scholarly journals Orientation of non-spherical particles in an axisymmetric random flow

2013 ◽  
Vol 719 ◽  
pp. 465-487 ◽  
Author(s):  
Dario Vincenzi
Keyword(s):  
Spherical Particles ◽  
Geometrical Shape ◽  
Stationary Probability ◽  
Rigid Particles ◽  
Stationary Probability Density Function ◽  
Random Flow ◽  
Axis Of Symmetry ◽  
Tumbling Motion ◽  
Preferential Alignment ◽  
Jeffery’S Equation

AbstractThe dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery’s equation; the random flow is Gaussian and has short correlation time. The stationary probability density function of orientations is calculated exactly. Four regimes are identified depending on the statistical anisotropy of the flow and on the geometrical shape of the particle. If $\boldsymbol{\lambda} $ is the axis of symmetry of the flow, the four regimes are: rotation about $\boldsymbol{\lambda} $, tumbling motion between $\boldsymbol{\lambda} $ and $- \boldsymbol{\lambda} $, combination of rotation and tumbling, and preferential alignment with a direction oblique to $\boldsymbol{\lambda} $.

Reshaping of the probability density function of nonlinear stochastic systems against abrupt changes

2019 ◽  
Vol 26 (7-8) ◽  
pp. 532-539
Author(s):  
Lei Xia ◽  
Ronghua Huan ◽  
Weiqiu Zhu ◽  
Chenxuan Zhu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Stochastic Systems ◽  
Stationary Probability ◽  
Markov Jump ◽  
Nonlinear Stochastic Systems ◽  
Stationary Probability Density ◽  
Abrupt Changes ◽  
Stationary Probability Density Function

The operation of dynamic systems is often accompanied by abrupt and random changes in their configurations, which will dramatically change the stationary probability density function of their response. In this article, an effective procedure is proposed to reshape the stationary probability density function of nonlinear stochastic systems against abrupt changes. Based on the Markov jump theory, such a system is formulated as a continuous system with discrete Markov jump parameters. The limiting averaging principle is then applied to suppress the rapidly varying Markov jump process to generate a probability-weighted system. Then, the approximate expression of the stationary probability density function of the system is obtained, based on which the reshaping control law can be designed, which has two parts: (i) the first part (conservative part) is designed to make the reshaped system and the undisturbed system have the same Hamiltonian; (ii) the second (dissipative part) is designed so that the stationary probability density function of the reshaped system is the same as that of undisturbed system. The proposed law is exactly analytical and no online measurement is required. The application and effectiveness of the proposed procedure are demonstrated by using an example of three degrees-of-freedom nonlinear stochastic system subjected to abrupt changes.

scholarly journals TUMBLING MOTION OF ELLIPTICAL PARTICLES IN VISCOUS TWO-DIMENSIONAL FLUIDS

2001 ◽  
Vol 12 (01) ◽  
pp. 127-139 ◽  
Author(s):  
GERALD H. RISTOW
Keyword(s):  
Finite Difference ◽  
Infinite System ◽  
System Size ◽  
Terminal Velocity ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Finite Difference Technique ◽  
Elliptical Particles ◽  
Tumbling Motion ◽  
The One

The settling dynamics of spherical and elliptical particles in a viscous Newtonian fluid are investigated numerically using a finite difference technique. The terminal velocity for spherical particles is calculated for different system sizes and the extrapolated value for an infinite system size is compared to the Oseen approximation. Special attention is given to the settling and tumbling motion of elliptical particles where their terminal velocity is compared with the one of the surface equivalent spherical particle.

scholarly journals The rheology of a suspension of nearly spherical particles subject to Brownian rotations

1972 ◽  
Vol 55 (4) ◽  
pp. 745-765 ◽  
Author(s):  
L. G. Leal ◽  
E. J. Hinch
Keyword(s):  
Constitutive Equations ◽  
Bulk Flow ◽  
Time Dependent ◽  
Spherical Particles ◽  
Experimental Investigations ◽  
Complex Materials ◽  
Rigid Particles ◽  
Dilute Suspension ◽  
Polymeric Solutions ◽  
Stress Patterns

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials.

