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Rise of Liquid in a Capillary Tube01:18

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When very thin cylindrical tubes, called capillaries, are dipped in a liquid, the liquid rises or falls in the tube compared to the surrounding liquid. This phenomenon is called capillary action. Capillary action occurs due to the combination of two opposing forces: the cohesive forces of the liquid, which cause it to stick to itself and form a rounded shape, and the adhesive forces between the liquid and the walls of the container, which cause the liquid to be attracted to the container walls.
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Capillarity in Fluid01:19

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Capillarity describes the movement of liquid in small spaces without external forces acting on it. The capillarity is driven by surface tension and adhesive interactions between the liquid and surrounding solid surfaces. This effect is often seen in narrow tubes, porous materials, and fine particles.
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As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Liquid/liquid displacement in a vibrating capillary.

Anatoliy Vorobev1, Sergei Prokopev2, Tatyana Lyubimova2,3

  • 1Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 27, 2023
PubMed
Summary

Mechanical vibrations can unexpectedly slow or stop fluid flow in porous materials. This study reveals how vibrations alter fluid dynamics in geological reservoirs, challenging common assumptions about fluid release.

Keywords:
capillary pressureliquid/liquid displacementmultiphase flowphase-field modellingtime-averaged approachvibrations

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Area of Science:

  • Physics
  • Geophysics
  • Fluid Dynamics

Background:

  • Mechanical vibrations are known to influence fluid distribution in porous media.
  • Existing theories often link vibration-induced fluid percolation changes to solid elasticity and fluid compressibility.
  • Observed long-range effects of vibrations in geological reservoirs (100m) contradict theories limited by short damping zones (cm).

Purpose of the Study:

  • To develop a non-elastic theory for time-averaged effects of small-amplitude, high-frequency vibrations on fluid flow.
  • To investigate the impact of translational vibrations on immiscible liquid/liquid displacement in capillary systems.
  • To understand how vibrations affect fluid displacement rates and menisci shapes in porous matrices.

Main Methods:

  • Development of a novel non-elastic theoretical framework.
  • Experimental examination of immiscible liquid/liquid displacement flows within a single capillary.
  • Application of translational vibrations to the capillary system.

Main Results:

  • Significant alterations in meniscus shapes were observed under strong-enough vibrations.
  • Vibrations were found to modify the rates of displacement flows.
  • Contrary to expectations, vibrations were shown to slow down or completely halt fluid displacement.

Conclusions:

  • The study presents a new theory explaining vibration-induced fluid flow changes beyond elastic deformation limits.
  • Vibrations can impede rather than facilitate fluid release in porous media, challenging conventional understanding.
  • Findings have implications for fluid dynamics in geological reservoirs and other porous systems subjected to vibrations.