Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Safronchik M. I. Plate Braking Against the Layerof «Delayed» Viscoplastic Fluid with Regard to Wall Sliding. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 2, pp. 88-93. DOI: 10.18500/1816-9791-2009-9-2-88-93

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Plate Braking Against the Layerof «Delayed» Viscoplastic Fluid with Regard to Wall Sliding

Safronchik Mariya Ilinichna, Saratov State University

The paper presents the problem of unstable viscoplastic fluid flow between parallel planes, one of which is fixed, while the other one is put in motion from a standstill under the influence of constant force. Viscoplastic fluid flow develops gradually. The border of the flow is not known in advance and is to be determined in the process of solving the task. The force applied to the upper plate is chosen so as to cause the effect of sliding along the two plates in the course of time. The task definition is given within the limits of five-parameter model, which permits to take up the difference between behavior under stress and without stress as well as possible sliding along the solid walls. Hysteresis of deformation is considered by means of Slibar – Pasly hypothesis. To take the possible sliding along the walls into account, a hypothesis, analogical to the well-known hypothesis for viscous fluid of Prof. N.P. Petrov, is suggested. The offered hypothesis also allows to describe the natural physical condition of smooth transition from «sticking» to «sliding». Moreover, the parameters included into it can be defined empirically. To solve the task with the required border, a modified method of Kolodner is used.  

  1. Slibar A., Paslay P.R. Retarded Flow of Bingam Materials // J. of Appl. Mech. 1959. March. P. 107–112.
  2. Сафрончик А.И., Сафрончик М.И., Неустановившееся «запаздывающее» течение Куэтта вязкопластичной среды между параллельными стенками // Математика. Механика: Сб. науч. тр. Саратов: Изд-во Сарат. ун-та. 2003. Вып. 5. С. 177–180.
  3. Kolodner J.J. Free boundary problem for the heat equation wich applications of change of phase // Com. on Pure and Appl. Math. 1956. V. IX, № 1.
  4. Сафрончик А.И. Некоторые задачи неустановившегося течения вязкопластичных сред: Дис. . . . канд. физ.-мат. наук. Ростов н/Д, 1962. 109 с.
  5. Сизиков В.С., Смирнов А.В., Федоров Б.А. Численное решение сингулярного интегрального уравнения Абеля обобщенным методом квадратур // Изв. вузов. Математика. 2004. № 8. С. 62–70.