Finding numerical solution of linear partial differential equations of first order with real coefficients

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order

Motion of spheres along a fluid-gas interface

A system of many spherical particles, suspended in a quiescent fluid and touching a planar free fluid-gas interface, is considered. Stick fluid boundary conditions at the sphere surfaces are assumed. The free surface boundary conditions are taken into account with the use of the method of images. For such a quasi-two-dimensional system, the one-sphere resistance operator is calculated numerically. Moreover, the corresponding friction and mobility tensors are constructed from irreducible multipole expansion. Finally, the long-distance terms of the two-sphere mobility tensor are evaluated explicitly up to the order of 1/r3, where r is the interparticle distance. Experiments which have motivated this work are outlined.     

Hydrodynamic interactions between spheres in a viscous fluid with a flat free surface or hard wall

Hydrodynamic interactions between spheres immersed in a low-Reynolds-number fluid flow close to a flat free surface or hard wall are investigated. The spheres may have different or equal radii, and may be separated from the boundary or at contact with the free surface. A simple and useful expression is derived for the propagator (Green operator) connecting centers of two spheres. In the derivation, the method of images and the displacement theorems are used. Symmetry of the displacement operators is explicitly shown. The significance of these results in efficient Stokesian and Brownian dynamics simulations is outlined. An example of an application is shown.     

The influence of oxygen on radiation-induced structural and functional changes in glyceraldehyde-3-phosphate dehydrogenase and lactate dehydrogenase

Proteins are major targets for oxidative damage due to their abundance in cells and high reactivity with free radicals. In the present study we examined the influence of oxygen on radiation-induced inactivation and structural changes of glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and lactate dehydrogenase (LDH). We chose these two enzymes because they occur at high concentrations and participate in the most important processes in organisms; furthermore, they show considerable similarity in their structure.Protein solutions were irradiated with X-rays in doses ranging from 0.1 to 0.7 kGy, in air and N₂O. The much higher radiation inactivation of GAPDH as compared to LDH is correlated with substantially greater structural changes in this protein, mainly involving the loss of free thiol groups (–SH). Of lesser importance in the differentiation of the radiosensitivity of the studied enzymes are tryptophan residues. Molecular oxygen, present during irradiation, increased to a significantly greater extent the inactivation and structural changes of GAPDH than that of LDH. The results suggest that the greater effect of oxygen on GAPDH is due to the higher efficiency of the superoxide radical, the higher amount of hydroperoxides generated, and the higher degree of unfolding of this protein.     

Dynamics of fibers in a wide microchannel

Dynamics of single flexible non-Brownian fibers, tumbling in a Poiseuille flow between two parallel solid plane walls, is studied with the use of the HYDROMULTIPOLE numerical code, based on the multipole expansion of the Stokes equations, corrected for lubrication. Fibers, which are closer to a wall, more flexible (less stiff) or longer, deform more significantly and, for a wide range of the system parameters, they faster migrate towards the middle plane of the channel. For the considered systems, fiber velocity along the flow is only slightly smaller than (and can be well approximated by) the Poseuille flow velocity at the same position. In this way, the history of a fiber migration across the channel is sufficient to determine with a high accuracy its displacement along the flow.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.     

Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements

Hydrodynamic properties of fibrinogen molecules were theoretically calculated. Their shape was approximated by the bead model, considering the presence of flexible side chains of various length and orientation relative to the main body of the molecule. Using the bead model, and the precise many-multipole method of solving the Stokes equations, the mobility coefficients for the fibrinogen molecule were calculated for arbitrary orientations of the arms whose length was varied between 12 and 18nm. Orientation averaged hydrodynamic radii and intrinsic viscosities were also calculated by considering interactions between the side arms and the core of the fibrinogen molecule. Whereas the hydrodynamic radii changed little with the interaction magnitude, the intrinsic viscosity exhibited considerable variation from 30 to 60 for attractive and repulsive interactions, respectively. These theoretical results were used for the interpretation of experimental data derived from sedimentation and diffusion coefficient measurements as well as dynamic viscosity measurements. Optimum dimensions of the fibrinogen molecule derived in this way were the following: the contour length 84.7nm, the side arm length 18nm, and the total volume 470nm(3), which gives 16% hydration (by volume). Our calculations enabled one to distinguish various conformational states of the fibrinogen molecule, especially the expanded conformation, prevailing for pH<4 and lower ionic strength, characterized by high intrinsic viscosity of 50 and the hydrodynamic radius of 10.6nm. On the other hand, for the physiological condition, that is, pH=7.4 and the ionic strength of 0.15M NaCl, the semi-collapsed conformation dominates. It is characterized by the average angle equal to <φ>=55°, intrinsic viscosity of 35, and the hydrodynamic radius of 10nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be -4kT units, confirming that they are oppositely charged than the central nodule. Results obtained in our work confirm an essential role of the side chains responsible for a highly anisotropic charge distribution in the fibrinogen molecule. These finding can be exploited to explain anomalous adsorption of fibrinogen on various surfaces.