Optimization, Dynamics and Stability of Non-Linear Separation Processes

In this thesis we develop a non convex non-linear programming problem that determines the minimum run time of a rapid, gel-free DNA separation technique called micelle end-labeled free solution electrophoresis (ELFSE). Micelle ELFSE is typically performed in capillary electrophoresis where the capillary length, electric field strength, and micelle drag tag size are the primary tuning variables. Using optimization, we demonstrate that capillary electrophoresis can be used to separate up to 600 bases in under 50 minutes. A significant improvement in performance is then shown to be achievable by using parallel capillaries which can separate up to 600 bases in under 5 minutes. Even more improvement is shown to be possible by using alternative separation modes, such as using an EOF counter-flow which enables 600 bases to be separated in under 4.5 minutes using a single capillary, and microfluidics utilizing snapshot detection to yield 600 bases in under 3.5 minutes. Long DNA, above 5000 bases, is particularly challenging to separate quickly. Using Brownian dynamics simulations we show the viability of integrating two DNA separation techniques: end-labeled DNA electrophoresis and entropic trapping. We present simulation results that demonstrate improved performance of the integrated device over entropic trapping alone. Brownian dynamics simulations are very computationally expensive, often taking over 24 hours per data point. We present an acceleration technique called projective integration which may be useful for simulations with a large amount of integration steps. We show that, using a model built from linear regression, periodic extrapolations can be used to decrease computational time. Finally we present the stability of the multi-component distillation column. We demonstrate, through the use of thermodynamics, that the distillation column is asymptotically stable when using pressure, temperature, and level control on the reboiler and condenser.