Publications:

Multicomponent lattice Boltzmann models for biological applications.
A. Montessori, I. Halliday, M. Lauricella, S. V. Lishchuk, G. Pontrelli, T. J. Spencer, S. Succi.
“Numerical methods and advanced simulation in biomechanics and biological processes” (Editors: M. Cerrolaza, S. Shefelbine, D. GarzónAlvarado), Academic Press, 2018.
[abstract] [publisher]The dynamics of deformable liquidfilled bodies (e.g. droplets, capsules, lipid vesicles) suspended in a fluid flow is a fascinating fundamental problem with increasing relevance for technological applications, for example, in drug delivery, or designing labonchip devices. In the present chapter we review two main families of lattice Boltzmann models for multicomponent flows, their mechanical properties and transport phenomena, with special focus on their application to biofluidic problems, such as the dynamics, merging and breakup of microfluidic droplets and the motion of deformable membranes and vesicles under geometrical confinement.

Interfacial microcurrents in continuumscale multicomponent lattice Boltzmann equation hydrodynamics.
I. Halliday, S. V. Lishchuk, T. J. Spencer, K. Burgin, T. Schenkel.
Comp. Phys. Comm. 219 (2017) 286.
[abstract] [doi]We describe, analyse and reduce microcurrent effects in one class of lattice Boltzmann equation simulation method describing immiscible fluids within the continuum approximation, due to Lishchuk et al. (2003). This model’s microcurrent flow field and associated density adjustment, when considered in the linear, lowReynolds number regime, may be decomposed into independent, superposable contributions arising from various error terms in its immersed boundary force. Error force contributions which are rotational (solenoidal) are mainly responsible for the microcurrent (corresponding density adjustment). Rotationally anisotropic error terms arise from numerical derivatives and from the sampling of the interfacesupporting force. They may be removed, either by eliminating the causal error force or by negating it. It is found to be straightforward to design more effective stencils with significantly improved performance.
Practically, the microcurrent activity arising in Lishchuk’s method is reduced by approximately three quarters by using an appropriate stencil and approximately by an order of magnitude when the effects of sampling are removed.

On the structural polydispersity of random copolymers adsorbed at interfaces: Comparison of surface and bulk distributions.
S. V. Lishchuk, R. Ettelaie, T. Annable.
Mol. Phys. 115 (2017) 1343.
[abstract] [doi]Synthesis of random copolymers leads to a structurally polydispersed distribution of polymer chains, where one of the constituent monomers prefers residing on the interface, while the others have a tendency for remaining in the bulk. Previous studies have demonstrated the very strong dependence of the level of adsorption with the degree of blockiness and number of adsorbing residues of the chains. Using selfconsistent field calculations, we obtain the distribution of the adsorbed copolymers and compare this with the bulk distribution of such chains. In our study, the whole range of structurally polydisperse chains in the distribution derived for a given random copolymer are simultaneously present and can compete with each other for adsorption. We show that the distribution of chains on the surface is grossly different to that in the bulk and is largely dominated by those rare chains at the tail end of the latter distribution.

Novel food grade dispersants: Review of recent progress.
R. Ettelaie, A. Zangin, S. V. Lishchuk.
Curr. Op. Coll. Int. Sci. 28 (2017) 46.
[abstract] [doi]Many foreseen advances in the design of food structures, suitable for ever demanding nutrient delivery systems, tailored controlled release, microencapsulation and protection of active ingredients, require a generation of superior dispersants than those currently provided by proteins. While the most efficient structure for such dispersants is relatively easy to specify, in foods they cannot simply be synthetically manufactured. The review highlights several possible strategies for realising more efficient food colloid stabilisers and summarises the key recent progress for each approach, both experimentally and theoretically. The emphasis is on those methods that lead to macromolecularly adsorbed layers. Practical aspects apart, we also discuss a number of interesting fundamental questions that each approach raises.

Dilatational viscosity of dilute particleladen fluid interface at different contact angles.
S. V. Lishchuk.
Phys. Rev. E 94 (2016) 063111.
[abstract] [doi]We consider a solid spherical particle adsorbed at a flat interface between two immiscible fluids and having arbitrary contact angle at the triple contact line. We derive analytically the flow field corresponding to dilatational surface flow in the case of a large ratio of dynamic shear viscosities of two fluids. Considering a dilute assembly of such particles we calculate numerically the dependence on the contact angle of the effective surface dilatational viscosity particleladen fluid interface. The effective surface dilatational viscosity is proportional to the size and surface concentration of particles and monotonically increases with the increase in protrusion of particles into the fluid with larger shear viscosity.

Detachment force of particles with pinning of contact line from fluid bubbles/droplets.
S. V. Lishchuk, R. Ettelaie.
Langmuir 32 (2016) 13040.
[abstract] [doi]Deformation of a spherical droplet or bubble containing a pair of particles on its surface is considered when equal but opposite forces are applied to the particles. The particles are placed opposite each other, thus providing a symmetric problem that is more amenable to analytical treatment. We extend our previous calculations concerning such arrangements with constant contact angles to situations where it is the contact line now that is pinned on the surface of the particles. The force–displacement curves are calculated as the particles are pulled apart and are found to be linear for small displacements. However, it is also found that the “Hookean constant” for the pinned contact line problem is different from the one derived for systems with a constant contact angle, the constant being larger if the pinned line is at the equator of the particles.

Local membrane length conservation in twodimensional vesicle simulation using a multicomponent lattice Boltzmann equation method.
I. Halliday, S. V. Lishchuk, T. J. Spencer, G. Pontrelli, P. C. Evans.
Phys. Rev. E 94 (2016) 023306.
[abstract] [doi]We present a method for applying a class of velocitydependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phasefield varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)] and underscore the importance of a correct vesicle membrane condition.

