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Effect of the eigenvalues of the velocity gradient tensor on particle collisions
- Vincent E. Perrin, Harmen J. J. Jonker
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- Journal:
- Journal of Fluid Mechanics / Volume 792 / 10 April 2016
- Published online by Cambridge University Press:
- 29 February 2016, pp. 36-49
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This study uses the eigenvalues of the local velocity gradient tensor to categorize the local flow structures in incompressible turbulent flows into different types of saddle nodes and vortices and investigates their effect on the local collision kernel of heavy particles. Direct numerical simulation (DNS) results show that most of the collisions occur in converging regions with real and negative eigenvalues. Those regions are associated not only with a stronger preferential clustering of particles, but also with a relatively higher collision kernel. To better understand the DNS results, a conceptual framework is developed to compute the collision kernel of individual flow structures. Converging regions, where two out of three eigenvalues are negative, posses a very high collision kernel, as long as a critical amount of rotation is not exceeded. Diverging regions, where two out of three eigenvalues are positive, have a very low collision kernel, which is governed by the third and negative eigenvalue. This model is not suited for particles with Stokes number $St\gg 1$, where the contribution of particle collisions from caustics is dominant.
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- By Jane E. Adcock, Yahya Aghakhani, A. Anand, Eva Andermann, Frederick Andermann, Alexis Arzimanoglou, Sandrine Aubert, Nadia Bahi-Buisson, Carman Barba, Agatino Battaglia, Geneviève Bernard, Nadir E. Bharucha, Laurence A. Bindoff, William Bingaman, Francesca Bisulli, Thomas P. Bleck, Stewart G. Boyd, Andreas Brunklaus, Harry Bulstrode, Jorge G. Burneo, Laura Canafoglia, Laura Cantonetti, Roberto H. Caraballo, Fernando Cendes, Kevin E. Chapman, Patrick Chauvel, Richard F. M. Chin, H. T. Chong, Fahmida A. Chowdhury, Catherine J. Chu-Shore, Rolando Cimaz, Andrew J. Cole, Bernard Dan, Geoffrey Dean, Alessio De Ciantis, Fernando De Paolis, Rolando F. Del Maestro, Irissa M. Devine, Carlo Di Bonaventura, Concezio Di Rocco, Henry B. Dinsdale, Maria Alice Donati, François Dubeau, Michael Duchowny, Olivier Dulac, Monika Eisermann, Brent Elliott, Bernt A. Engelsen, Kevin Farrell, Natalio Fejerman, Rosalie E. Ferner, Silvana Franceschetti, Robert Friedlander, Antonio Gambardella, Hector H. Garcia, Serena Gasperini, Lorenzo Genitori, Gioia Gioi, Flavio Giordano, Leif Gjerstad, Daniel G. Glaze, Howard P. Goodkin, Sidney M. Gospe, Andrea Grassi, William P. Gray, Renzo Guerrini, Marie-Christine Guiot, William Harkness, Andrew G. Herzog, Linda Huh, Margaret J. Jackson, Thomas S. Jacques, Anna C. Jansen, Sigmund Jenssen, Michael R. Johnson, Dorothy Jones-Davis, Reetta Kälviäinen, Peter W. Kaplan, John F. Kerrigan, Autumn Marie Klein, Matthias Koepp, Edwin H. Kolodny, Kandan Kulandaivel, Ruben I. Kuzniecky, Ahmed Lary, Yolanda Lau, Anna-Elina Lehesjoki, Maria K. Lehtinen, Holger Lerche, Michael P. T. Lunn, Snezana Maljevic, Mark R. Manford, Carla Marini, Bindu Menon, Giulia Milioli, Eli M. Mizrahi, Manish Modi, Márcia Elisabete Morita, Manuel Murie-Fernandez, Vivek Nambiar, Lina Nashef, Vincent Navarro, Aidan Neligan, Ruth E. Nemire, Charles R. J. C. Newton, John O'Donavan, Hirokazu Oguni, Teiichi Onuma, Andre Palmini, Eleni Panagiotakaki, Pasquale Parisi, Elena Parrini, Liborio Parrino, Ignacio Pascual-Castroviejo, M. Scott Perry, Perrine Plouin, Charles E. Polkey, Suresh S. Pujar, Karthik Rajasekaran, R. Eugene Ramsey, Rahul Rathakrishnan, Roberta H. Raven, Guy M. Rémillard, David Rosenblatt, M. Elizabeth Ross, Abdulrahman Sabbagh, P. Satishchandra, Swati Sathe, Ingrid E. Scheffer, Philip A. Schwartzkroin, Rod C. Scott, Frédéric Sedel, Michelle J. Shapiro, Elliott H. Sherr, Michael Shevell, Simon D. Shorvon, Adrian M. Siegel, Gagandeep Singh, S. Sinha, Barbara Spacca, Waney Squier, Carl E. Stafstrom, Bernhard J. Steinhoff, Andrea Taddio, Gianpiero Tamburrini, C. T. Tan, Raymond Y. L. Tan, Erik Taubøll, Robert W. Teasell, Mario Giovanni Terzano, Federica Teutonico, Suzanne A. Tharin, Elizabeth A. Thiele, Pierre Thomas, Paolo Tinuper, Dorothée Kasteleijn-Nolst Trenité, Sumeet Vadera, Pierangelo Veggiotti, Jean-Pierre Vignal, J. M. Walshe, Elizabeth J. Waterhouse, David Watkins, Ruth E. Williams, Yue-Hua Zhang, Benjamin Zifkin, Sameer M. Zuberi
- Edited by Simon D. Shorvon, Frederick Andermann, Renzo Guerrini
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- Book:
- The Causes of Epilepsy
- Published online:
- 05 March 2012
- Print publication:
- 14 April 2011, pp ix-xvi
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