Effective rheology of bubbles moving in a capillary tube.

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train, considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.

[1]  J. G. Contreras,et al.  Measurement of inelastic, single- and double-diffraction cross sections in proton–proton collisions at the LHC with ALICE , 2012, The European physical journal. C, Particles and fields.

[2]  M. Z. Mehta,et al.  J/psi and psi(2S) production in pp collisions at sqrt(s) = 7 TeV , 2011, 1111.1557.

[3]  J. G. Contreras,et al.  J/ψ polarization in pp collisions at √s=7 TeV. , 2011, 1111.1630.

[4]  S. H. Kim,et al.  Rapidity and transverse momentum dependence of inclusive J/psi production in pp collisions at root s=7 TeV , 2011 .

[5]  M. L. Ferrer,et al.  Measurement of the differential cross-sections ofinclusive, prompt and non-prompt J/ψ production in proton–proton collisions at √s = 7 TeV , 2011 .

[6]  B. Kniehl,et al.  World data ofJ/ψproduction consolidate nonrelativistic QCD factorization at next-to-leading order , 2011, 1105.0820.

[7]  F. Bossù,et al.  Phenomenological interpolation of the inclusive J/psi cross section to proton-proton collisions at 2.76 TeV and 5.5 TeV , 2011, 1103.2394.

[8]  M. Beuzekom,et al.  Measurement of J/psi production in pp collisions at root s=7 TeV , 2011, 1103.0423.

[9]  M. Z. Mehta,et al.  Prompt and non-prompt J/ψ production in pp collisions at $\sqrt{s} = 7$ TeV , 2011 .

[10]  V. Papadimitriou,et al.  Heavy quarkonium: progress, puzzles, and opportunities , 2010, 1010.5827.

[11]  B. Kniehl,et al.  Reconciling J/ψ production at HERA, RHIC, Tevatron, and LHC with nonrelativistic QCD factorization at next-to-leading order. , 2010, Physical review letters.

[12]  K. Chao,et al.  J/ψ(ψ') production at the Tevatron and LHC at O(α(s)4v4) in nonrelativistic QCD. , 2010, Physical review letters.

[13]  H. K. Wöhri,et al.  Towards the experimental clarification of quarkonium polarization , 2010, 1006.2738.

[14]  M. Kowalski,et al.  The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events , 2010, 1001.1950.

[15]  Lindenstruth,et al.  Alignment of the ALICE Inner Tracking System with cosmic-ray tracks , 2010 .

[16]  J. Lansberg.  On the mechanisms of heavy-quarkonium hadroproduction , 2008, 0811.4005.

[17]  T. Ullrich,et al.  Heavy flavor in heavy-ion collisions at RHIC and RHIC II , 2008, 0806.1013.

[18]  J. Lansberg,et al.  Possible solution of the J/psi production puzzle. , 2007, Physical review letters.

[19]  Warren J. Busscher,et al.  Flow and Transport in Porous Media , 1982 .

[20]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[21]  P. Faccioli,et al.  European Laboratory for Particle Physics J/ψ Polarization from Fixed-target to Collider Energies , 2008 .

[22]  Dylan R. Nelson,et al.  NON-LINEAR DYNAMICS AND CHAOS , 2007 .