arXiv subjects

Piotr Szymczak

Publications and source records attributed to Piotr Szymczak.

29 records · Page 2Linked to original sources

arXiv2013

Generalization of the Rotne-Prager-Yamakawa mobility and shear disturbance tensors

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 is 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.

physics.flu-dyn↗

arXiv2013

Interacting length scales in the reactive-infiltration instability

The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We show that the commonly used "thin-front" model is a limiting case of a more general theory, which also includes convection-dominated dissolution as another special case. The wavelength of the instability is bounded from below, and lies in the range 1mm to 1km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small.

physics.geo-ph↗

arXiv2012

Network models of dissolution of porous media

We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: as the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant.

physics.flu-dyn↗

arXiv2012

Reactive-infiltration instabilities in rocks. Fracture dissolution

A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system.

physics.flu-dyn↗

arXiv2011

Structural transitions in hypersphere fluids: predictions of Kirkwood's approximation

We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D=3,4,5 and 6, proceeding from the YBG hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurence of a structural transition in the D->Infinity limit .

cond-mat.stat-mech↗

arXiv2011

Instabilities in the dissolution of a porous matrix

A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We show that the "inlet" instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g. carbonate cements) is small, the instability in the steady-state equations is dominant.

physics.geo-ph↗

arXiv2010

The initial stages of cave formation: Beyond the one-dimensional paradigm

The solutional origin of limestone caves was recognized over a century ago, but the short penetration length of an undersaturated solution made it seem impossible for long conduits to develop. This is contradicted by field observations, where extended conduits, sometimes several kilometers long, are found in karst environments. However, a sharp drop in the dissolution rate of CaCO_3 near saturation provides a mechanism for much deeper penetration of reactant. The notion of a "kinetic trigger" - a sudden change in rate constant over a narrow concentration range - has become a widely accepted paradigm in speleogenesis modeling. However, it is based on one-dimensional models for the fluid and solute transport inside the fracture, assuming that the dissolution front is planar in the direction perpendicular to the flow. Here we show that this assumption is incorrect; a planar dissolution front in an entirely uniform fracture is unstable to infinitesimal perturbations and inevitably breaks up into highly localized regions of dissolution. This provides an alternative mechanism for cave formation, even in the absence of a kinetic trigger. Our results suggest that there is an inherent wavelength to the erosion pattern in dissolving fractures, which depends on the reaction rate and flow rate, but is independent of the initial roughness. In contrast to one-dimensional models, two-dimensional simulations indicate that there is only a weak dependence of the breakthrough time on kinetic order; localization of the flow tends to keep the undersaturation in the dissolution front above the threshold for non-linear kinetics.

physics.geo-ph↗

arXiv2010

Prediction of a Structural Transition in the Hard Disk Fluid

Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction η*~0.718, a value which is in substantial agreement with the packing fraction, η~0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. We next show that the same method of analysis predicts that exponential damping of oscillations in the hard sphere fluid becomes impossible when λ= 4nπσ^3 [1 + H(1)]>/- 34.81, where H(1) is the contact value of the correlation function, n is the number density and σ is the sphere diameter, in exact agreement with the condition, λ>/- 34.8, first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.

cond-mat.stat-mech↗

arXiv2007

Tightening of knots in proteins

We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they diffuse around and eventually slide off. The waiting times of the jumps are increasingly stochastic as the temperature is raised. Larger knots do not return to their native locations when a protein is released after stretching.

q-bio.BM↗

arXiv2006

Protein folding in a force-clamp

Kinetics of folding of a protein held in a force-clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force-clamp are distinct.

q-bio.BM↗

arXiv2005

Stretching of proteins in a force-clamp

Mechanically induced protein unfolding in the force-clamp apparatus is shown, in a coarse-grained model of ubiquitin, to have lognormal statistics above a treshold force and exponential below it. Correspondingly, the mean unfolding time is slowly varying and exponentially decreases as a function of the force. The time dependencies of the end-to-end distances are also distinct. The time sequence of unfolding events weakly depends on force and much of it resembles that for stretching at constant speed. A more complicated time dependence arises for integrin.

q-bio.BM↗