Marek Bukowicki, M.Sc. 

Recent publications
1.  Bukowicki M., EkielJeżewska M.L., Different bending models predict different dynamics of sedimenting elastic trumbbells, SOFT MATTER, ISSN: 1744683X, DOI: 10.1039/C8SM00604K, Vol.14, pp.57865799, 2018 Abstract: The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at lowReynoldsnumber. We use the beadspring approximation of a filament and the Rotne–Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or – alternatively – by the ‘cosine’ (also called the Kratky–Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic longlasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky–Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky–Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads wellseparated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own. Affiliations:
 
2.  Bukowicki M., Gruca M., EkielJeżewska M.L., Dynamics of elastic dumbbells sedimenting in a viscous fuid: oscillations and hydrodynamic repulsion, JOURNAL OF FLUID MECHANICS, ISSN: 00221120, DOI: 10.1017/jfm.2015.31, Vol.767, pp.95108, 2015 Abstract: Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low Reynolds number are investigated using the pointparticle model. The evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling. We find that elasticity (which breaks the timereversal symmetry of the motion) significantly affects the system dynamics. This is remarkable when taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length nonperiodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbells: their centres of mass move apart from each other horizontally. This motion is fast for moderate values of the spring constant k, and slows down when k tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal timedependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centreofmass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understanding general features of systems with a larger number of elastic particles, in regular and random configurations. Keywords:complex fluids, lowReynoldsnumber flows, Stokesian dynamics Affiliations:
 
3.  Gruca M., Bukowicki M., EkielJeżewska M.L., Periodic and quasiperiodic motions of many particles falling in a viscous fluid, PHYSICAL REVIEW E, ISSN: 15393755, DOI: 10.1103/PhysRevE.92.023026, Vol.92, pp.023026110, 2015 Abstract: The dynamics of regular clusters of many nontouching particles falling under gravity in a viscous fluid at low Reynolds number are analyzed within the pointparticle model. The evolution of two families of particle configurations is determined: two or four regular horizontal polygons (called “rings”) centered above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated in which the longlasting clusters are centered around periodic solutions for the relative motions, and they are surrounded by regions of chaotic scattering in a similar way to what was observed by Janosi et al. [Phys. Rev. E. 56, 2858 (1997)] for three particles only. These findings suggest that we should consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid. Keywords:Stokes equations, particle clusters, sedimentation, chaotic scattering, periodic orbits Affiliations:

Conference abstracts
1.  EkielJeżewska M.L., Bukowicki M., Hydrodynamic and elastic interactions of sedimenting flexible fibers, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.221, 2017  
2.  Bukowicki M., EkielJeżewska M.L., Symmetric pair of elongated particles settling at low Reynolds number regime, Bulletin of the American Physical Society, ISSN: 00030503, Vol.62, No.14, pp.250, 2017  
3.  Gruca M., Bukowicki M., EkielJeżewska M., Chaotic Scattering and Periodic Dynamics of Regular Clusters of Particles Sedimenting in a Viscous Fluid, 6th International Symposium on Bifurcations and Instabilities in Fluid Dynamics, 20150715/0717, Paryż (FR), pp.48, 2015 Abstract: Dynamics of a cluster of nonBrownian particles falling under gravity in a viscous fluid at lowReynoldsnumer regime has been extensively studied in the literature both for small and large number of particles and oscillating motions have been discovered. In this work we investigate dynamics of clusters of many nonBrownian particles in regular configurations settling under gravity in a viscous fluid. The point particle approximation is applied for the hydrodynamic interactions. We find out that a wide range of regular initial configurations of many particles leads to very long lifetime of the cluster with periodic and quasiperiodic relative motions of particles. We vary the relative distance between the particles and observe how does it affect the dynamics. Several types of periodic and quasiperiodic solutions are discovered. For broad range of initial configurations we show that a slight change of initial conditions has a large influence on the system lifetime – we observe chaotic scattering. Keywords:complex fluids, Stokesian dynamics, lowReynoldsnumber regime Affiliations:
 
4.  EkielJeżewska M.L., Bukowicki M., Gruca M., Hydrodynamic repulsion of elastic dumbbells, Bulletin of the American Physical Society, ISSN: 00030503, Vol.60, No.21, pp.1, 2015 Abstract: Dynamics of two identical elastic dumbbells, settling under gravity in a viscous fluid at low Reynolds number are analyzed within the pointparticle model. Initially, the dumbbells are vertical, their centers are aligned horizontally, and the springs which connect the dumbbell's beads are at the equilibrium. The motion of the beads is determined numerically with the use of the RungeKutta method. After an initial relaxation phase, the system converges to a universal timedependent solution. The elastic dumbbells tumble while falling, but their relative motion is not periodic (as in case of rigid dumbbells or pairs of separated beads). The elastic constraints break the timereversal symmetry of the motion. As the result, the horizontal distance between the dumbbells slowly increases  they are hydrodynamically repelled from each other. This effect can be very large even though the elastic forces are always much smaller than gravity. [For the details, see M. Bukowicki, M. Gruca, M. L. EkielJezewska, J. Fluid Mech. 767, p. 95 (2015).] Stokes equations, dumbbells, pointparticle model, hydrodynamic repulsion Affiliations:
 
5.  Gruca M., Bukowicki M., EkielJeżewska M., Periodic and quasiperiodic motions of many particles falling under gravity in a viscous fluid, Jülich Soft Matter Days, 20141111/1114, Jülich (DE), pp.102, 2014 Abstract: We investigate the dynamics of many particles settling under gravity in a viscous fluid within a Stokes flow regime. We consider two families with a very wide range of regular initial configurations of many pointparticles which lead to periodic and quasiperiodic motion. We vary the relative distance between the particles and observe how does it affect the dynamics. We observe the oscillations under some outofphase rearrangements of the particles and obtain several types of periodic motions for specified range of initial conditions. We also see a large influence of initial conditions on the cluster lifetime. Keywords:complex fluid, lowReynoldsnumber regime Affiliations:
 
6.  Bukowicki M., Gruca M., EkielJeżewska M., Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion, Jülich Soft Matter Days, 20141111/1114, Jülich (DE), pp.99, 2014 Abstract: Periodic motion of several particles falling under gravity in a viscous fluid was theoretically and experimentally observed in a range of systems, including some fourparticle configurations or a pair of rigid rods. In addition to its fundamental significance, such a motion is considered as important to understand general features of sedimenting random swarms, and suspensions. In this work, we consider a symmetric system of two elastic fibres, modeled as elastic dumbbells, sedimenting in a vertical plane. We focus on the problem how the elasticity (which breaks timereversal symmetry of the motion) affects the system's dynamics. The point particle model is used. We observe oscillating, but nonperiodic motion of the elastic particles. Independently of the value of the spring constant, the hydrodynamic repulsion appears between the dumbbells. The trajectory shift is slower when k tends to 0 or to infinity – in these limiting cases we recover the periodic dynamics reported in the literature. For a given finite but nonzero spring constant we observe existence of a universal timedependent trajectory to which the system converge. Keywords:Stokesian dynamics, elastic dumbbells, hydrodynamics repulsion Affiliations:
