Kim, Ho Jun (2008-05). Theoretical and numerical studies of chaotic mixing. Doctoral Dissertation. Thesis uri icon

abstract

  • Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ? ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.
  • Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties

    of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to

    carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral

    element algorithm for solution of the incompressible Navier-Stokes and species transport

    equations is developed. Using Taylor series expansions in time marching, the new algorithm

    employs an algebraic factorization scheme on multi-dimensional staggered spectral element

    grids, and extends classical conforming Galerkin formulations to nonconforming spectral

    elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the

    mixing device using spectral element and fourth order Runge-Kutta discretizations in space and

    time, respectively. Comparative studies of five different techniques commonly employed to

    identify the chaotic strength and mixing efficiency in microfluidic systems are presented to

    demonstrate the competitive advantages and shortcomings of each method. These are the stirring

    index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the

    probability density function of the stretching field, and mixing index inverse, based on the

    standard deviation of scalar species distribution. Series of numerical simulations are performed

    by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ? ln(Pe) scaling is demonstrated for fully

    chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the

    actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are

    identified in a zeta potential patterned straight micro channel, where a continuous flow is

    generated by superposition of a steady pressure driven flow and time periodic electroosmotic

    flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold

    of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in

    two-dimensional cavity.

publication date

  • May 2008