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Related Concept Videos

Excess Pressure Inside a Drop and a Bubble01:13

Excess Pressure Inside a Drop and a Bubble

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The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.
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Viscosity01:17

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When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
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Pressure Variation in a Fluid at Rest01:11

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In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
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Viscosity of Fluid01:19

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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
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Euler's Equations of Motion01:28

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In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
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Surface Tension of Fluid01:22

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Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
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Updated: Jan 14, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
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Steady bubbles and drops in inviscid fluids.

David Meyer1, Lukas Niebel2, Christian Seis2

  • 1Instituto de Ciencias Matemáticas, Calle Nicolás Cabrera 13-15, 28049 Madrid, Spain.

Calculus of Variations and Partial Differential Equations
|October 20, 2025
PubMed
Summary
This summary is machine-generated.

We found new non-spherical bubble and drop solutions for fluid dynamics, revealing richer possibilities with surface tension compared to simpler models. This advances understanding of fluid interfaces and vortex dynamics.

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Area of Science:

  • Fluid Dynamics
  • Mathematical Physics

Background:

  • The two-phase Euler equations describe fluid interfaces.
  • Hill's spherical vortex is a known solution for uniform vortices.

Purpose of the Study:

  • Construct steady, non-spherical traveling wave solutions for two-phase flows with surface tension.
  • Investigate the influence of surface tension on vortex dynamics.

Main Methods:

  • Perturbative approach around Hill's spherical vortex.
  • Bifurcation analysis using the Crandall-Rabinowitz theorem.
  • Implicit function theorem for non-critical Weber numbers.

Main Results:

  • Successfully constructed non-spherical bubble and drop solutions.
  • Solutions exhibit uniform vorticity and surface vortex sheets.
  • Flow behavior is sensitive to Weber numbers.

Conclusions:

  • Surface tension significantly enriches the dynamics of two-phase Euler equations.
  • Non-spherical solutions exist, unlike the uniqueness of spherical Hill's vortex in one-phase models.