MIXING AND SEPARATION PROCESSES AT MICRO-NANO SCALES

Course objectives

The class aims at providing the theoretical basis and the computational skills for the design of mixing/reaction and separation processes in micro/nanofluidic devices. The theoretical toolbox is composed of Stokes flow theory, dynamical system approach to mass transport in laminar flows (with specific focus on deterministic chaos), macro-transport theory in periodic media for the determination of effective transport parameters. These theoretical approaches are applied to the optimal design of microfluidic reactors and separators for the identification of analytical targets and small-scale production of high-added-value products. The optimal design results from the numerical solution of the transport-reaction equations through in-house codes and commercial software. Specific emphasis is placed on clinical biomedical and pharmaceutical applications.

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STEFANO CERBELLI Lecturers' profile

Program - Frequency - Exams

Course program
**Part I: Kinematic Approach to Convective Transport** Review of scalar and vector quantities. Einstein notation. Stokes flows in single-phase and multiphase systems. Two-dimensional flows and stream function. Notes on the numerical solution of Stokes flows. Convective transport: advection equation. Local deformation and stretching factor. Heuristic introduction to deterministic chaotic flows. The dynamical systems approach. Conservative systems. Poincaré recurrence theorem. Nontrivial recurrence. Ergodicity and mixing. Poincaré sections. Lyapunov exponents. --- **Part II: Convection and Diffusion** The convection–diffusion equation in closed and open systems. Asymptotic properties and mixing indices. Scalar variance. Mixing properties of chaotic laminar flows. --- **Part III: Applications to Microreactors** Mixing-controlled reactions. CFD project: design of a continuous chaotic-flow microreactor. --- **Part IV: Applications to Microfluidic Devices for Liquid Chromatography** Adsorption: phenomenological aspects and equilibrium isotherms. Dispersion in laminar flows. Brenner’s macrotransport theory. Taylor–Aris dispersion. Liquid chromatography (LC) and gas chromatography (GC): separation principle, efficiency, and resolution factor. Hydrodynamic chromatography (HDC). Transport/adsorption models of chromatographic devices. CFD project: design of a microchannel for HDC.
  • Lesson code10610448
  • Academic year2025/2026
  • CourseNanotechnology Engineering
  • Curriculum32343-01
  • Year2nd year
  • Semester1st semester
  • SSDING-IND/24
  • CFU6