Modeling of nonlinear effects in the theory of the flow of polymer liquids when superposition periodic oscillations on a stationary shear flow

2021 ◽  
Author(s):  
Gleb O. Rudakov ◽  
Aleksandr A. Laas ◽  
Mariya A. Makarova ◽  
Anzhela S. Malygina ◽  
Grigoriy V. Pyshnograi
Keyword(s):  
Shear Flow ◽  
Nonlinear Effects ◽  
Periodic Oscillations ◽  
Polymer Liquids

Relaxation dynamics of entangled polymer liquids in steady shear flow

2003 ◽  
Vol 47 (2) ◽  
pp. 469-482 ◽  
Author(s):  
Javier Sanchez-Reyes ◽  
Lynden A. Archer
Keyword(s):  
Shear Flow ◽  
Steady Shear ◽  
Relaxation Dynamics ◽  
Steady Shear Flow ◽  
Polymer Liquids ◽  
Entangled Polymer

Finite-amplitude convection in the presence of an unsteady shear flow

1995 ◽  
Vol 287 ◽  
pp. 225-249 ◽  
Author(s):  
Philip Hall
Keyword(s):  
Shear Flow ◽  
Critical Size ◽  
Low Frequency ◽  
Nonlinear Effects ◽  
Finite Amplitude ◽  
Present Calculation ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boussinesq Fluid

The effect of an unsteady shear flow on the planform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the shear flow it is well-known, if non-Boussinesq effects can be neglected, that convection begins in the form of a supercritical bifurcation to rolls. Subcritical convection in the form of say hexagons can be induced by non-Boussinesq behaviour which destroys the symmetry of the basic state. Here it is found that the symmetry breaking effects associated with an unsteady shear flow are not sufficient to cause subcritical convection so the problem reduces to the determination of how the orientations of roll cells are modified by an unsteady shear flow. Recently Kelly & Hu (1993) showed that such a flow has a significant stabilizing effect on the linear stability problem and that, for a wide range of Prandtl numbers, the effect is most pronounced in the low-frequency limit. In the present calculation it is shown that the stabilizing effects found by Kelly & Hu (1993) do survive for most frequencies when nonlinear effects and imperfections are taken into account. However a critical size of the frequency is identified below which the Kelly & Hu (1993) conclusions no longer carry through into the nonlinear regime. For frequencies of size comparable with this critical size it is shown that the convection pattern changes in time. The cell pattern is found to be extremely complicated and straight rolls exist only for part of a period.

Transient acoustic processes in a low-Mach-number shear flow

1992 ◽  
Vol 238 ◽  
pp. 509-536 ◽  
Author(s):  
Meng Wang ◽  
D. R. Kassoy
Keyword(s):  
Mach Number ◽  
Shear Flow ◽  
Acoustic Waves ◽  
Layer Structure ◽  
Acoustic Streaming ◽  
Nonlinear Effects ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Mean Flow ◽  
Transverse Waves

A systematic perturbation procedure, based on a small mean flow Mach number and large duct Reynolds number, is employed to formulate and solve an initial-boundary-value problem for acoustic processes in a shear flow contained within a rigid-walled parallel duct. The results describe the general transient evolution of acoustic waves driven by a plane source located at a given duct cross-section. Forced bulk oscillations near the source and oblique wave generation are shown to result from refraction of the basic planar axial disturbance by the shear flow. Refraction also causes the axial waves to exhibit higher-order amplitude variations in the transverse direction. As the source frequency approaches certain critical values, specific refraction-induced oblique waves evolve into amplifying purely transverse waves. As a result, the magnitude of the refraction effect increases with time, and quasi-steady solutions do not exist. The analysis is extended to the thin acoustic boundary layer adjacent to the solid walls to examine the shear-layer structure induced by the variety of acoustic waves in the core flow. Nonlinear effects and acoustic streaming are shown to be negligibly small on the scale of a few axial wavelengths.

Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow

1995 ◽  
Vol 297 ◽  
pp. 123-152 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Finite Deformation ◽  
Surface Elasticity ◽  
Nonlinear Effects ◽  
Numerical Results ◽  
Critical Threshold ◽  
Simple Shear Flow ◽  
Elastic Membranes ◽  
Membrane Thinning

The transient deformation of liquid capsules enclosed by elastic membranes subject to simple shear flow is studied numerically using a new implementation of the boundary element method. The numerical results for capsules with spherical unstressed shapes and varying degrees of surface elasticity are compared with the predictions of an asymptotic theory for small deformations due to Barthès-Biesel and coworkers, and the significance of nonlinear effects due to finite deformation is assessed. It is found that the capsules exhibit continuous elongation when the dimensionless shear rate becomes larger than a critical threshold, in agreement with recent experimental observations of capsules with polymerized interfaces. Membrane failure at large deformations is discussed with respect to membrane thinning and development of excessive elastic tensions, and it is argued that the location where the membrane is likely to rupture due to continued deformation is insensitive to the precise mechanism of rupture. The numerical results suggest that a dilute suspension of capsules behaves like shear-thinning medium with some elastic properties. Results of oblate spheroidal capsules suggest that the points of maximum membrane thinning and tension coincide but their location depends upon the unstressed capsule shape.

Quasi-Periodic Oscillations in Dwarf Novae

1979 ◽  
Vol 46 ◽  
pp. 77-88
Author(s):  
Edward L. Robinson
Keyword(s):  
Binary Systems ◽  
Outer Edge ◽  
Light Curves ◽  
Close Binary ◽  
Bright Spot ◽  
Dwarf Novae ◽  
Periodic Oscillations ◽  
High Frequencies ◽  
Short Period ◽  
Typical Time

Three distinct kinds of rapid variations have been detected in the light curves of dwarf novae: rapid flickering, short period coherent oscillations, and quasi-periodic oscillations. The rapid flickering is seen in the light curves of most, if not all, dwarf novae, and is especially apparent during minimum light between eruptions. The flickering has a typical time scale of a few minutes or less and a typical amplitude of about .1 mag. The flickering is completely random and unpredictable; the power spectrum of flickering shows only a slow decrease from low to high frequencies. The observations of U Gem by Warner and Nather (1971) showed conclusively that most of the flickering is produced by variations in the luminosity of the bright spot near the outer edge of the accretion disk around the white dwarf in these close binary systems.

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