Lagrangian chaos and multiphase processes in vortex flows. (English) Zbl 1222.76023
Summary: We discuss experimental and numerical studies of the effects of Lagrangian chaos (chaotic advection) on the stretching of a drop of an immiscible impurity in a flow. We argue that the standard capillary number used to describe this process is inadequate since it does not account for advection of a drop between regions of the flow with varying velocity gradient. Consequently, we propose a Lagrangian-generalized capillary number \(C_{\text L}\) number based on finite-time Lyapunov exponents. We present preliminary tests of this formalism for the stretching of a single drop of oil in an oscillating vortex flow, which has been shown previously to exhibit Lagrangian chaos. Probability distribution functions (PDFs) of the stretching of this drop have features that are similar to PDFs of \(C_{\text L}\). We also discuss on-going experiments that we have begun on drop stretching in a blinking vortex flow.
MSC:
| 76B47 | Vortex flows for incompressible inviscid fluids |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
| 76F20 | Dynamical systems approach to turbulence |
References:
| [1] | Aref, H., J. Fluid Mech., 143, 1 (1984) · Zbl 0559.76085 |
| [2] | Ottino, J. M.; Leong, C. W.; Rising, H.; Swanson, P. D., Nature, 333, 419 (1988) |
| [3] | Solomon, T. H.; Gollub, J. P., Phys. Rev. A, 38, 6280 (1988) |
| [4] | Camassa, R.; Wiggins, S., Phys. Rev. A, 43, 774 (1991) · Zbl 0936.76509 |
| [5] | Solomon, T. H.; Tomas, S.; Warner, J. L., Phys. Rev. Lett., 77, 2682 (1996) |
| [6] | Solomon, T. H.; Lee, A. T.; Fogleman, M. A., Physica D, 157, 40 (2001) · Zbl 1049.76064 |
| [7] | Castiglione, P.; Crisanti, A.; Mazzino, A.; Vergassola, M.; Vulpiani, A., J. Phys. A, 31, 7197 (1998) · Zbl 0940.76090 |
| [8] | Rallison, J. M., Ann. Rev. Fluid Mech., 16, 45 (1984) · Zbl 0604.76079 |
| [9] | Stone, H. A., Ann. Rev. Fluid Mech., 26, 65 (1994) · Zbl 0802.76020 |
| [10] | Milliken, W. J.; Leal, L. G., J. Non-Newtonian Fluid Mech., 40, 355 (1991) |
| [11] | Gollub, J. P.; Solomon, T. H., Phys. Scripta, 40, 430 (1989) |
| [12] | Chandrasekhar, S., Hydrodynamic and hydromagnetic stability (1961), Dover: Dover New York · Zbl 0142.44103 |
| [13] | Willaime, H.; Cardoso, O.; Tabeling, P., Phys. Rev. E, 48, 288 (1993) |
| [14] | Solomon, T. H.; Tomas, S.; Warner, J. L., Phys. Fluids, 10, 342 (1998) |
| [15] | Solomon TH. Transport and boundary layers in Rayleigh-Bénard convection, PhD thesis, 1990; Solomon TH. Transport and boundary layers in Rayleigh-Bénard convection, PhD thesis, 1990 |
| [16] | Pervez, M. S.; Solomon, T. H., Exp. Fluids, 17, 135 (1994) |
| [17] | Solomon, T. H.; Weeks, E. R.; Swinney, H. L., Phys. Rev. Lett., 71, 3975 (1993) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