Detachment force of particles from fluid droplets.
R. Ettelaie, S. V. Lishchuk.
Soft Matter 11 (2015) 4251.
[abstract] [doi] [pdf]We calculate the deformation of a spherical droplet, resulting from the application of a pair of opposite forces to particles located diametrically opposite at the two ends of the droplet. The freeenergy analysis is used to calculate the force–distance curves for the generated restoring forces, arising from the displacement of the particles relative to each other. While the logarithmic dependence of the “de Gennes–Hooke” constant on the particle to droplet size ratio, ν, is rather well known in the limit of very small ν, we find that for more realistic particle to droplet size ratios, i.e. ν=0.001 to 0.01, the additional constant terms of O(1) constitute a significant correction to previously reported results. We derive the restoring force constant to be 2πγ[0.5ln(ν/2)]⁻¹, in perfect agreement with the exact seminumerical analysis of the same problem. The deviation from the linear force–displacement behaviour, occurring close to the point of detachment, is also investigated. A study of the energy dissipated shows it to be an increasingly dominant component of the work done during the detachment of the particles, as ν decreases. This indicates the existence of a significantly higher energy barrier to desorption of very small particles, compared to the one suggested by their adsorption energy alone. The influence of the line tension on the detachment force is also considered. It is shown that where line tension is important, the contact angle is no longer a constant but instead alters with the displacement of the particles from their equilibrium positions.

Effective surface dilatational viscosity of highly concentrated particleladen interfaces.
S. V. Lishchuk.
Phys. Rev. E 90 (2014) 053005.
[abstract] [doi] [arxiv]The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with halfimmersed monodisperse rigid spherical nonBrownian particles in the limit of high particle concentration. The derivation is based upon the facts that (i) highly concentrated particle arrays in a plane form a hexagonal structure and (ii) the dominant contribution to the viscous dissipation rate arises in the thin gaps between neighboring particles.

Effective surface shear viscosity of an incompressible particleladen fluid interface.
S. V. Lishchuk.
Phys. Rev. E 89 (2014) 043003.
[abstract] [doi] [arxiv]The presence of even a small amount of surfactant at the particleladen fluid interface subjected to shear makes surface flow incompressible if the shear rate is small enough [T. M. Fischer et al., J. Fluid Mech. 558, 451 (2006)]. In the present paper the effective surface shear viscosity of a flat, lowconcentration, particleladen incompressible interface separating two immiscible fluids is calculated. The resulting value is found to be 7.6% larger than the value obtained without account for surface incompressibility.

The influence of the liquid slab thickness on the planar vapor–liquid interfacial tension.
S. Werth, S. V. Lishchuk, M. Horsch, H. Hasse.
Physica A 392 (2013) 2359.
[abstract] [doi] [arxiv]One of the long standing challenges in molecular simulation is the description of interfaces. On the molecular length scale, finite size effects significantly influence the properties of the interface such as its interfacial tension, which can be reliably investigated by molecular dynamics simulation of planar vapor–liquid interfaces. For the LennardJones fluid, finite size effects are examined here by varying the thickness of the liquid slab. It is found that the surface tension and density in the center of the liquid region decreases significantly for thin slabs. The influence of the slab thickness on both the liquid density and the surface tension is found to scale with 1/S³ in terms of the slab thickness S, and a linear correlation between both effects is obtained. The results corroborate the analysis of A. Malijevský, G. Jackson, J. Phys.: Condens. Matter 24 (2012) 464121, who recently detected an analogous effect for the surface tension of liquid nanodroplets.
Highlights:
 Finitesize effects on fluid interfaces are examined by molecular simulation.
 The Janecek correction scheme is employed to account for longrange interactions.
 The vapor–liquid surface tension decreases significantly for thin planar slabs.
 The influence of the slab thickness S on the surface tension scales with 1/S^{3}.
 Analogous results of Malijevsky and Jackson regarding droplets are corroborated.

Multiple component lattice Boltzmann equation for fluidfilled vesicles in flow.
I. Halliday, S. V. Lishchuk, T. Spencer, G. Pontrelli, C. M. Care.
Phys. Rev. E 87 (2013) 023307.
[abstract] [doi]We document the derivation and implementation of extensions to a twodimensional, multicomponent lattice Boltzmann equation model, with Laplace law interfacial tension. The extended model behaves in such a way that the boundary between its immiscible drop and embedding fluid components can be shown to describe a vesicle of constant volume bounded by a membrane with conserved length, specified interface compressibility, bending rigidity, preferred curvature, and interfacial tension. We describe how to apply this result to several, independent vesicles. The extended scheme is completely Eulerian, and it represents a twoway coupled vesicle membrane and flow within a single framework. Unlike previous methods, our approach dispenses entirely with the need explicitly to track the membrane, or boundary, and makes no use whatsoever of computationally expensive and intricate interface tracking and remeshing. Validation data are presented, which demonstrate the utility of the method in the simulation of the flow of high volume fraction suspensions of deformable objects.

Modelling of the aluminium alloy Al 2024 from the microscale to the macroscale: intergranular corrosion.
R. Akid, S. V. Lishchuk, K. Worden, A. Bałkowiec, J. Michalski, K. J. Kurzydlowski.
“Aluminium alloy corrosion of aircraft structures” (Editors: J. A. DeRose, T. Suter, T. Hack, R. Adey), WIT press, 2013.
[abstract] [publisher] [contents]Aluminiumbased alloys show good resistant to uniform (general) corrosion. However they are much more susceptible to various types of localised corrosion, in particular intergranular corrosion (IGC), where localised attack occurs along the grain boundaries leaving the grains themselves largely unaffected. In order to estimate the progress of such corrosion in a given sample, it is possible to generate a numerical model. While there has been much effort spent in the development of electrochemistrybased models, the use of grey and blackbox models remains largely unexplored. Cellular Automata (CA) models that have recently been exploited to model the progression of uniform corrosion may be developed to address localised corrosion, more specifically IGC. A probabilistic approach is chosen because it enables the simulation of complex interactions by replacing the chemical processes by a discrete proxy.

