Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force

Asokan, K.; Kumar, C. V. Anil; Dasan, J.; Radhakrishnan, K.; Kumar, K. Satheesh; Ramamohan, T. R.

doi:10.1016/j.jnnfm.2005.06.003

Cited by 14 publications

(14 citation statements)

References 91 publications

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“…This represents the first step to extend the results summarized by Asokan et al (2005), to the low Reynolds number regime. In this paper, we extend these results to prolate spheroidal particle suspensions as a prelude to a study of more complex suspensions.…”

Section: Introductionmentioning

confidence: 72%

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Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

Madhukar

Kumar

Ramamohan

et al. 2010

Sadhana

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Abstract. The problem of determining the force acting on a particle in a fluid where the motion of the fluid and the particle is given has been considered in some detail in the literature. In this work, we propose an example of a new class of problems where, the fluid is quiescent and the effect of an external periodic force on the motion of the particle is determined at low non-zero Reynolds numbers. We present an analysis of the dynamics of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers including the effects of both convective and unsteady inertia. The inclusion of both forms of inertia leads to a nonlinear integro -differential equation which is solved numerically for the velocity and displacement of the individual particle. We show that a 'normal stress' like parameter can be evaluated using standard techniques of Batchelor. Hence this system allows for an experimentally accessible measurable macroscopic parameter, analogous to the 'normal stress', which can be related to the dynamics of individual particles. We note that this 'normal stress' arises from the internal fluctuations induced by the periodic force. In addition, a preliminary analysis leading to a possible application of separating particles by shape is presented. We feel that our results show possibilities of being technologically important since the 'normal stress' depends strongly on the controllable parameters and our results may lead to insights in the development of active dampeners and smart fluids. Since we see complex behaviour even in this simple system, it is expected that the macroscopic behaviour of such suspensions may be much more complex in more complex flows. 660 K Madhukar et alKeywords. Low Reynolds number; quiescent fluid; periodically forced prolate spheroids; aspect ratio; inertial effects and particle separation.

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Section: Introductionmentioning

confidence: 72%

“…This chaotic dynamics can be controlled by controlling system parameters (Kumar & Ramamohan 1998). These results restricted to zero Reynolds numbers and simple shear flows have been summarized by Asokan et al (2005).…”

Section: Introductionmentioning

confidence: 99%

Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

Madhukar

Kumar

Ramamohan

et al. 2010

Sadhana

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“…In addition, the study of the dynamics and rheology of a suspension of periodically forced particles in a sheared Newtonian fluid has gained importance for over a decade because of its fundamental consequences and its potential technological implications. The main results pertaining to this area have been summarized in a review by Asokan et al (2005). The system considered is an ideal physical system for testing the effects of periodic forcing at the level of individual particles on rheological parameters at a macroscopic level.…”

Section: Introductionmentioning

confidence: 99%

“…Since the rheological parameters are obtained by suitable averages over all the individual particles, this system is an ideal system to study the fundamentally and technologically important question of the conditions under which an average over a large number of individually chaotically varying particles itself varies chaotically. The work summarized by Asokan et al (2005) has provided some partial answers to this question. In the case of dilute suspensions, the periodic forcing appears both in the equations of the dynamics of the individual particles and in the equations of the rheological properties.…”

Section: Introductionmentioning

confidence: 99%

The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers

Ramamohan¹,

Shivakumara²,

Madhukar³

2011

Fluid Dyn. Res.

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We study the effects of both convective and unsteady inertia on the dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles, at low Reynolds numbers, in a quiescent Newtonian fluid. The inclusion of inertia results in additional terms in the equation governing the dynamics of the particle that represent a fading memory of the entire history of the particle motion. The inclusion of convective inertia in the low Reynolds number limit makes the memory term nonlinear. Several tests were performed to show that the results presented in this paper are physically reasonable and correct. A perturbation analysis of the problem yields strong evidence that the results of our simulations are correct. It is observed that there is a preferred direction in this system which manifests itself in the properties of the solution. This preferred direction is identified as the direction of the initial motion of the particle. We present here results on the behavior of various parameters with respect to Reynolds numbers and the amplitude of the periodic force. These include phase-space plots between particle displacement and particle velocity and the variation of a rheological parameter, namely a 'normal stress' with respect to Reynolds number and the amplitude of the periodic force. We believe that our results may be technologically important since the rheological parameter depends strongly on controllable parameters such as the Reynolds number and the amplitude of the periodic force. Further, this system is one of the simplest systems whose rheology shows non-Newtonian behavior, such as the presence of a normal stress. In addition, this system represents a physically realizable system for experimentally testing the frameworks developed to calculate the collective behavior of systems of oscillators with memory.

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“…However, even simpler experiments ͑in different geometries͒ with only a few particles in a liquid also find complex behavior. [16][17][18][19] For example, a dilute suspension of particles falling through a liquid can result in nontrivial swirling motions of the particles due to their hydrodynamic interactions. [20][21][22][23][24][25][26][27] Pushing to even further dilution, simulations found that even three spheres falling through a liquid have nontrivial interactions, and exhibit sensitive dependence on their initial positions.…”

Section: Introduction and Prior Workmentioning

confidence: 99%

Complex dynamics of three interacting spheres in a rotating drum

et al. 2010

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Numerous studies have demonstrated the potential for particles in fluids to exhibit complicated dynamical behavior. In this work, we study a horizontal rotating drum filled with pure glycerol and three large, heavy spheres. The rotation of the drum causes the spheres to cascade and tumble and thus interact with each other. We find several different behaviors of the spheres depending on the drum rotation rate. Simpler states include the spheres remaining well separated, or states where two or all three of the spheres come together and cascade together. We also see two more complex states, where two or three of the spheres move erratically. The main signature of this erratic motion is that pairs of spheres intermittently approach each other ͑sometimes colliding͒ and then separate; the time between collisions is variable even for a fixed rotation rate. We characterize these disordered states and find a complex phase space with a rich set of behaviors. This experiment serves as a simple model system to demonstrate complex behavior in simple fluid dynamical systems.

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Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force

Cited by 14 publications

References 91 publications

Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers

Complex dynamics of three interacting spheres in a rotating drum

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