TY - JOUR

T1 - Mathematical model of the flotation complex particle-bubble within the framework of Lagrangian formalism

AU - Moshkin, N. P.

AU - Kondratiev, S. A.

N1 - Publisher Copyright: © Published under licence by IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11/20

Y1 - 2020/11/20

N2 - A model of the interaction of a spherical gas bubble and a rigid particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model takes into account oscillations of the bubble surface and the attached to it solid cylindrical particle in infinite volume of ideal incompressible liquid. The capillary force holding the particle on the bubble is due to the shape of the meniscus surface, which determines the wetting edge angle. The series with respect Legendre polynomials is used to present small axisymmetric oscillations of the particle-bubble system. Potential and kinetic energies are expressed through coefficients of this series. Particle adhesion condition to bubble surface is implemented through Lagrange multipliers. The dependence of the particle size and its density is demonstrated as a result of the numerical integration of the resulting dynamic system of differential equations.

AB - A model of the interaction of a spherical gas bubble and a rigid particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model takes into account oscillations of the bubble surface and the attached to it solid cylindrical particle in infinite volume of ideal incompressible liquid. The capillary force holding the particle on the bubble is due to the shape of the meniscus surface, which determines the wetting edge angle. The series with respect Legendre polynomials is used to present small axisymmetric oscillations of the particle-bubble system. Potential and kinetic energies are expressed through coefficients of this series. Particle adhesion condition to bubble surface is implemented through Lagrange multipliers. The dependence of the particle size and its density is demonstrated as a result of the numerical integration of the resulting dynamic system of differential equations.

UR - http://www.scopus.com/inward/record.url?scp=85097092261&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1666/1/012037

DO - 10.1088/1742-6596/1666/1/012037

M3 - Conference article

AN - SCOPUS:85097092261

VL - 1666

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012037

T2 - 9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics

Y2 - 7 September 2020 through 11 September 2020

ER -