Partner: Piotr Szymczak

University of Warsaw (PL)

Recent publications
1.Gruziel M., Szymczak P., From ribbons to tubules: a computational study of the polymorphism in aggregation of helical filaments, SOFT MATTER, ISSN: 1744-683X, DOI: 10.1039/c5sm00652j, Vol.11, pp.6294-6304, 2015
Abstract:

A simple, coarse-grained model of chiral, helical filaments is used to study the polymorphism of fibrous aggregates. Three generic morphologies of the aggregates are observed: ribbons, in which the filaments are joined side-by-side, twisted, helicoidal fibrils, in which filaments entwine along each other and tubular forms, with filaments wound together around a hollow core of the tube. A relative simplicity of the model allows us to supplement numerical simulations with an analytic description of the elastic properties of the aggregates. The model is capable of predicting geometric and structural characteristics of the composite structures, as well as their relative stabilities. We also investigate in detail the transitions between different morphologies of the aggregates.

Affiliations:
Gruziel M.-other affiliation
Szymczak P.-University of Warsaw (PL)
2.Żuk P.J., Wajnryb E., Mizerski K.A., Szymczak P., Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2013.668, Vol.741, pp.R5-1-13, 2014
Abstract:

The Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equal-sized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, different-sized beads, which we illustrate with an example.

Keywords:

complex fluids, computational methods, low-Reynolds-number flows, mathematical foundations, suspensions

Affiliations:
Żuk P.J.-other affiliation
Wajnryb E.-IPPT PAN
Mizerski K.A.-other affiliation
Szymczak P.-University of Warsaw (PL)
3.Mizerski K.A., Wajnryb E., Żuk P.J., Szymczak P., The Rotne-Prager-Yamakawa approximation for periodic systems in a shear flow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.4871113, Vol.140, pp.184103-1-9, 2014
Abstract:

Rotne-Prager-Yamakawa approximation is a commonly used approach to model hydrodynamic interactions between particles suspended in fluid. It takes into account all the long-range contributions to the hydrodynamic tensors, with the corrections decaying at least as fast as the inverse fourth power of the interparticle distances, and results in a positive definite mobility matrix, which is fundamental in Brownian dynamics simulations. In this communication, we show how to construct the Rotne-Prager-Yamakawa approximation for the bulk system under shear flow, which is modeled using the Lees-Edwards boundary conditions.

Keywords:

Tensor methods, Hydrodynamics, Shear flows, Brownian dynamics, Boundary value problems

Affiliations:
Mizerski K.A.-other affiliation
Wajnryb E.-IPPT PAN
Żuk P.J.-other affiliation
Szymczak P.-University of Warsaw (PL)
4.Wajnryb E., Mizerski K.A., Żuk P.J., Szymczak P., Generalization of the Rotne-Prager-Yamakawa mobility and shear disturbance tensors, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2013.402, Vol.731, pp.R3-1-12, 2013
Abstract:

The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all long-range terms (i.e. decaying as R−3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions.

Keywords:

computational methods, low-Reynolds-number flows, suspensions

Affiliations:
Wajnryb E.-IPPT PAN
Mizerski K.A.-other affiliation
Żuk P.J.-other affiliation
Szymczak P.-University of Warsaw (PL)
5.Gruziel M., Dzwolak W., Szymczak P., Chirality inversions in self-assembly of fibrillar superstructures: a computational study, SOFT MATTER, ISSN: 1744-683X, DOI: 10.1039/c3sm27961h, Vol.9, pp.8005-8013, 2013
Abstract:

The formation of aggregates of helical fibrils is analyzed numerically. The aggregate morphology, chirality and stability are studied as a function of temperature and helical pitch of individual fibrils. The simulations show the existence of a critical pitch above which the handedness of the aggregates is opposite to that of the constituting fibrils. We also observe and analyze the process of spontaneous chirality inversion of individual fibrils within the aggregates. This inversion is accompanied by a helical wave propagating along the fibril axis, with a kink separating left-handed and right-handed regions moving along the fibril. The frequency of this process is strongly dependent on the initial pitch of the fibrils with a local maximum near the critical pitch.

Affiliations:
Gruziel M.-other affiliation
Dzwolak W.-University of Warsaw (PL)
Szymczak P.-University of Warsaw (PL)
6.Sikora M., Dieter A., Korczyk P.M., Prodi-Schwab A., Szymczak P., Cieplak M., Geometrical and electrical properties of indium tin oxide clusters in ink dispersions, LANGMUIR, ISSN: 0743-7463, DOI: 10.1021/la203886b, Vol.28, No.2, pp.1523-1530, 2012
Abstract:

The analysis of the TEM images of indium tin oxide (ITO) clusters in ink solutions deposited from ink dispersions reveals that their geometry arises from a diffusion limited cluster aggregation (DLCA) process. We model films of ITO clusters as built through deposition of DLCA clusters made of primary spherical nanoparticles of 13 nm in diameter.
The deposition is then followed by a further compactification process that imitates sintering. We determine the conductivity of the sintered films by mapping the problem to that of the resistor network in which the contact regions between the touching spheres provide the dominant electric resistance. For a given volume fraction, conductivity of the sintered films is shown to be larger than that for the randomly packed spheres. However, the larger a typical radius of gyration of the clusters the smaller the enhancement. We also provide numerical tests for the routines used in the interpretation of the TEM images.

Keywords:

cluster aggregation, ITO

Affiliations:
Sikora M.-other affiliation
Dieter A.-other affiliation
Korczyk P.M.-IPPT PAN
Prodi-Schwab A.-other affiliation
Szymczak P.-University of Warsaw (PL)
Cieplak M.-other affiliation
7.Ekiel-Jeżewska M.L., Gubiec T., Szymczak P., Stokesian dynamics of close particles, PHYSICS OF FLUIDS, ISSN: 1070-6631, DOI: 10.1063/1.2930881, Vol.20, pp.63102-1-10, 2008
Abstract:

Stokesian dynamics simulations of close particles are reported, taking into account lubrication forces and many-body hydrodynamic interactions between spheres. A periodic trajectory of three particles maintaining a permanent proximity to each other has been found and analyzed. This solution is used as a benchmark to study the accuracy and stability of various numerical integration schemes. In particular, different methods of preventing unphysical overlaps of the particles are considered and potential artifacts discussed.

Keywords:

Kinematics, Renormalization, Surface dynamics, Lubrication, Hydrodynamics

Affiliations:
Ekiel-Jeżewska M.L.-IPPT PAN
Gubiec T.-other affiliation
Szymczak P.-University of Warsaw (PL)