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On a question posed by G.I. Taylor.

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In this talk, we shall look into a question raised by G.I. Taylor with regard to the study of the spreading (usually referred to as ‘Dispersion’) of dissolved solutes in a fluid medium. The interplay between molecular diffusion and the variations in fluid velocity were studied by G.I. Taylor. Neither a simple molecular diffusion nor a simple convection can account for the effective mixing of solutes. The main question raised by Taylor was to find an expression for the Dispersion tensor in terms of the molecular diffusion and the convective field. We shall try to answer this question of Taylor in case of heterogeneous flow fields and molecular diffusion. Our approach is via the theory of Homogenization. We shall discuss a complete solution to the question of Taylor when the convective field is purely periodic in space. We shall also present some recent calculations which give an expression for the ‘Taylor Dispersion’ when the convective field is locally periodic i.e., when the fluid velocity has macroscopic modulations. These results are obtained via the study of integral curves associated with an ODE . We shall discuss a new notion of convergence in moving coordinates which might be helpful in the study of various problems in fluid dynamics. We shall also try to discuss the difficulties that are present in giving a complete solution to the original question raised by G.I. Taylor.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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