Chemical and Biological Engineering

A full year study of an important problem or topic in chemical and biological engineering culminating in a senior thesis. Projects may be experimental, computational, or theoretical. Topics selected by the students from suggestions by the faculty. Written thesis, poster presentation, and oral defense required. The senior thesis is recorded as a double course in the spring. Departmental permission required.

Elements of fluid mechanics relevant to liquids and gases at subsonic conditions are studied, beginning with unidirectional flows and macroscopic balances; flows without inertia treated via lubrication approximation and Stokes' equations; and effects of inertia in inviscid and boundary layer flows. The course introduces hydrodynamic stability theory and turbulent flows.

Linear ordinary differential equations (systems of first-order equations, method of Frobenius, two-point boundary-value problems); spectrum and Green's function; matched asymptotic expansions; partial differential equations (classification, characteristics, uniqueness, separation of variables, transform methods, similarity); and Green's function for the Poisson, heat, and wave equations, with applications to selected problems in chemical, civil, and mechanical engineering.

A systematic treatment of chemical thermodynamics from an advanced point of view. It explores the equilibrium properties of chemical systems under a wide range of conditions and applications to problems of a chemical engineering nature, with an emphasis on multicomponent mixtures and reactive systems.

The elements of chemical rate processes; reactor properties in continuous flow; staged, steady-state, and transient operations; optimal distribution of properties; and stability. The effect of physical transport rates when coupled with chemical rates on reactor design and characteristics is examined.

Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.

A survey of modeling and solutions methods for problems involving heat, mass and momentum transport. Topics include conservation equations, conductive heat transfer, species diffusion, kinematics and dynamics of viscous flows, the Navier-Stokes equations, scaling principles and approximation techniques, boundary layer theory, convective heat and mass transfer, multi-component energy and mass transfer, buoyancy-driven convection, transport in ionic solutions, introduction to instability and turbulence.

Emphasizes the connection between microstructural features of materials (e.g., grain size, boundary regions between grains, defects) and their properties, and how processing conditions control structure. Topics include thermodynamics and phase equilibria, microstructure, diffusion, kinetics of phase transitions, nucleation and crystal growth, phase separation, spinodal decomposition, glass formation, and the glass transition.

This course examines methods for simulating matter at the molecular and electronic scale. Molecular dynamics, Monte Carlo and electronic structure methods will be covered with emphasis on hands-on experience in writing and/or exercising simulation codes for atomistic and electronic structure simulation.

An overview of the behavior of small particles dispersed in liquids. Assessment is made of the hydrodynamic, Brownian, electrostatic, and dispersion forces acting among particles. Electrokinetic phenomena generated by an applied electric field; stabilization and flocculation of aqueous dispersions; and collection of particles in deep-bed filters are studied.

An exploration of the connection between macroscopic behavior of dispersions and microscopic forces; forces induced by grafted, adsorbing, and nonadsorbing polymer; equilibrium phase behavior; hindered sedimentation and transient settling processes; diffusion and photon correlation spectroscopy; and rheology of concentrated dispersions.

Statistical mechanics provides the basis for understanding the equilibrium and nonequilibrium properties of matter in terms of the microscopic details of molecular interactions and structure. The course aims to provide students with working knowledge of the fundamentals and applications of statistical mechanics.

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscious liquid fast enough to avoid crystallization. Although this route to the vitreous state - supercooling - has been known for millenia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. The course will address both the theory and applications of supercooled liquids and glasses.

Fundamentals and practice of polymer synthesis, both at the laboratory and industrial scales. Mechanism, kinetics, and range of application of important polymerization methods: condensation, free-radical, anionic, cationic, coordination; polymerization thermodynamics; chemical reactions on polymers; selected industrial processes (e.g., polyesterification, emulsion polymerization, high- and low-pressure routes to polyethylene).

An introduction to the dynamics of suspended liquid and solid particles in gas media. Processes of particle nucleation, coagulation, condensation, deposition, and transport are examined. Atmospheric aerosols and particle activation in the supersaturated environment of clouds are considered in addition to combustion, ceramic, and pharmaceutical aerosol applications. Theoretical modeling approaches and experimental methods are reviewed.

The mechanics of viscous flows. The course explores the kinematics and dynamics of viscous flows; solution of the Navier Stokes equations; the behavior of vorticity; the boundary layer approximation; laminar boundary layer with and without pressure gradient; separation; integral relations and approximate methods; compressible laminar boundary layers; instability and transition; and turbulent boundary layers and self-preserving turbulent shear flows.

Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, fluorescence and infrared imaging, and photoemission spectroscopy. Emphasis is placed on application of the techniques for uncovering the material structure-property relationship, including energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.

Collective behaviors are all around us, from bird flocking, to mosh pit dynamics, to how the cells in our bodies work together. In this course, we explore not only how to understand and quantify these behaviors, but also how we can start to engineer them to reduce traffic, heal faster, develop new materials, and introduce new robotics approaches. The course spans three modules: hands-on training in analyzing real-world swarming systems; fundamental concepts underlying collective behaviors; and key case studies in manipulating these systems.