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Related Concept Videos

Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Standing Waves01:17

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Buoyancy and Stability for Submerged and Floating Bodies01:11

Buoyancy and Stability for Submerged and Floating Bodies

In fluid mechanics, buoyancy and stability are key concepts for understanding the behavior of submerged and floating bodies. When a stationary body is fully or partially submerged in a fluid, the fluid exerts a force on the body known as the buoyant force. This force acts vertically upward through a point called the center of buoyancy, which is the center of the displaced fluid volume. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...

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Related Experiment Video

Updated: Jul 13, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Rippling instability of a collapsing bubble

da Silveira R1, Chaieb, Mahadevan

  • 1Department of Physics, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Science (New York, N.Y.)
|February 26, 2000
PubMed
Summary

Air bubbles rising in viscous liquids create slow-bursting domes that fold into wavy patterns. This geometric phenomenon, driven by gravity and bending forces, predicts a specific number of ripples, confirmed by experiments.

Area of Science:

  • Fluid dynamics
  • Rheology
  • Surface physics

Background:

  • