A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
T. F. Oliveira ◽  
F.R. Cunha
Keyword(s):  
Small Deformation ◽  
Theoretical Work ◽  
High Viscosity ◽  
Theoretical Description ◽  
Nonlinear Frequency ◽  
Viscous Drops ◽  
Nonlinear Frequency Response ◽  
Continuum Description ◽  
Arbitrary Frequency ◽  
Stationary Shape

This theoretical work shows how the knowledge of the emulsion microscale, including drop stretching and orientation leads to a continuum description of emulsion flows. A first order small deformation theory is explored for describing the rheology of an emulsion of high viscosity drops undergoing unsteady shear flows. The stationary shape and the interfacial velocity of a drop are used in order to obtain the contribution of the drop to the effective stress tensor of the emulsion. A complex rheology including the nonlinear frequency response of the emulsion under oscillatory shear at arbitrary frequency forcing and strain amplitude is identified.

scholarly journals Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation

2008 ◽  
Vol 607 ◽  
pp. 209-234 ◽  
Author(s):  
Y.-N. YOUNG ◽  
J. BŁAWZDZIEWICZ ◽  
V. CRISTINI ◽  
R. H. GOODMAN
Keyword(s):  
Length Distribution ◽  
Period Doubling ◽  
Small Deformation ◽  
High Viscosity ◽  
Boundary Integral ◽  
Drop Shape ◽  
Viscous Drops ◽  
Flow Vorticity ◽  
Creeping Flows ◽  
Vorticity Component

We have shown that high-viscosity drops in two-dimensional linear creeping flows with a non-zero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Experimental Study of Time-Frequency Effect of Rocks

2012 ◽  
Vol 204-208 ◽  
pp. 755-760
Author(s):  
Xin Lin Wan ◽  
Su Zhang
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Sine Wave ◽  
Intersection Point ◽  
Frequency Effect ◽  
Nonlinear Frequency ◽  
Time Frequency ◽  
Physical Mechanisms ◽  
Nonlinear Frequency Response ◽  
Water Saturated

Sine wave loading experiments are carried out on MTS for pump-oil saturated Nanjing sandstones and water saturated Dali marbles. The Young’s modulus and velocities of longitudinal wave and transverse wave increase with the frequency, and there are notable dispersions. The existence of micro defects in saturated rocks result in hysteresis at the sinusoidal loading experiments. The variation curves of instantaneous Young’s modulus with stress for loading and unloading intersect, and an “X” shape figure is obtained. As the frequency of the sinusoidal wave increases, the position of the intersection point moves to higher modulus area. Thus the modulus dispersion increases. Some physical mechanisms of nonlinear frequency response of rock are revealed. The results obtained are very important for nonlinear wave study, and the theoretical study and application of earthquake and engineering.

scholarly journals Nonlinear frequency response of the multi-resonant ring cavities

2020 ◽  
Vol 18 ◽  
pp. 103279 ◽  
Author(s):  
Andrey A. Nikitin ◽  
Vitalii V. Vitko ◽  
Mikhail A. Cherkasskii ◽  
Alexey B. Ustinov ◽  
Boris A. Kalinikos
Keyword(s):  
Frequency Response ◽  
Nonlinear Frequency ◽  
Nonlinear Frequency Response
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