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

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.

Keywords

solid particles / precipitation rate / influence of a vessel head

References

[1] Zababakhin EI. Some cases of viscous fluid motion. In: Questions of modern experimental and theoretical physics. Leningrad: Nauka; 1984:58–68. (in Russ).

[2] Забабахин Е.И. Некоторые случаи движения вязкой жидкости // Вопросы современной экспериментальной и теоретической физики. Л.: Наука, 1984. С. 58–68.

[3] Zdeshchits VM, Sidorenko VD. Collision of solids in a viscous fluid. Visnik KTU. 2010;26:59–61. (in Russ).

[4] Здещиц В.М., Сидоренко В.Д. Столкновение твердых тел в вязкой жидкости // Вiсник КТУ. 2010. № 26. С. 59–61.

[5] Sedov LI. Plane problems of hydrodynamics and aerodynamics. Moscow: Nauka; 1980. (in Russ).

[6] Седов Л.И. Плоские задачи гидродинамики и аэродинамики. М.: Наука, 1980.

[7] 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

[8] ГОСТ 9378-93. Образцы шероховатости поверхности (сравнения). Межгосударственный стандарт. Минск: Межгосударственный совет по стандартизации, метрологии и сертификации, 2002. [дата обращения: 17.05.2023] Режим доступа: https://meganorm.ru/Data2/1/4294847/4294847416.pdf

[9] Kondratyev AS. Settlement of polymodal solids in Newtonian fluids. Moscow: Sputnik+; 2014. (in Russ).

[10] Кондратьев А.С. Осаждение полимодальных твердых частиц в ньютоновских жидкостях. М.: Спутник+, 2014.

[11] 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).

[12] Кондратьев А.С., Ньа Т.Л., Швыдько П.П. Методология и методы расчета движения дисперсных твердых частиц в трубопроводах. М.: Мос. Политех. 2020.

[13] 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).

[14] Бэтчелор Дж. Влияние броуновского движения на среднее напряжение в суспензии сферических частиц // Гидродинамическое взаимодействие частиц в суспензиях. Механика. Новое в зарубежной науке. М.: Мир, 1980. Вып. 22. С. 124–153.

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