Dipartimento di Scienze di Base e Applicate per l'Ingegneria

Seminario di Adrian Muntean (TU/e)

Aula 1B1

Titolo: Case studies in averaging Smoluchovski-like interactions

 Abstract:

The talk has two remotely connected parts:

Firstly, we present a continuum PDE-ODE model for 
collagen self-assembly describing the interplay betweenthe change in the polymer distribution and the 
evolution of monomers. We endow the model with periodiccoefficients, where the small parameter is interpreted in this context as the ratio of lengths of monomers
and fibrils. After applying a fixed-point homogenization argument and proving corrector estimates, we use the microscopic information incorporated in the first 
order correctors to explain the so-called turbidity 
measurement.

Secondly, we present a PDE model for  the continuum 
motion of populations of hot colloidal particles at thepore scale inside a heterogeneous  (periodic or locally-periodic) porous material. The focus is now on 
deriving macroscopic equations  and the corresponding 
effective transport coefficien ts that account for 
the intimate  interplay between the Smoluchowski 
aggregation and dissolution of size classes and the 
deposition of the biggest colloid populations on the 
pores surface in the presence of diffusion/dispersion. To reach this goal, we combine gradient-like estimates 
for both the temperature and the concentration of 
colloidal populations with the concept of two-scale 
convergence by Nguetseng and Allaire.

In both cases, we compare qualitatively our multiscale modelling, mathematical analysis, and simulation 
results with experimental data.

This work on collagen growth is jointly with 
B. van Lith and C. Storm (Eindhoven), while the 
approach on the motion of hot colloids in porous media 
is a work together with O. Krehel (Eindhoven) and 
T. Aiki (Tokyo).

References and Literature for Further Reading:

[1] B.S. van Lith, A. Muntean, A. Muntean:  A continuummodel for hierarchical fibril assembly. Europhysics Letters (EPL), 106 (2014), 08004.

[2] O. Krehel, T. Aiki, A. Muntean: A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization. Networks and Heterogeneous Media, 
to appear,  (2014)