Role of threebody interactions in formation of bulk viscosity in liquid argon.
S. V. Lishchuk.
J. Chem. Phys. 136 (2012) 164501.
[abstract] [doi] [pdf] [arxiv]With the aim of locating the origin of discrepancy between experimental and computer simulation results on bulk viscosity of liquid argon, a molecular dynamic simulation of argon interacting via ab initio pair potential and tripledipole threebody potential has been undertaken. Bulk viscosity, obtained using GreenKubo formula, is different from the values obtained from modeling argon using LennardJones potential, the former being closer to the experimental data. The conclusion is made that manybody interatomic interaction plays a significant role in formation of bulk viscosity.

ms2: Ein Werkzeug zur Berechnung thermodynamischer Stoffeigenschaften mittels molekularer Simulation.
S. Deublein, B. Eckl, J. Stoll, S. V. Lishchuk, G. GuevaraCarrion, C. W. Glass, T. Merker, M. Bernreuther, H. Hasse, J. Vrabec.
Chem. Ing. Tech. 84 (2012) 114.
[abstract] [doi] [journal cover image]Dieser Beitrag stellt das molekulare Simulationsprogramm ms2 vor, das zur Berechnung thermodynamischer Stoffdaten von Fluiden im Gleichgewicht dient. Mit ms2 können Stoffdaten von Reinstoffen und Mischungen ermittelt werden, die aus kleinen, elektroneutralen Molekülen bestehen. Es lassen sich Molekulardynamik und MonteCarloSimulationen durchführen. Zugängliche Stoffdaten sind unter anderem thermische und kalorische Eigenschaften, Dampf/FlüssigkeitsGleichgewichte und Transportgrößen. ms2 ist optimiert auf kurze Antwortzeiten auf unterschiedlicher Hardware und einfache Bedienbarkeit. Hilfsprogramme unterstützen die Verwendung von ms2.
This work presents the molecular simulation program ms2 that is designed for the calculation of thermodynamic properties of fluids in equilibrium. With ms2, thermodynamic properties can be calculated for pure fluids and mixtures that consist of small electroneutral molecules. Both molecular dynamics and Monte Carlo simulations can be performed. The calculation of thermal and caloric data for homogeneous states as well as vaporliquid equilibria and transport properties is supported. ms2 is designed to achieve short response times on different hardware and straightforward handling. Feature tools facilitate the interpretation of input and output files.

ms2: A molecular simulation tool for thermodynamic properties.
S. Deublein, B. Eckl, J. Stoll, S. V. Lishchuk, G. GuevaraCarrion, C. W. Glass, T. Merker, M. Bernreuther, H. Hasse, J. Vrabec.
Comp. Phys. Comm. 182 (2011) 2350.
[abstract] [doi] [ms2 website]This work presents the molecular simulation program ms2 that is designed for the calculation of thermodynamic properties of bulk fluids in equilibrium consisting of small electroneutral molecules. ms2 features the two main molecular simulation techniques, molecular dynamics (MD) and MonteCarlo. It supports the calculation of vapor–liquid equilibria of pure fluids and multicomponent mixtures described by rigid molecular models on the basis of the grand equilibrium method. Furthermore, it is capable of sampling various classical ensembles and yields numerous thermodynamic properties. To evaluate the chemical potential, Widomʼs test molecule method and gradual insertion are implemented. Transport properties are determined by equilibrium MD simulations following the Green–Kubo formalism. ms2 is designed to meet the requirements of academia and industry, particularly achieving short response times and straightforward handling. It is written in Fortran90 and optimized for a fast execution on a broad range of computer architectures, spanning from single processor PCs over PCclusters and vector computers to highend parallel machines. The standard Message Passing Interface (MPI) is used for parallelization and ms2 is therefore easily portable to different computing platforms. Feature tools facilitate the interaction with the code and the interpretation of input and output files. The accuracy and reliability of ms2 has been shown for a large variety of fluids in preceding work.
Highlights:
 ms2 is an open source molecular simulation program for the calculation of thermodynamic properties.
 Accessible properties are thermal and caloric data, vapor–liquid equilibria and transport properties.
 ms2 is designed for a fast execution, while obtaining highly accurate results.
 Feature tools facilitate the simulation work with ms2.

Multiscale interaction of particulate flow and the artery wall.
I. Halliday, M. A. Atherton, C. Care, M. W. Collins, D. Evans, P. C. Evans, D. R. Hose, A. Khir, C. S. König, R. Krams, P. Lawford, S. V. Lishchuk, G. Pontrelli, V. Ridger, T. J. Spencer, Y. Ventikos, D. C. Walker, P. N. Watton.
Med. Eng. Phys. 33 (2011) 840.
[abstract] [doi]We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying the widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of particulate flow (blood is not a continuum fluid), and proceed to propose, then validate all the key components in a multiplycoupled, multiscale modeling strategy (in qualitative terms only, note). Eventually, this strategy should lead to a quantitative, patientspecific understanding of the coupling between particulate flow and the endothelial state.

