First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
Faculty of Science
Course unit
SC01122842, A.A. 2014/15

Information concerning the students who enrolled in A.Y. 2012/13

Information on the course unit
Degree course First cycle degree in
IF0320, Degree course structure A.Y. 2008/09, A.Y. 2014/15
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Number of ECTS credits allocated 8.0
Type of assessment Mark
Website of the academic structure
Department of reference Department of Chemical Sciences
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge DIEGO FREZZATO CHIM/02
Other lecturers MIRCO ZERBETTO CHIM/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses CHIM/02 Physical Chemistry 2.0
Basic courses CHIM/03 General and Inorganic Chemistry 2.0
Core courses CHIM/01 Analytical Chemistry 4.0

Course unit organization
Period Second semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 8.0 64 136.0 No turn

Start of activities 02/03/2015
End of activities 12/06/2015
Show course schedule 2019/20 Reg.2017 course timetable

Examination board
Examination board not defined

Prerequisites: Knowledge about basic mathematical concepts (vector and matrix calculus, ordinary derivatives, partial derivatives of multivariate functions, integration) and equilibrium Themodynamics should have gained from previous courses. Essential issues are however recalled in the first part of this course.
Target skills and knowledge: The main objective is to let the student aware that the description of pollutants dynamics in the environment requires a quantitative analysis which starts from a simplification of the real problem (complex and untreatable in detail), goes through the theoretical modelling of the simplified problem (build-up and parameterization of differential equations), and ends with numerical handling (solution of the equations) by means of suitable computational tools. The student will gain the methodological basis to reach it. In particular, it will be clear that there exists a hierarchy of approaches of increasing complexity, more or less adequate to treat the specific problem; the student will acquire critical view and sensitivity to select the suitable approach. Moreover, knowledge will be gained about the theoretical principles implemented in common software packages used to monitor/predict pollutants dynamics, so to be conscious in handling the input parameters when using these tools. The student will be also able to face scientific publications, having acquired the conventional terminology.
Examination methods: Oral examination.
Assessment criteria: Concise exposition with rigorous scientific language is requested to the student. Positive evaluation will be given to students able to tackle pollutants dynamics with a quantitative approach, going beyond the mere qualitative description. When a practical problem is posed, the student should be able to demonstrate capability to recognize those essential traits which are needed to build a likely theoretical model to describe the physical situation.
Course unit contents: - Essentials of equilibrium Thermodynamics
- Equilibrium partitioning of chemical species amongst several phases-compartments: air, aerosol, water, suspension in water, aquatic biota, sediments, soil, terrestrial biota. Partition coefficients. Experimental data and numerical exercises.
- Essentials of chemical kinetics: velocity reaction, kinetic laws, reaction mechanism, Arrhenius law.
- Inter-compartment transfer. Mass balance, Mackay’s classification (three levels of complexity). Exercises.
- Introduction to the pollutant transport in the single compartment. Classification of the dynamical processes: advection, local dynamics (molecular diffusion, turbulence, hydrodynamic dispersion), reactive processes, source-sink terms. Definition of flux of matter. Mathematical build-up of the Advection-Diffusion-Reaction (ADR) equation for the time evolution of the pollutant concentration field.
- Local transport due to molecular diffusion. Description on statistical basis (Brownian motion) and the non-equilibrium Thermodynamics view. Build-up of the diffusion equation. Diffusion in inhomogeneus/anisotropic, homogeneus/anisotropic, homogeneus/isotropic media. Analitical solution for unbounded diffusion in homogeneus/isotropic media. Relation between diffusion coefficients and root mean squared displacements of molecules. Diffusion in liquids, link between diffusion coefficients and viscous friction, Stokes-Einstein relation. Diffusion in the gas phase. Tables of data. Numerical exercises.
- Turbolence in fluid media. Phenomenology of eddies, essentials of Kolmogorov theory. Turbolence in the low atmospheric layers. Effect of turbulence on pollutants transport, the related diffusive-like contribution in the ADR equation. Eddy diffusion coefficients, their experimental determination and theoretical modelling. Prandtl relation. Models for vertical dispersion in air. Turbolence and shear dispersion in surface water (oceans, bays, lakes, rives, etc). Essentials of Gaussian Plume Models in air. Detailed numerical treatment of vertical dispersion in air. Exercises.
- Dispersion in groundwater. Properties of saturated and unsaturated zones, aquifers. Pressure head, hydraulic head. Darcy law for water flux. Permeability. Hydrodynamic dispersion of pollutants. Retardation factor due partirtioning amogst soil, water and air. Exercizes.
- Weigth of the several contributions to the ADR equation. Peclet and Damkoehler numbers. Matching at the interfaces.
- Pollutants transport on the long legth-scale. Essentials of fluid dynamics, Navier-Stokes equations, tools for their numerical solution, finite-elements schemes. Model of transport in air, atmospheric circulation, winds. Mention to software packages of broad usage and demonstrations.
Planned learning activities and teaching methods: The course develops with a close alternation of lectures given by two teachers: contents (Frezzato) and related exercises (Zerbetto). The lectures are given with the help of slides previously uploaded on the webpage of the teacher of reference. Numerical exercises and examples are made to facilitate the understanding of the formal issues, and to stimulate the students. Some exercises are made in a computer room with a PC at disposal for each student.
Additional notes about suggested reading: Beside the suggested textbooks for insights, the bulk of contents is entirely provided by the slides prepared by the teachers. Although inspiration is taken from the textbooks, the presentation reflects the personal point of view on the matter, and gives a self-contained frame, rigorous and formal, to the issues.
Textbooks (and optional supplementary readings)
  • Anu Ramaswami, Jana B. Milford, Mitchell J. Small, Integrated Environmental Modeling - Pollutant Transport, Fate, and Risk in the Environment. Hoboken (New Jersey): Wiley, 2005. Monografia per approfondimenti.
  • John S. Gilliver, Introduction to Chemical Transport in the Environment. New York: Cambridge University Press, 2007. Per approfondimenti sui metodi matematici e numerici
  • Donald Mackay, Multimedia Environmental Models - The fugacity Approach (2nd Ed.). --: CRC Press - Taylor & Francis Group, 2001. Tratta gli aspetti termodinamici delle fasi e lo scambio tra compartimenti Cerca nel catalogo