Experiment Solution Velocity and Pressure Field in the Mixing Process Computer Simulation

2014 ◽  
Vol 693 ◽  
pp. 68-73
Author(s):  
Helena Kravarikova
Keyword(s):  
Rotation Axis ◽  
Flow Density ◽  
Geometrical Shape ◽  
Technical Equipment ◽  
Mixing Process ◽  
Rotational Movement ◽  
Complex Process ◽  
Axis Of Symmetry ◽  
Process Computer ◽  
Solution Velocity

The process of mixing materials is a very complex process. The mixing process is used for homogenisation of substances. Rather than propose a real mixer, you must first construct a mixer for operational purposes experimental solutions. Experimental solutions are most often realized in laboratory conditions. Experimental mixers are made according to the requirements of power mixers, fluid flow, density and viscosity of the mixed fluid. To investigate the mixing process in the Laboratory mixers are made on the basis of the criteria of non-dimensional simplex. For designing operating mixers can also use analytical solutions of technical equipment and the mixing process. It is now possible to implement solutions using FEM numerical simulation of this phenomenon.The homogeneity of the mixed substances, mixer performs rotational movement about the axis of rotation. In most cases, the rotational movement of the stirrer describes the geometrical shape of the mixer. Usually rotation axis Mixer is the axis of symmetry. The shape and dimensions of the stirrer depends on the desired performance of mixer, the type of flow, the type and quantity of mixed materials.

scholarly journals Polystyrene-Based Nanocomposites with Different Fillers: Fabrication and Mechanical Properties

Polymers ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 2457
Author(s):  
Olga A. Moskalyuk ◽  
Andrey V. Belashov ◽  
Yaroslav M. Beltukov ◽  
Elena M. Ivan’kova ◽  
Elena N. Popova ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Elastic Moduli ◽  
Spherical Particles ◽  
Linear Elastic ◽  
Rigid Particles ◽  
Different Types ◽  
Non Linear ◽  
Multi Walled Carbon Nanotubes ◽  
Carbon Fillers ◽  
Walled Carbon Nanotubes

The paper presents a comprehensive analysis of the elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and mica), and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Block samples of composites with different filler concentrations were fabricated by melt technology, and their linear and non-linear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of a composite, with the highest rise of about 80% obtained with carbon fillers. Non-linear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than linear ones. A non-linearity modulus βs comprising the combination of linear and non-linear elastic moduli of a material demonstrated considerable changes correlating with those of the Young’s modulus. The changes in non-linear elasticity of fabricated composites were compared with parameters of bulk non-linear strain waves propagating in them. Variations of wave velocity and decay decrement correlated with the observed enhancement of materials’ non-linearity.

scholarly journals The extensional viscosity of a dilute suspension of spherical particles at intermediate microscale Reynolds numbers

1980 ◽  
Vol 99 (3) ◽  
pp. 513-529 ◽  
Author(s):  
G. Ryskin ◽  
G. Ryskin ◽  
J. M. Rallison
Keyword(s):  
Uniaxial Extension ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Extensional Viscosity ◽  
Spherical Particles ◽  
Rigid Sphere ◽  
Rigid Spheres ◽  
Viscous Drops ◽  
Rigid Particles ◽  
Dilute Suspension

The extensional viscosity of a dilute suspension of spherical particles (rigid spheres, viscous drops or gas bubbles) is computed for the case when the Reynolds number of the microscale disturbance motionRis not restricted to be small, as in the classical analysis of Einstein and Taylor. However, the present theory is restricted to steady axisymmetric pure straining flow (uniaxial extension). The rate of energy dissipation is expressed using the Bobyleff-Forsythe formula and then conditionally convergent integrals are removed explicitly. The problem is thereby reduced to a determination of the flow around a particle, subject to pure straining at infinity, followed (for rigid particles) by an evaluation of the volume integral of the vorticity squared. In the case of fluid particles, further integrals over the volume and surface of the particle are required. In the present paper, results are obtained numerically for 1 [les ]R[les ] 1000 for a rigid sphere, for a drop whose viscosity is equal to the viscosity of the ambient fluid, and for an inviscid drop (gas bubble). For the last case, limiting results are also obtained forR→ ∞ using Levich's approach.All of these results show a strain-thickening behaviour which increases with the viscosity of the particle. The possibility of experimental verification of the results, which is complicated by the inapplicability of the approximation of material frame-indifference in this case, is discussed.

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