SIMULATION OF QUASISTATATICS OF THE PROCESS OF FORMATION OF A LIQUID MENISK TYPE OF HANGING DROP ON THE SUBJECT OF METHODOLOGICAL PROVISION OF MEASUREMENT
DOI:
https://doi.org/10.31471/1993-9981-2021-1(46)-33-42Keywords:
hanging drop, quasi-statistics, meniscusAbstract
A mathematical model has been developed for describing a capillary surface of the hanging drop type in the form of a system of fifth-order nonlinear differential equations, which corresponds to five geometric characteristics of the meniscus: the distance from the meniscus axis to a given point on the capillary surface, the distance from the plane normal to the meniscus surface at an umbilical point to a given point on capillary surface, the angle between the axis of symmetry and the normal to the capillary surface at a given point, the area and volume of the capillary surface bounded by a cut of the horizontal plane passing through a given point. By reducing the equation to a dimensionless form, it was possible to reduce to one setting parameter - the reduced Gaussian curvature at the umbilical point. The numerical solution of the obtained model with the subsequent reduction of the geometric and physical characteristics of the capillary surface to the radius of the capillary made it possible to simulate a quasi-static sequence of the meniscus surfaces. This made it possible to form a methodological basis for determining the static and dynamic surface characteristics of interfaces. Also, modeling the quasi-statics of meniscus formation made it possible to determine with high accuracy the values of the characteristics of the meniscus in extreme cases, such as the moment of maximum pressure in the meniscus and the moment of separation from the end of the capillary. This is the methodological basis for such well-known methods for determining surface characteristics as the method of maximum pressure in the meniscus and the stalagmometric method. Also, if the obtained results are interpreted as a quasi-statics of changes in the parameters of a hanging drop of a solution of surfactants (hanging bubble) at a constant volume, it is possible to determine the dynamics of changes in surface tension. The numerical solution of the system of differential equations and the interpretation of the obtained tabulated results was carried out in the MathWorks MATLAB environment, which made it possible to form multilevel systematized data arrays of capillary surfaces, which can be basic for further interpretation, depending on the task at hand.
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