Vibration effects on a fluid flow in porous media and study of nonlinear gravity waves in the Lagrangian description
In [1], we considered the problem of a droplet moving in the capillary where under the influence of a variable force the contact angle was modulated, and due to the existing hysteresis the drop performed a translational motion in a hydrostatic pressure field. This idea has been further developed and generalized in a number of papers [2-4]. We note a very good review on vibration effects on a fluid flow presented in [5] (see also [6]). An analysis of the existing data and considerations of the mechanism of the vibratory stimulation of a fluid flow were represented in 2007 [7]. There is no complete clarity in this matter so far. The models under study can conditionally be reduced to the model with a step (or asymmetric) characteristic of viscosity vs. flow rate, which results in the appearance of a detection effect. The absence of high-quality experimental data precludes the development of theory and understanding of the physical mechanisms. We assume that the slow dynamics effects mentioned above are related to the problem of interaction between the fluid and the skeleton of porous rocks. We intend to use the experimental setup of a “physical pendulum” for a study of the small-amplitude vibration effects on a fluid flow.
In a series of papers [8-11], an asymptotic theory of weakly nonlinear vortical waves in deep water was developed. A solution for linear spatial periodic waves in an infinitely deep fluid was constructed and analyzed. A distinctive feature of these waves is the presence of vorticity in the direction of propagation. An expression for the horizontal drift velocity of fluid particles averaged with respect to the wavelength was found [12]. Standing surface waves in a viscous fluid of infinite depth were studied. The problem solution is given in the linear and quadratic approximations. The case of long (compared with the boundary layer thickness) waves was analyzed in detail. The trajectories of the fluid particles were determined and an expression for the vorticity was found [13]. A method for describing the wave packet on the surface of an infinitely deep viscous fluid as part of the Lagrangian approach was developed. The case where the reverse Reynolds number is of the order of the wave steepness squared was analyzed. Expressions for the fluid particle trajectories were determined with accuracy up to the steepness cubed. Conditions under which the evolution of the wave packet envelope is described by the nonlinear Schrödinger equation with a dissipation term that is linear in amplitude were specified. The rule by which such a term can be properly added to the evolution equation of arbitrary order was formulated [14].
References to Section 4
1. Averbakh V, Vlasov S, Zaslavsky Yu (2000) Motion of the liquid droplet in the capillary under the action of static force and acoustic field. Radiophysics and Quantum Electronics 43(2): 155–161.
2. Abrashkin A, Averbach V, Vlasov S (2003) Mass Transfer of the Liquid Phase in a Partially Saturated Porous Medium Under the Action of Low-Frequency Elastic Vibrations. Radiophysics and Quantum Electronics 46(3): 235–244.
3. Abrashkin A, Raevsky M (2002) Dynamics of Unstable Moistening Films and Single Drops in a Capillary under Vibration [in Russian]. Bulletin of the Russian Academy of Sciences: Physics 66(12): 1730-1736.
4. Abrashkin A, Averbakh V, Vlasov S, Zaslavsky Yu, Soustova I, Sudarikov R, Troitskaya Yu (2005) A possible mechanism of the acoustic action on partially fluid-saturated porous media. Acoustical Physics 51(Appendix): 19–30.
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7. Serdyukov S, Kurlenya M (2007) Mechanism of Oil Production Stimulation by Low-Intensity Seismic Fields. Acoustical Physics 53(5): 703–714.
8. Abrashkin A, Zen'kovich D (1990) Vortical Stationary Waves on a Shear Flow [in Russian]. Izvestiya, Atmospheric and Oceanic Physics 26(1): 35–45.
9. Abrashkin A (1996) Three-dimensional Gouyon waves. Fluid Dynamics 31(4): 583-587.
10. Abrashkin A (1996) Standing vortex waves in deep water. Fluid Dynamics 31(3): 470–473.
11. Abrashkin A (1991) Gravity Surface Waves of the Envelope in a Vortical Fluid [in Russian]. Izvestiya, Atmospheric and Oceanic Physics 27(6): 633–637.
12. Abrashkin A (2008) Three-dimensional waves on the surface of a viscous fluid. Fluid Dynamics 43(6): 915–922.
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14. Abrashkin A, Bodunova Yu (2013) Packet of gravity surface waves at high Reynolds numbers. Fluid Dynamics 48(2): 223–231.
