Natural frequencies of longitudinal oscillations of a droplet in the constriction of the capillary tube

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


2015, Vol. 1. №2(2)

Natural frequencies of longitudinal oscillations of a droplet in the constriction of the capillary tube

About the authors:

Amir A. Gubaidullin, Dr. Sci. (Phys.-Math.), Professor, Сhief Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID, Scopus AuthorID,

Aleksei Yu. Maksimov, Lead Engineer, CompMechLab® LLC, Peter the Great St. Petersburg Polytechnic University; eLibrary AuthorID, ORCID,


The actual problem of improving wave technologies of enhanced oil recovery lies in challenges of fi nding the frequency of longitudinal oscillations of oil droplets (ganglion), jammed in the narrowing of pores. To determine the natural frequencies of droplets computer modeling can be used. As a mathematical model for the numerical study Navier – Stokes equations or Lattice-Boltzmann method can be used. However, to obtain preliminary estimates and solve engineering problems it is convenient to have a formula that allows, even approximately, getting the desired result. In this paper a formula is obtained for the natural frequencies of longitudinal oscillations of a droplet surrounded by immiscible with its fl uid in the narrowing of capillary conical shape.  Comparison of the results of calculations by the formula with the numerical solution of the problem has been carried out. The analysis of the frequency of the droplet oscillations in the static pressure difference, surface tension and contact angle of wetting has been carried out.


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