the absence of interactions, and the rheology of a dilute suspension of spheroids remains indeterminate. A combination of inertia and stochastic orientation fluctuations eliminates the indeterminacy. The steady-state Jeffery-orbit distribution arising from a balance of inertia and thermal fluctuations is shown to be of the Boltzmann equilibrium form, with a potential that depends on $C$, the particle aspect ratio ($\unicode[STIX]{x1D705}$), and a dimensionless shear rate ($Re\,Pe_{r}$, $Re$ and $Pe_{r}$ being the Reynolds and rotary Péclet numbers), and therefore lends itself to a novel thermodynamic interpretation in $C{-}\unicode[STIX]{x1D705}{-}Re\,Pe_{r}$ space. In particular, the transition of the potential from a single to a double-well structure, below a critical $\unicode[STIX]{x1D705}$, has similarities to a thermodynamic phase transition, and the small-$C$ and large-$C$ minima are therefore identified with spinning and tumbling phases. The hysteretic dynamics within the two-phase tumbling–spinning envelope renders the rheology sensitively dependent on the precise shear rate history, the signature in simple shear flow being a multivalued viscosity at a given shear rate. The tumbling–spinning transition identified here is analogous to the coil–stretch transition in the polymer physics literature. It should persist under more general circumstances, and has implications for the suspension stress response in inhomogeneous shearing flows.

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