A cellular automaton model for predicting intergranular corrosion.
S. V. Lishchuk, R. Akid, K. Worden, J. Michalski.
Corr. Sci. 53 (2011) 2518.
[abstract] [doi]The cellular automata (CA) methodology is applied to the case of intergranular corrosion. Appropriate CA rules are generated which can reproduce and predict the advance of a corrosion front. The proposed model shows qualitative and quantitative agreement with experimental intergranular corrosion data obtained from an aluminium AA2024 alloy in chloride solutions.
Highlights:
 Cellular automata allows new approach to simulating intergranular corrosion.
 Intergranular corrosion of ‘real’ microstructures is simulated in 3D.
 Diffusion processes are modelled using a random walk process.
 Differential evolution algorithm is used to calibrate the adjustable parameters.
 Cellular automata may be further modified to include additional physical phenomena.

Contribution of Hbond vibrations to heat capacity of water.
S. V. Lishchuk, N. P. Malomuzh, P. V. Makhlaichuk.
Phys. Lett. A 375 (2011) 2656.
[abstract] [doi]The origin of the anomalously large value of the heat capacity of liquid water is discussed. Comparing the temperature dependence of the heat capacities for water with those for argon and hydrogen sulfide, we separate contributions of the translational and rotational degrees of freedom. The residual part is considered as being caused by the specific contributions of the transversal vibrations of Hbonds. The estimate for the number of Hbonds per molecule is obtained from the analysis of this contribution. This estimate is in quite good agreement with the estimates which follow from the analysis of the specific volume, heat of evaporation, and kinematic shear viscosity.
Highlights:
 Different contributions to the heat capacity of liquid water are analyzed.
 Contributions of the translational and rotational degrees of freedom are separated.
 The contribution of the transversal vibrations of Hbonds is calculated.
 The number of Hbonds per molecule is estimated.

Why thermodynamic properties of normal and heavy water are similar to those of argonlike liquids?
S. V. Lishchuk, N. P. Malomuzh, P. V. Makhlaichuk.
Phys. Lett. A 374 (2010) 2084.
[abstract] [doi]The Letter is devoted to the explanation of the argonlike behavior of the thermodynamic properties of water. It is shown that this phenomenon is caused by the averaged interparticle potentials which form due to rotation of water molecules. The general structure of the averaged potentials is proposed. The physical nature for the considerable shift of the triple point of water in comparison with the one obtained by extrapolation in the homological series is discussed.

Selfconsistent field theory simulation of block copolymer films adsorbed on surfaces of azimuthally symmetric particles.
S. V. Lishchuk.
J. Phys. A 42 (2009) 465401.
[abstract] [doi]A method is proposed for solving selfconsistent field theory equations for thin block copolymer films adsorbed on a surface of axially symmetric particles. The method is applied to the case of thin diblock copolymer film adsorbed on a prolate spheroidal particle. Twodimensional analogues of lamellar and cylindrical morphologies are observed.

Multiscale interaction of flow and the artery wall.
I. Halliday, S. V. Lishchuk, M. A. Atherton, C. Care, M. W. Collins, D. Evans, P. C. Evans, D. R. Hose, A. Khir, R. Krams, P. Lawford, V. Ridger, Y. Ventikos, D. C. Walker, P. N. Watton.
Proc. 2^{nd} Micro and Nano Flows Conference (2009).
[abstract] [url]We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying their widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of flow, and proceed to propose, then validate (in practical, qualitative terms, at least) a multiply coupled, multiscale modeling strategy, which, eventually, aims at a quantitative, patientspecific understanding of the coupling between the flow and the endothelial state.

Effective surface viscosities of a particleladen fluid interface.
S. V. Lishchuk, I. Halliday.
Phys. Rev. E 80 (2009) 016306.
[abstract] [doi]The Einstein formula for the effective shear viscosity of low Reynolds number suspension flows is generalized to the case of flat, lowconcentration, particleladen interfaces separating two immiscible fluids. The effective surface shear and dilational viscosities of this system is found to be η_{s}=^{5}⁄_{3}(η_{1}+η_{2})Rϕ and ζ_{s}=5(η_{1}+η_{2})Rϕ, correspondingly, where η_{1} and η_{2} are the shear viscosities of two bulk fluids and ϕ is the surface concentration of spherical particles of radius R. The formula is found to be in excellent agreement with data obtained using multicomponent lattice Boltzmann equation simulation.

Scattering of light on surfactantladen liquid–liquid crystal interface.
S. V. Lishchuk.
Chem. Eng. Comm. 196 (2009) 854.
[abstract] [doi] [pdf]The spectrum of surface quasielastic light scattering (SQELS) on a surfactantladen interface between nematic liquid crystal and isotropic fluid is calculated for the case when the surfactant film induces homeotropic anchoring of the nematic director. The result can be used for determination of the surface tension, compressional modulus, and a combination of the surface viscosity coefficients from the experimental SQELS data.

Saddlesplay modulus of a particleladen fluid interface for hard disks.
S. V. Lishchuk.
Europhys. Lett. 85 (2009) 56001.
[abstract] [doi] [pdf] [arxiv]The scaledparticle theory equation of state for the twodimensional harddisk fluid on a curved surface is proposed and used to determine the saddlesplay modulus of a particleladen fluid interface. The resulting contribution to saddlesplay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddlesplay modulus of a simple fluid interface.

A cellular automaton based model for predicting intergranular corrosion in aerospace alloys.
S. V. Lishchuk, R. Akid, K. Worden.
Proc. EUROCORR–2008 (2008).
[abstract] [url]The cellular automata (CA) model is proposed for predicting intergranular corrosion. The appropriate CA rules are generated which can reproduce and predict the advance of a corrosion front The proposed model shows qualitative and quantitative agreement with experimental data on an aluminium Al2024 alloy in chloride solutions.

The model of alkylphenol micelles bound to respective antibodies on the solid surface.
A. Tsargorodskaya, S. V. Lishchuk, A. Nabok.
Coll. Surf. A 324 (2008) 117.
[abstract] [doi]The model of binding of micelles of nonylphenol molecules to respective antibodies immobilized on the solid surface is proposed. The actual dimensions of micelles obtained from AFM measurements were used in modelling and allowed to predict the shape of the micelle. An account of nonspherical shape of micelles and their simultaneous binding to several antibodies allows estimation of the micelle binding energy.

