Transport in Transitory Systems: a Microdroplet Model

• Author: J. Meiss, University of Colorado.


• Oral or poster: oral.


• Downloadable presentation/poster: click here.


• Abstract:
  A dynamical systems is transitory if it is nonautonomous only on a compact interval of time. Such dynamics is appropriate to the study of, for example, fluid mixing in open pipe flows. In this talk I will discuss a simple model for the flow within a droplet in a sinuous pipe of finite length. We derive an action-flux formula to compute the volumes of lobes quantifying transport between past- and future-invariant regions for a globally Liouville flow--such flows arise from incompressible vector fields and have a Lagrangian-like generating form. This method requires relatively little Lagrangian information about the codimension-one surfaces bounding the lobes, relying only on the generalized actions of loops on the lobe boundaries. These are easily computed since the vector fields are autonomous before and after the time-dependent transition. A goal is to build the most efficient laminar mixer by tuning the pipe shape.