Analysis of collisions of precipitating solid particles with a wall in a viscous liquid

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Abstract

BACKGROUND: When calculating velocities of free precipitation of solid particle in a viscous Newtonian liquid, it is assumed that influence of incoming vessel head can be neglected. Necessity of considering this factor grows with a vessel head getting closer and with decrease of particles’ geometrical size.

AIMS: Development of the method of calculating solid particles’ precipitation rate in a Newtonian fluid considering the incoming vessel head and definition the limits of its application.

METHODS: The known analytical model of motion of precipitating disperses solid particles when approaching a vessel head is analyzed. It is shown that the known model of calculation of solid particles’ precipitation rate near the vessel head needs to be refined.

RESULTS: The proposed modification of the analytical model of definition the solid particles’ precipitation rate considering the existence of a vessel head helps to ensure more credible results from physical standpoint. Recommendations regarding the influence of the Brownian motion of fluid’s molecules on motion of precipitating solid particles are given.

CONCLUSION: Practical value of the study lies in ability to calculate solid particles’ precipitation rate near to a vessel head.

About the authors

Alexander S. Kondratiev

Moscow Polytechnic University

Author for correspondence.
Email: ask41@mail.ru
ORCID iD: 0009-0001-2030-5165
SPIN-code: 6739-0496

Dr. Sci. (Tech.), Professor of the Industrial Heat Power Engineering Department

Russian Federation, Moscow

Pavel P. Shvydko

Sistemotekhnika

Email: Shvydko.P@gmail.com
ORCID iD: 0009-0007-8030-6403
SPIN-code: 8347-3886

Project Manager

Russian Federation, Moscow

References

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  2. Zdeshchits VM, Sidorenko VD. Collision of solids in a viscous fluid. Visnik KTU. 2010;26:59–61. (in Russ).
  3. Sedov LI. Plane problems of hydrodynamics and aerodynamics. Moscow: Nauka; 1980. (in Russ).
  4. GOST 9378-93. Obraztsy sherokhovatosti poverkhnosti (sravneniya). Mezhgosudarstvennyy standart. Minsk: Mezhgosudarstvennyy sovet po standartizatsii, metrologii i sertifi-katsii; 2002. (in Russ). [дата обращения: 17.05.2023] Режим доступа: https://meganorm.ru/Data2/1/4294847/4294847416.pdf
  5. Kondratyev AS. Settlement of polymodal solids in Newtonian fluids. Moscow: Sputnik+; 2014. (in Russ).
  6. Kondratyev AS, Nya TL, Shvydko PP. Methodology and methods for calculating the movement of dispersed solid particles in pipelines. Moscow: Mos. Politekh; 2020. (in Russ).
  7. Batchelor J. The influence of Brownian motion on the average stress in a suspension of spherical particles. In: Hydrodynamic interaction of particles in suspensions. Mechanics. New in foreign science. Moscow: Mir;22:124–153. (in Russ).

Supplementary files

Supplementary Files
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1. JATS XML
2. Fig. 1. Configuration of collocation of a precipitating solid particle and a flat surface of a vessel head.

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