Modelbased prognosis for intergranular corrosion.
S. V. Lishchuk, R. Akid, K. Worden.
Proc. 4^{th} European Workshop on Structural Health Monitoring (2008) 340.
[abstract] [url]Among the advantages of Aluminiumbased alloys for structural use is their corrosion resistance. However, while Aluminium alloys are highly resistant to uniform (general) corrosion, they are much more susceptible to types of localised corrosion, especially intergranular corrosion, which is a localised attack along the grain boundaries which leaves the grains themselves largely unaffected. In order to estimate the progress of such corrosion in a given sample, it is considered possible to generate a numerical model of some sort. While there has been much effort spent in the development of electrochemistrybased models, the use of grey and blackbox models remains largely unexplored. One exception to this is the use of Cellular Automata (CA) models which have recently been exploited to model the progression of uniform corrosion. The object of the current paper is to apply the CA methodology to the case of intergranular corrosion. The first phase of the work has been concerned with generating appropriate CA rules which can qualitatively reproduce observed physics, and this work is reported here. A model is proposed which shows qualitative agreement with experimental data on the advance of the corrosion front.

Multicomponent lattice Boltzmann method for fluids with a density contrast.
S. V. Lishchuk, I. Halliday, C. M. Care.
Phys. Rev. E 77 (2008) 036702.
[abstract] [doi]We present and verify a multicomponent lattice Boltzmann simulation scheme for two immiscible and incompressible fluids with a large density contrast. Our method is constructed from a continuum approximation description of a single inhomogeneous, and essentially incompressible, fluid. The equations that arise from this analysis are mapped onto an established multicomponent lattice Boltzmann method. The approach avoids the computational expense of a numerical solution of the fluid pressure field in a separate step. We present results obtained with our model which validate the initial assumptions and verify correct static and dynamic operation of the model up to a fluid density contrast ratio of more than 500. The paper concludes with an example that illustrates the potential utility of the approach by modeling a gas bubble rising under gravity and breaking through a free surface.

Role of the orientation disorder in the formation of fragility of glassy water and glycerollike liquids.
S. V. Lishchuk, T. V. Lokotosh, S. Magazù, N. P. Malomuzh, F. Migliardo.
Phys. Rev. E 76 (2007) 061504.
[abstract] [doi]The role of H bonds in the formation of the fragility and dielectric properties of highly viscous liquids is investigated. The heuristic supposition about the proportionality between the logarithm of the shear viscosity and oscillatory contributions to the meansquare displacement of a molecule is presented. Concrete calculations are carried out for the Hbond subsystem of the twodimensional model lattice water. The conjecture on the interrelation between the phase transition in the subsystem of H bonds and the glassification point is formulated. It is shown that (i) the glassification temperature is proportional to the Hbonding energy and (ii) the fragilities of glycerollike liquids differ from each other as a consequence of distinct interaction energies between H bonds. The existence of a close connection between the fragility parameter and dielectric permittivity is established.

Waves at surfactantladen liquid–liquid crystal interface.
S. V. Lishchuk.
Phys. Rev. E 76 (2007) 011711.
[abstract] [doi] [arxiv]A theoretical study is presented of surface waves at a monomolecular surfactant film between an isotropic liquid and a nematic liquid crystal for the case when the surfactant film is in the isotropic twodimensional fluid phase and induces homeotropic (normal to the interface) orientation of the nematic director. The dispersion relation for the surface waves is obtained, and different surface modes are analyzed with account being taken of the anchoring induced by the surfactant layer, the curvature energy of the interface, and the anisotropy of the viscoelastic coefficients. The dispersion laws for capillary and dilatational surface modes retain structure similar to that in isotropic systems, but involve anisotropic viscosity coefficients. Additional modes are related to relaxation of the nematic director field due to anchoring at the interface. The results can be used to determine different properties of nematicsurfactantisotropic interfaces from experimental data on surface light scattering.

Equation of state of the harddisk fluid on a sphere from PercusYevick equation.
S. V. Lishchuk.
Physica A 369 (2006) 266.
[abstract] [doi]The Percus–Yevick equation is solved numerically for hard disks on a sphere. The effect of curvature of the hosting surface is calculated, and an empirical correction to the equation of state is proposed.

A deformable elastic membrane embedded in a lattice Boltzmann fluid.
S. V. Lishchuk, C. M. Care.
arXiv:condmat/0607382 (2006).
[abstract] [arxiv]A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived from a free energy functional with a value which is dependent upon the geometric properties of the membrane. The method is validated in two dimensions with a free energy functional which imposes the constraint of constant membrane length, constant enclosed area, a bending rigidity and a preferred curvature. The method is shown to recover the expected equilibrium shape in the absence of flow and deformation in the presence of an applied shear flow. The method may have applications in a number of mesoscopic simulations, including discrete models of blood cells.

Shear viscosity of bulk suspensions at low Reynolds number with the threedimensional lattice Boltzmann method.
S. V. Lishchuk, I. Halliday, C. M. Care.
Phys. Rev. E 74 (2006) 017701.
[abstract] [doi]We report threedimensional parallel Lagrangian particle simulations using the lattice Boltzmann method, conducted at a low Reynolds number. Using modified LeesEdwards boundary conditions and directly calculated viscous dissipation, we show that it is possible to recover excellent agreement with the Einstein viscosity formula in the low concentration limit and to predict viscosity corrections for larger concentrations.

