Simulation of particle dynamics in a viscous fluid near a plane wall

Baranov, V. E.; Мартынов, С. И.

doi:10.1134/s0965542510090101

Cited by 5 publications

(6 citation statements)

References 7 publications

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“…The numerical results are returned in processed form, so that the dynamics of the system of particles can be visualized. A similar program was used in [11,14,15].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In view of the hydrodynamic interaction between the particles in the fluid, and were determined using the results obtained in [11][12][13][14][15] for various viscous flows in the Stokes approximation. This method makes it possible to take into account the interaction of a large number of particles, including the case of a near-wall flow.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Changing the direction of the applied moments, we can change the vortex flow around the system of particles, thus changing the displacement direction of the entire system. The hydrodynamic interactions of all particles in the system are taken into account using the results of [11][12][13][14][15]. In the last configuration, we reverse the direction the internal moments acting on C and F and compute the dynamics of the structure.…”

Section: Dynamics Of a Chain Of Particles Moving In A Viscous Fluid Duementioning

confidence: 99%

“…In [11] a method based on the results of [12][13][14][15] was proposed, in which the dynamics of an aggregate was represented as that of its constituent particles with allowance for both internal forces or imposed constraints retaining the particles in the aggregate and the hydrodynamic interaction between the particles. The method provides good agreement with experimental results concerning the dynamics of model aggregates.…”

mentioning

confidence: 99%

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Dynamics of chain particle aggregates in viscous flow

Мартынов

Tkach

2016

Comput. Math. and Math. Phys.

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The dynamics of aggregates consisting of chains of particles and their union in the form of a two-dimensional network in viscous flow is numerically simulated. It is assumed that the particles in a chain can move relative to each other so that the distance between two neighboring ones remains unchanged. The hydrodynamic interaction forces between all particles in an aggregate are taken into account. The deposition of particle chains and their dynamics in a linear flow are considered in the case an unbounded fluid volume and near a flat wall. The interaction forces between the particles necessary for retaining them in a chain are calculated, and places of the most probable breakage in the chain are determined.In recent years, there has been increasingly more interest in the study of colloidal suspensions, which is motivated by the creation of new materials with predetermined properties as based on viscous fluids with added particles and by the possibility of controlling these properties via variations in the particle microstructure caused by applied external fields.Due to the interaction of fluid particles, they can form structures (including periodic ones) or aggregates in the particles are retained by the interaction forces [1,2]. Aggregates vary in size and shape and can have a rather rigid or deformable structure. In the literature, much attention has been given to the dynamics of aggregates representing chains of particles. This is associated primarily with the study of structure formation in magnetic fluids, which can be controlled by external magnetic fields. The application of a magnetic field to a magnetic fluid leads to the formation of particle structures that change the physical properties of the fluid. Droplet aggregates, friable fractal clusters, and chain aggregates can be formed in magnetic fluids. The last case is typical of systems with large particles and low particle concentrations. The formation of chain aggregates has been observed in numerous experimental studies (analysis of rheological, diffusive, optical properties) and in numerical studies of magnetic fluid structures (Monte Carlo simulation, the molecular dynamics method) [3,4]. Observed agglomerates reach dozens of microns in size. The mechanism responsible for this structurization in magnetic fluids is the interaction of particles possessing a magnetic moment. In early works, particle chains were modeled by undeformable ellipsoids of revolution [5], which made it possible to use well-known results from the fluid dynamics of such aggregates. This representation of chains was underlain by works concerning the fluid dynamics of doublets of particles [6,7]. Another approach to the study of such aggregates is based on their representation in the form of chains of spherical particles retained in a particular configuration by dipole-dipole interaction forces [8]. As a rule, only pairwise interactions between particles are considered. However, this approach does not take into account the hydrodynamic interaction of the particles with the surr...

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“…The numerical results are returned in processed form, so that the dynamics of the system of particles can be visualized. A similar program was used in [11,14,15].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Dynamics Of a Chain Of Particles Moving In A Viscous Fluid Duementioning

confidence: 99%

mentioning

confidence: 99%

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Dynamics of chain particle aggregates in viscous flow

Мартынов

Tkach

2016

Comput. Math. and Math. Phys.

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“…Äëÿ ýòîãî ââîäèòñÿ äîïîëíèòåëüíàÿ ôèêòèâíàÿ ÷àñòèöà B , ñèì-ìåòðè÷íàÿ äàííîé A îòíîñèòåëüíî ïëîñêîé ñòåíêè β è ÷àñòèöà C , ñèììåòðè÷íàÿ äàííîé A îòíîñèòåëüíî ïëîñêîé ñòåíêè α (Ðèñ. 2.1 à), à çàòåì èñïîëüçóåòñÿ ôîðìà çàïèñè ðåøåíèÿ çàäà÷è î âçàèìîäåéñòâèè äâóõ ÷àñòèö A è B , A è C [11]. Àíàëîãè÷íî ââîäèòñÿ äîïîëíèòåëüíàÿ ôèêòèâíàÿ ÷àñòèöà D , ñèììåòðè÷íàÿ B è C îòíîñèòåëüíî ñòåíîê α è β ñîîòâåòñòâåííî, è èñïîëüçóåòñÿ ôîðìà çàïèñè ðåøåíèÿ î âçàèìîäåéñòâèè äâóõ ÷àñòèö B è D , C è D [11].…”

Section: ïîñòàíîâêà çàäà÷è è ìåòîä ðåøåíèÿunclassified

Dynamics of sedimentation of particle in a viscous fluid in the presence of two flat walls

Мартынов¹,

Pronkina²,

Dvoryaninova

et al. 2018

Zhurnal SVMO

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The model problem of sedimentation of a solid spherical particle in a viscous fluid bordering two solid planar surfaces is considered. To find the solution of the hydrodynamic equations in the approximation of small Reynolds numbers with boundary conditions on a particle and on two planes, a procedure developed for numerical simulation of the dynamics of a large number of particles in a viscous fluid with one plane wall is used. The procedure involves usage of fictive particles located symmetrically to real ones with respect to the plane. To solve the problem of the real particle’s sedimentation in the presence of two planes, a system of fictive particles is introduced. An approximate solution was found using four fictive particles. Basing on this solution, numerical results are obtained on dynamics of particle deposition for the cases of planes oriented parallel and perpendicular to each other. In particular, the values of linear and angular velocities of a particle are found, depending on the distance to each plane and on the direction of gravity. In the limiting case, when one of the planes is infinitely far from the particle, we obtain known results on the dynamics of particle sedimentation along and perpendicular to one plane.

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Comments on the paper by O.B. Gus’kov “A self-consistent field method applied to the dynamics of viscous suspensions”, JAMM Vol. 77, No. 4, pp. 401–411, 2013

Martynov¹

2015

Journal of Applied Mathematics and Mechanics

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Simulation of particle dynamics in a viscous fluid near a plane wall

Cited by 5 publications

References 7 publications

Dynamics of chain particle aggregates in viscous flow

Dynamics of chain particle aggregates in viscous flow

Dynamics of sedimentation of particle in a viscous fluid in the presence of two flat walls

Comments on the paper by O.B. Gus’kov “A self-consistent field method applied to the dynamics of viscous suspensions”, JAMM Vol. 77, No. 4, pp. 401–411, 2013

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