Dr. B.J. Meulenbroek


Mathematics for engineers.




Bernard Meulenbroek is assistant professor in the Mathematical Physics section. He is interested
in the mathematical modelling of flow through porous media. In the previous years he has worked
with both academic and industrial partners on a number of applied problems such as (microbial)
enhanded oil recovery, CO2 sequestration and geothermal energy.

Modelling these problems often leads to a set of coupled partial differential equations (PDEs).
These PDEs are highly nonlinear as dictated by the physics of the underlying (applied) problem,
which leads to challenging mathematical problems. A further complication can be the presence of
so called "degenerate diffusion", which means that the PDEs become (almost) hyperbolic. Using
analytical and numerical methods the model equations are solved and the stability of the resulting
solution profiles is studied.

In an ongoing project he is working on the (prevention of) clogging of geothermal systems; this is
challenging from a modelling as well as a mathematical perspective. Temperature effects are now
expected to play a large role, which means that our terms in the PDEs (e.g. reaction rates) may
become highly nonlinear. In another project he will focus on the interface stability in two-phase
flow in the case of degenerate diffusion.

Two videos about his 2018 paper can be found on the YouTube-channel:

www.youtube.com/c/mathemagician [choose the "scientific videos"-section].

Recent publications:

  •  Meulenbroek, Bernard, Rouhollah Farajzadeh, and Hans Bruining., "Process-based upscaling
    of reactive flow in geological formations", submitted.

  •  Meulenbroek, Bernard, Negar Khoshnevis Gargar, and Hans Bruining., "The effect of saturationdependent capillary diffusion on radial Buckley-Leverett flow", submitted.

  •  Lopez-Peña, Luis A., Bernard Meulenbroek, and Fred Vermolen. "Conditions for upscalability
    of bioclogging in pore network models."Computational Geosciences 22.6 (2018): 1543-1559.

  •  Lopez-Peña, Luis A., Bernard Meulenbroek, and Fred Vermolen. "A network model for the biofilm growth in porous media and its effects on permeability and porosity."Computing and Visualization in Science (2019): 1-12.

  • Meulenbroek, Bernard, Rouhollah Farajzadeh, and Hans Bruining. "The effect of interface movement and viscosity variation on the stability of a di usive interface between aqueous and gaseous CO2."Physics of Fluids 25.7 (2013): 074103.

  • Farajzadeh, R., et al. "An empirical theory for gravitationally unstable flow in porous media."Computational Geosciences 17.3 (2013): 515-527.