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Vincenzi D. Effect of internal friction on the coil-stretch transition in turbulent flows. SOFT MATTER 2021; 17:2421-2428. [PMID: 33491720 DOI: 10.1039/d0sm01981j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A polymer in a turbulent flow undergoes the coil-stretch transition when the Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and the relaxation time of the polymer, surpasses a critical value. The effect of internal friction on the transition is studied by means of Brownian dynamics simulations of the elastic dumbbell model in a homogeneous and isotropic, incompressible, turbulent flow and analytical calculations for a stochastic velocity gradient. The results are explained by adapting the large deviations theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic dumbbell with internal viscosity. In turbulent flows, a distinctive feature of the probability distribution of polymer extensions is its power-law behaviour for extensions greater than the equilibrium length and smaller than the contour length. It is shown that although internal friction does not modify the critical Weissenberg number for the coil-stretch transition, it makes the slope of the probability distribution of the extension steeper, thus rendering the transition sharper. Internal friction therefore provides a possible explanation for the steepness of the distribution of polymer extensions observed in experiments at large Weissenberg numbers.
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Anand P, Ray SS, Subramanian G. Orientation Dynamics of Sedimenting Anisotropic Particles in Turbulence. PHYSICAL REVIEW LETTERS 2020; 125:034501. [PMID: 32745414 DOI: 10.1103/physrevlett.125.034501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Revised: 05/12/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on (to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes, and Froude numbers. Orientational moments from the simulations compare well with analytical predictions in the inertialess rapid-settling limit, with both exhibiting a nonmonotonic dependence on spheroid aspect ratio. Deviations arise at Stokes numbers of order unity due to a spatially inhomogeneous particle concentration field resulting from a preferential sweeping effect; as a consequence, the time-averaged particle settling velocities exceed the orientationally averaged estimates.
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Affiliation(s)
- Prateek Anand
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Ganesh Subramanian
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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Bhatnagar A. Statistics of relative velocity for particles settling under gravity in a turbulent flow. Phys Rev E 2020; 101:033102. [PMID: 32289925 DOI: 10.1103/physreve.101.033102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Accepted: 02/07/2020] [Indexed: 06/11/2023]
Abstract
We study the joint probability distributions of separation R and radial component of the relative velocity V_{R} of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no-gravity case. Distributions of V_{R} for fixed values of R show a power-law dependence on V_{R} for a range of V_{R}; the exponent of the power law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) Moments of the distributions are anisotropic; degree of anisotropy depends on particle's Stokes number, but does not depend on R for small values of R. (b) Mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.
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Affiliation(s)
- Akshay Bhatnagar
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
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Agasthya L, Picardo JR, Ravichandran S, Govindarajan R, Ray SS. Understanding droplet collisions through a model flow: Insights from a Burgers vortex. Phys Rev E 2019; 99:063107. [PMID: 31330678 DOI: 10.1103/physreve.99.063107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2018] [Indexed: 11/06/2022]
Abstract
We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of polydisperse suspensions in this enhancement. Our work uncovers an important principle, which, if valid for realistic turbulent flows, may be a factor in how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.
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Affiliation(s)
- Lokahith Agasthya
- Indian Institute for Science Education and Research, Pune, 411008, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.,Department of Physics and INFN, University of Rome Tor Vergata,Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Jason R Picardo
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - S Ravichandran
- Nordita, KTH Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
| | - Rama Govindarajan
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
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Picardo JR, Vincenzi D, Pal N, Ray SS. Preferential Sampling of Elastic Chains in Turbulent Flows. PHYSICAL REVIEW LETTERS 2018; 121:244501. [PMID: 30608752 DOI: 10.1103/physrevlett.121.244501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2018] [Indexed: 06/09/2023]
Abstract
A string of tracers interacting elastically in a turbulent flow is shown to have a dramatically different behavior when compared to the noninteracting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: An elastic chain is trapped in the vortical regions. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain via the number of links that form it is also examined.
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Affiliation(s)
- Jason R Picardo
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | | | - Nairita Pal
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
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Roy A, Gupta A, Ray SS. Inertial spheroids in homogeneous, isotropic turbulence. Phys Rev E 2018; 98:021101. [PMID: 30253548 DOI: 10.1103/physreve.98.021101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Indexed: 11/07/2022]
Abstract
We study the rotational dynamics of inertial disks and rods in three-dimensional, homogeneous, isotropic turbulence. In particular, we show how the alignment and the decorrelation timescales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia-which leads to a preferential sampling of the local flow geometry-on the statistics of both disks and rods in a turbulent flow. Our results are important for a variety of natural and industrial settings where the turbulent transport of asymmetric, spheroidal inertial particles is ubiquitous.
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Affiliation(s)
- Amal Roy
- Department of Mathematics, Indian Institute of Science, Bangalore 560012, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Anupam Gupta
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
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Meibohm J, Pistone L, Gustavsson K, Mehlig B. Relative velocities in bidisperse turbulent suspensions. Phys Rev E 2017; 96:061102. [PMID: 29347374 DOI: 10.1103/physreve.96.061102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2017] [Indexed: 06/07/2023]
Abstract
We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St[over ¯], so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St[over ¯] is large enough.
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Affiliation(s)
- J Meibohm
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - L Pistone
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - K Gustavsson
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - B Mehlig
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
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