Dielectric permittivity of glycerol in the high viscosity region.
I. V. Blazhnov, N. P. Malomuzh, S. V. Lishchuk.
Chem. Phys. Lett. 418 (2006) 230.
[abstract] [doi]The temperature dependence of the quasistatic dielectric permittivity of highly viscous glycerol is considered in terms of the approach developed in the work [I.V. Blazhnov, N.P. Malomuzh, S.V. Lishchuk, J. Chem. Phys. 121 (2004) 6435]. The microinhomogeneous structure of supercooled glycerol and the frequency dispersion of dielectric permittivity play substantial role in its description. The temperature dependence of the static dielectric permittivity of liquid that surrounds nuclei is determined. The temperature dependencies of the effective polarizability and the mean square value of the dipole moment of molecules in liquid that surrounds nuclei are discussed.

Properties of the Hbond network for twodimensional lattice water model.
S. V. Lishchuk, T. V. Lokotosh, N. P. Malomuzh.
J. Chem. Phys. 122 (2005) 244504.
[abstract] [doi]A microscopic Hamiltonian of the hydrogenbond network in twodimensional lattice water is proposed, which describes the formation and disruption of the H bonds, their bending, and which satisfies the Bernal–Fowler rules [J. D. Bernal and R. H. Fowler, J. Chem. Phys.1, 515 (1933)]. The thermodynamic properties of the Hbond network are studied using the method of manyparticle irreducible distribution functions, which is a generalization of the Kikuchi cluster approach [R. Kikuchi, Phys. Rev. 81, 988 (1951)] and the Bethe–Peierls quasiactivities method [H. A. Bethe, Prog. R. Soc. A150, 552 (1935)]. The temperature dependencies of the average number of H bonds per molecules, the contribution of the H bonds into the heat capacity of the system, and the parameters describing the correlations between the states of molecules on the neighboring sites are investigated. It is shown that depending on the magnitude of the interaction between the H bonds in the Hbond subsystem either smooth or sharp firstorder phase transition can occur. The role of different factors in the formation of the properties of the Hbond network is discussed.

Comment on “Fluctuations of elastic interfaces in fluids: Theory, latticeBoltzmann model, and simulation”.
S. V. Lishchuk, C. M. Care.
Phys. Rev. E 71 (2005) 053201.
[abstract] [doi]The formulas for the force exerted by the interface upon the fluids, given by Stelitano and Rothman [Phys. Rev. E 62, 6667 (2000)] are corrected.

Temperature dependence of density, thermal expansion coefficient and shear viscosity of supercooled glycerol as a reflection of its structure.
I. V. Blazhnov, N. P. Malomuzh, S. V. Lishchuk.
J. Chem. Phys. 121 (2004) 6435.
[abstract] [doi]The relationship of the microstructure of supercooled, highly viscous glycerol to the temperature dependence of its density, thermal expansion coefficient, and shear viscosity are discussed. The character of this temperature dependence at the transition from low viscosity state to the solidamorphous state(solidified state without nuclei) is described with help of function ψ, which can be interpreted as the effective number of degrees of freedom responsible for the change of viscosity of glycerol over a broad range; these degrees of freedom are those related to the αrelaxation process. It is shown that the change in effective activation energy of the viscosity is completely determined by the parameter ψ. The change in the shear viscosity of glycerol due to the influence of the solidphase nuclei is considered. It is shown that the introduction of the parameter φ, equal to the specific volume occupied by the nuclei of the solid phase, together with ψ provides a natural explanation of the temperature dependence of density and thermal expansion coefficients of glycerol in its liquid,solidamorphous, glassy, and crystal states. The peculiarities of the temperature dependence of φ(T) and ψ(T) for glycerol and oterphenyl are compared.

Shape of an isotropic droplet in a nematic liquid crystal: the role of surfactant.
S. V. Lishchuk, C. M. Care.
Phys. Rev. E 70 (2004) 011702.
[abstract] [doi]We investigate theoretically, and numerically, the shape of a droplet of an isotropic fluid immersed in a nematic liquid crystal in the presence of an interfacial layer of surfactant; the droplet size is assumed to be small compared to the extrapolation length of the nematic and homeotropic alignment is favored by the anchoring energy at the nematicisotropic interface. In a certain range of droplet sizes, the droplets are found to be lens shaped with the rotation axis aligned along the imposed director field and the aspect ratio dependent upon the ratio of anchoring strength and surface tension coefficients. For anchoring strengths large compared to the surface tension, the curvature of the edge of lens is controlled by the bending rigidity of surfactant.

A latticeBoltzmann scheme for a nematicisotropic interface.
S. V. Lishchuk, C. M. Care, I. Halliday.
J. Phys. Cond. Mat. 16 (2004) S1931.
[abstract] [doi]A lattice Boltzmann (LB) model of an interface between a nematic and an isotropic fluid is presented. The method is used to study, in two dimensions, the properties of a deformable colloidal droplet of an isotropic fluid suspended in a nematic matrix. The isotropic fluid is modelled by a standard lattice Bhatnagar–Gross–Krook (LBGK) scheme. The LB model of the nematic is a modified LBGK scheme in which a tensor density is used to recover the variable order parameter nematodynamics scheme proposed by Qian and Sheng. The interface between the two fluids is modelled by introducing appropriate forcing at the interface. The stress balance is achieved using an extension of a method proposed by Lishchuk et al, and the torque balance is achieved with an appropriate surface molecular field. The resulting interface algorithm recovers the macroscopic equations developed by Rey. Results are presented for the dependence of the shape of the droplet and the nematic defects upon the surface tension and the anchoring strength. A discussion is also presented of the effect of curvature rigidity on the droplet shape.

