Breadcrumb

Making the smallest jet

Supervisor: Jens Eggers

Theme: Fluid Dynamics

Many applications in the new field of microfluidics require the
production of the smallest possible structures.
The idea of this project is to harness the nonlinear character of
fluid motion to make extremely small structures, rather than being
obliged to engineer them mechanically. As the starting point,
we take the selective withdrawal experiment, in which a viscous
fluid is withdrawn through a capillary from near an interface between
two fluids. As a result, the interface deforms into a sharp
tip. As the rate of withdrawal is increased, the fluid on the other
side of the interface is entrained as a thin jet into the capillary.

However, as one approaches the transition to entrainment, the thickness
of the jet does not go to zero, as expected for a continuous transition.
Instead, the interface shape jumps from a tip to a jet of finite thickness.
Upon reducing the flow rate, the jet disappears when it is still of
an appreciable thickness: generically one sees a first-order (discontinuous)
transition.

In this project, we propose to deploy some of the unique analytical
and numerical tools developed in Bristol to search for the smallest
jet. The idea is that one needs to tune additional parameters of the
problem, hitherto unexplored, to turn the transition from first order to
second order (continuous). As one reaches the critical state, the
characteristic scale of the problem goes to zero. This permits to
search for a self-similar description of the problem, which permits
the application of a range of powerful analytical tools.

This project offers training and experience in a variety of analytical and
numerical methods. We also entertain close collaborations with
groups performing experiments in the area, and on this system in particular.


Publications

  • Numerical analysis of tips in viscous flow (2009)
    J. Eggers, S. Courrech du Pont
    Phys. Rev. E, vol: 79, Page: 066311
    URL provided by the author
  • Sink flow deforms the interface between a viscous liquid and air into a tip singularity (2006)
    S. Courrech du Pont, J. Eggers
    Phys. Rev. Lett., vol: 96, Page: 034501
    URL provided by the author
  • Physics of liquid jets (2008)
    J. Eggers and E. Villermaux
    Rep. Progr. Phys., vol: 71, Page: 036601
    URL provided by the author