Short Course "Capillarity in Porous Media at Different Scales"

This online short course will take place in the framework of InterPore from 12 to 15 January 2021, and will be given by Majid Hassanizadeh (Utrecht University).

General Information

12-15 January 2021, 2 - 5 pm CET

Online short course

This short course is organized by InterPore.

Members and associated international members of SFB 1313 and IRTG DROPIT are invited to attend the short course. Participants will get 3 credits for attending the course.

Interpore members

  • 100 € students
  • 150 € academic
  • 200 € industry

Interpore non-members

  • 125 € students
  • 190 € academic
  • 300 € industry

Please note that in order to register to the short course, an InterPore account is needed. InterPore membership for 2020 must be current in order to qualify for membership rates. In order to register as a InterPore Member, you need your InterPore Membership verification code (visit: .

In this short course, a systematic approach is taken to the understanding of capillarity in porous media at different scales. Current definitions of capillary pressure, which have mainly an empirical character, are revisited and it is shown that they are special cases of a more general theory of capillarity.

First, capillary pressure is defined at pore scale based on the equation of momentum conservation for a fluid-fluid interface. It is shown that, even at microscale, capillary pressure is equal to the difference in pressures of the two fluids only under static conditions. General equations for dynamic or non- equilibrium conditions are derived. Then, capillary pressure at the macroscale (Darcy scale) is introduced based on principle of thermodynamics, and its relationship to fluid pressures under static and dynamic conditions is explored. Non-equilibrium capillarity theory and its effects on the modelling of moisture transport and two-phase flow processes are discussed. Computational and experimental studies are presented that investigate new generalized equations in variety of systems, such as water infiltration into dry soil, penetration of liquids into absorbing hygienic tissues, and moisture transport in fuel cells.

Short course includes 12 hours of lectures in four days, including exercises. Lecture materials will be distributed ahead of the class.

Lecture 1 (3 hrs) – 12 Jan 2021

1. Capillarity at pore scale

a. Concepts of wettability and surface tension, and their link to interfacial energy.

b. The difference between surface tension and interfacial tension.

c. Will water always go up in a capillary tube (the role of fluid-solid interfaces)

d. Quantitative analysis of rise (or fall) of fluid-fluid interfaces in a capillary tube.

e. What is the correct definition of capillary pressure?

f. Young’s and Young-Laplace equations in circular and noncircular tubes

g. Momentum balance equation for a fluid-fluid and fluid-solid interfaces

h. Two-phase displacement in a tube; capillarity under dynamic conditions

i. Micromodel studies of two-phase flow

Lecture 2 (3 hrs) – 13 Jan 2021

2. Capillarity at macroscale; fundamentals

a. Measurement of capillary pressure-saturation curves at REV scale

b. Various features of capillary pressure-saturation curves for hydrophobic and hydrophilic porous media

c. Link between capillary pressure-saturation curve and pore-scale capillarity

d. Derivation of capillarity equation at REV scale based on principles of rational thermodynamics

e. Experimental studies of non-equilibrium capillarity during unsaturated or two-phase flow

f. Practical significance of non-equilibrium capillarity in describing unsaturated or two-phase flow processes

Lecture 3 (6 hrs) – 14-15 Jan 2021

3. Capillarity at macroscale; computational and experimental studies

a. Experimental and/or computational determination of capillary pressure-saturation curves for different kinds of porous media (soils, fuel cells, paper, tissues)

b. Equations of two-phase flow including dynamic capillarity and their behavior

c. Experimental studies of capillarity in soils and macroscale modelling

d. Experimental studies of capillarity in hygienic products (diapers) and macroscale modelling


The short course is given by Majid Hassanizadeh (Utrecht University, The Netherlands).

Prof. Hassanizadeh is an Emeritus Professor of Hydrogeology at the Faculty of Geosciences of Utrecht University. His recent appointments have been: Professor at the Faculty of Civil Engineering and Geosciences, Delft University of Technology (2001-2003), and Professor at Utrecht University (2004-2018). He was the editor of Advances in Water Resources from 1991 till 2001. He is now on the editorial boards of Transport in Porous Media (since 1989), Journal of Porous Media (since 2009), among others. He co-founded the International Society for Porous Media (InterPore) in 2008, and has been Managing Director of InterPore since then. He has organized more than 50 conferences, workshops, and short courses, and has been invited or keynote speaker in a large number of international meetings.  He is elected Fellow of American Geophysical Union (2002), elected Fellow of American Association for Advancement of Science (2007); has received honorary degree of Doctor-Ingenieur from Stuttgart University (2008); and is a recipient of von Humboldt Prize (2010) and Don and Betty Kirkham Soil Physics Award from SSSA (2011). He was selected as 2012 Darcy Lecturer by the US National Groundwater Association (2011). He was awarded a research grant of 2.3 MEuro by the European Research Council (2013). He is recipient of Royal medal of honor of The Netherlands, Ridder in de Orde van Nederlandse Leeuw (Knight in the Order of Netherlands Lion), July 2015, and recipient of Robbert E. Horton Medal from American Geophysical Union (2019).

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