Generalized lattice Boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter.
C. M. Care, I. Halliday, K. Good, S. V. Lishchuk.
Phys. Rev. E 67 (2003) 061703.
[abstract] [doi] [arxiv]A lattice Boltzmann (LB) scheme is described, which recovers the equations developed by QianSheng for the hydrodynamics of a nematic liquid crystal with a tensor order parameter. The standard mesoscopic LB scalar density is generalized to a tensor quantity and the macroscopic momentum, density, and tensor order parameter are recovered from appropriate moments of this mesoscopic density. A single lattice Boltzmann equation is used with a direction dependent Bhatnagar, Gross, and Krook (BGK) collision term, with additional forcing terms to recover the antisymmetric terms in the stress tensor. A ChapmanEnskog analysis is presented, which demonstrates that the QianSheng scheme is recovered, provided a lattice with sixthorder isotropy is used. The method is validated against analytical results for a number of cases including flow alignment of the order tensor and the Miesowicz viscosities in the presence of an aligning magnetic field. The algorithm accurately recovers the predicted changes in the order parameter in the presence of aligning flow, and magnetic, fields. Preliminary results are given for an extension of the method to model the interface between isotropic and nematic fluids.

Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents.
S. V. Lishchuk, C. M. Care, I. Halliday.
Phys. Rev. E 67 (2003) 036701.
[abstract] [doi]We present an algorithm for inserting an interface between the immiscible phases of a multicomponent lattice Boltzmann fluid which is based solely upon the appropriate continuum physics: stress boundary conditions and continuity of velocity. Results are presented for the algorithm when applied to static, neutrally buoyant drops. It is shown that the present algorithm gives a significant reduction in the spurious velocities which are reported for previous schemes and a concomitant improvement in the isotropy of the interface.

Lekner summation of dipolar interaction in quasitwodimensional simulations.
S. V. Lishchuk.
Mol. Phys. 100 (2002) 3789.
[abstract] [doi]The Lekner method for calculation of electrostatic interactions in periodically replicated simulation cells is extended to quasitwodimensional systems of particles with dipolar interactions. The electric field, potential energy, forces and torques are expressed through rapidly converging series of modified Bessel functions. The method contains no arbitrary parameters, and has no limitations on the simulation box width.

Velocity distribution of water molecules in pores under microwave electric field.
S. V. Lishchuk, J. Fischer.
Int. J. Therm. Sci. 40 (2001) 717.
[abstract] [doi]In order to understand the transport of water in pores under the influence of a microwave electric field the velocity distribution function of the water molecules is thought to be a key quantity. First, bulk water under the influence of an alternating electric field is studied by using a kinetic equation. As rotation occurs on a faster time scale and translation on a slower time scale it is argued that the velocity distribution for the bulk water is a Maxwell–Boltzmann distribution. Next, the nonequilibrium molecular dynamics simulation method is applied to study the behaviour of TIP3P water molecules under microwave electric field in a slit pore with thermostated walls. The water heats up till it reaches a steady state temperature. It is found that in the transient process as well as in the steady state the velocity distribution function is a Maxwell–Boltzmann distribution for the corresponding temperature. Hence, there is no convective mass transport due to a direct influence of the electric field.

Cluster approach to the problems of diffusion and viscosity in supercooled states of glycerollike liquids.
S. V. Lishchuk, N. P. Malomuzh.
Chem. Phys. Lett. 309 (1999) 307.
[abstract] [doi]To explain the temperature dependence of selfdiffusion coefficients, static shear viscosity, and electrical conductivity of highly viscous electrolytes, the cluster representations developed by the authors are used. The interconnection of the enumerated transport coefficients with the most important kinetic characteristic of supercooled states — the lifetime of weakly bound clusters — is established. Internal selfconsistency of the proposed formulas and their accord with experimental results is discussed. Interpretation of Vogel–Tamman–Fulcher temperature relationship is given.

Clusterization in supercooled states of glycerollike liquids and its manifestations in different phenomena.
S. V. Lishchuk, N. P. Malomuzh.
J. Chem. Phys. 106 (1997) 6160.
[abstract] [doi]The present work is devoted to investigation of the temperature and frequency dependencies of the different relaxing values in highlyviscous glycerollike liquids. The consideration is based on microinhomogeneous structure conception, allowing us to give the consecutive explanation to both the thermodynamic and kinetic properties. The main attention is paid to analysis of heat capacity, dielectrical permeability and longitudinal sound velocity. The influence of measuring time and preparation one of highlyviscous states on observed values are discussed.

Определение параметров спектральных линий молекулярного рассеяния света с помощью регуляризованных частотных моментов.
С. В. Лищук, Н. П. Маломуж, Ш. Ф. Файзуллаев, С. А. Османов.
Ўзбекистон физика журнали 3 (1997) 41.
[abstract] [1st page]Лоренц типидаги секин камаювчи спектрал функциялар ҳам тўла тўплами яхши аниқланадиган танланган частота моментлари ёрдамида спектрал чизиқлар параметрларини аниқлашнинг янги, бевосита услуби баён этилади. Танланган частота моментлари спектрал чизиқларнинг интеграл характеристикаси бўлганлиги туфайли тасодифий хатоликларга унчи сезгир эмас. Таклиф этилаётган услуб бензол иккиланган ўриндошларинда анизотропия релаксация вақтини аниқлаш учун бир ёки бир неча лоренцианлар суперпозициясидан иборат контурларга нисбатан кўлланилган.
A new direct method of determination of spectral line parameters is expounded by means of regularized frequency moments, complete set of which is well defined even for slowly declined spectral functions of Lorentz type. Regularized frequency moments are integral properties of spectral lines and therefore they are least sensitive to random errors. As an illustration the developped method was applied to contoures corresponded to one or superposition of several Lorenzians for determination of relaxation time of anisotropy of disubstituted benzene molecules.

