Quantifying mixing processes Rob Sturman Department of Mathematics - PowerPoint PPT Presentation

Quantifying mixing processes Rob Sturman Department of Mathematics University of Leeds Graduate course, Spring 2007 Leeds Rob Sturman Quantifying mixing processes

Aim of a mixing process To mix : 1. trans. a. To put together or combine (two or more substances or things) so that the constituents or particles of each are interspersed or diffused more or less evenly among those of the rest; to unite (one or more substances or things) in this manner with another or others; to make a mixture of, to mingle, blend. (OED) To produce a mixture : Substances that are mixed, but not chemically combined. Mixtures are nonhomogeneous, and may be separated mechanically. (Hackh’s Chemical Dictionary) Rob Sturman Quantifying mixing processes

Mixing is intuitive Rob Sturman Quantifying mixing processes

Mixing via stretching and folding "None other than Osborne Reynolds advocated in a 1894 lecture demonstration that, when stripped of details, mixing was essentially stretching and folding and went on to propose experiments to visualize internal motions of flows." [Ottino, Jana, Chakravarthy, 1994] Rob Sturman Quantifying mixing processes

Mixing via chaotic advection Mixing of two highly viscous fluids between eccentric cylinders [Ottino, 1989] Rob Sturman Quantifying mixing processes

An mixer based on a chaotic dynamical system The Kenics R � Mixer (a) (b) (c) (d) (e) (f) (g) (h) from [Galaktionov et al. , Int. Polymer Proc. 18 138–50 (2003)] Rob Sturman Quantifying mixing processes

Mixing via MHD A magnetohydrodynamic chaotic stirrer, [Qian & Bau, 2002] Rob Sturman Quantifying mixing processes

Oceanographic Mixing Plankton bloom at the Shetland islands. [NASA] Rob Sturman Quantifying mixing processes

Duct flows Schematic view of a duct flow with concatenated mixing elements Red and blue blobs of fluid mix well under a small number of applications Changing only the position of the centres of rotation can have a marked effect on the quality of mixing Rob Sturman Quantifying mixing processes

Mixing through turbulence Scalar concentration distribution from a high resolution numerical simulation of a turbulent flow in a two-dimensional plane for a Schmidt number of 144 and a Reynolds number of 22. (Courtesy of G. Brethouwer and F . Nieuwstadt) Rob Sturman Quantifying mixing processes

Mixing via dynamos magnetic field generated by inductive processes by the motions of a highly conducting fluid. The prescribed velocity is of a type known to be a fast dynamo, i.e., capable of field amplification in the limit of infinite conductivity (Cattaneo et al. 1995). Rob Sturman Quantifying mixing processes

A good definition... THOMASINA: When you stir you rice pudding, Septimus, the spoonful of jam spreads itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backward, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before. Do you think this odd? SEPTIMUS: No. THOMASINA: Well, I do. You cannot stir things apart. SEPTIMUS: No more you can, time must needs run backward, and since it will not, we must stir our way onward mixing as we go, disorder out of disorder into disorder until pink is complete, unchanging and unchangeable, and we are done with it for ever. Arcadia , Tom Stoppard Rob Sturman Quantifying mixing processes

How to quantify all this... Danckwerts (1952): "...two distinct parameters are required to characterize the ’goodness of mixing’...the scale of segregation...and the intensity of segregation" [Denbigh, 1986] How big? How does � this compare with � this? How wide? Rob Sturman Quantifying mixing processes