Равновесные и неравновесные свойства сильновязких жидкостей типа глицерина.
С. В. Лищук.
Дис... канд. физ.мат. наук: 01.04.02 / Одесский гос. унт им. И.И.Мечникова. — О., 1997. — 131л.
[annotation] [synopsis]Диссертация содержит результаты: 5 работ, опубликованных в реферированных журналах, 1 работы, опубликованной в сборнике «Труды 2^{ой} Всеукраинской конференции молодых учёных», и 4 работ, опубликованных в тезисах национальных и международных конференций.
В диссертации иццледуется природа равновесных и неравновесных свойств сильновязких жидкостей типа глицерина. Детально изучаются температурная и частотная зависимости теплоёмкости, диэлектрической проницаемости, вязкоупругих модулей. Рассмотрение основывается на предположении о микронеоднородном строении переохлаждённых состояний сильновязких жидкостей. Предложены новые методы определения времени колебательной релаксации и отделения аппаратных эффектов. Проведено всестороннее сравнение с экспериментальными данными.
The thesis contains the results of: 5 papers published in refereed journals, one paper published in Proceedings of 2nd Ukrainian Conference of Young Scientists, and 4 abstracts of national and international conferences.
The nature of equilibrium and nonequilibrium properties of highly viscous glycerollike liquids is investigated. The temperature and frequency dependencies of heat capacity, dielectric permeability, viscoelastic moduli are studied. The consideration is based on the assumption about microinhomogeneous structure of supercooled states for highlyviscous liquids. The new methods for determination of vibrational relaxation time and the separation of instrumental effects are proposed. The comprehensive comparison with experimental data is made.

Особенности спектров молекулярного рассеяния света в сильновязких жидкостях типа глицерина.
С. В. Лищук, Н. П. Маломуж.
Журнал физической химии 70 (1996) 404.
English translation:
The spectra of molecular light scattering in highviscosity glycerollike liquids.
S. V. Lishchuk, N. P. Malomuzh.
Russian J. Phys. Chem. 70 (1996) 369.
[abstract] [url] [pdf]Исследованы механизмы формирования тонкой структуры спектров поляризованной и деполяризованной составляющух молекулярного рассеяния света в сильновязких жидкостях. Рассмотрены температурные зависимости параметров спектров. Обсуждение проведено на основании концепции о микронеоднородном строении переохлажденных состояний сильновязких жидкостей.
The mechanisms of formation of fine structures in the spectra of the polarized and depolarized components of molecular light scattering in highviscosity liquids are studied. The temperature dependences of spectral parameters are examined. The results are treated in terms of the concept of a microheterogeneous structure of supercooled highviscosity liquids.

Температурная зависимость релаксирующих параметров переохлажденных жидкостей типа глицерина.
С. В. Лищук, Н. П. Маломуж.
Журнал физической химии 69 (1995) 1694.
English translation:
Influence of temperature on relaxing parameters for supercooled glycerollike liquids.
S. V. Lishchuk, N. P. Malomuzh.
Russian J. Phys. Chem. 69 (1995) 1539.
[abstract]Обсуждена частотная дисперсия теплоемкости, диэлектрической проницаемости и скорости звука в сильновязких состояниях глицериноподобных жидкостей. Особенное внимание уделено температурным зависимостям предельнонизкочастотных значений указанных величин, весьма чувствительных к предположению о существовании сильносвязанных кластеров.
The frequency dispersion of the specific heat, dielectric constant, and sound velocity for glycerollike liquids in highly viscous states is discussed. Particular attention is paid to the influence of temperature on these parameters in the lowfrequency limit; they are found to be highly sensitive to the postulated existence of the strongly bound clusters.

Релаксационные процессы в переохлажденном глицерине и их проявление в оптических экспериментах.
С. В. Лищук.
Труди 2ої всеукраїнської конференції молодих вчених (1995) сс. 47–56.

The peculiarities of molecular and stimulated impulsive light scattering in supercooled states of glycerollike liquids.
S. V. Lishchuk, N. P. Malomuzh.
J. Mol. Struct. 348 (1995) 205.
[abstract] [doi]Fine structure of molecular and stimulated impulsive light scattering spectra is discussed in frames of approach based on representation of microinhomogeneous structure of highly viscous glycerollike liquids.

Особенности вынужденного импульсного рассеяния света в переохлажденном глицерине.
С. В. Лищук, Н. П. Маломуж.
Журнал физической химии 69 (1995) 110.
English translation:
Specific features of induced pulsedlight scattering in supercooled glycerol.
S. V. Lishchuk, N. P. Malomuzh.
Russian J. Phys. Chem. 69 (1995) 98.
[abstract]Исследованы физические параметры оптического сигнала, формирующегося в глицерине под действием интенсивного импульсного излучения. Рассмотрение основано на концепции о микронеоднородном строении переохлажденных сильновязких состеояний глицериноподобных жидкостей. Проведено детальное сравнение с экспериментальными данными.
The physical parameters of the optical signal generated in glycerol under the action of intense pulsed radiation are studied. The phenomenon is analyzed using the concept of a microheterogeneous structure of supercooled highviscosity states of glycerollike liquids. A detailed comparison with experiment is given.

Определение времени колебательной релаксации жидкостей с помощью соотношения ЛандауПлачека.
С. В. Лищук, Н. П. Маломуж, Ш. Ф. Файзуллаев.
Фізика рідкого стану 21 (1993), прийнято до друку.
English translation:
Determination of vibrational relaxation time of liquids with help of LandauPlaczek ratio.
S. V. Lishchuk, N. P. Malomuzh, Sh. F. Faizullaev.
[abstract] [preprint]A new method of determination of the vibrational relaxation time of liquids based on using the LandauPlaczek ratio is proposed. The influence of molecular anisotropy effects is taken into account. The effectiveness of the method is illustrated on the example of substituted benzene.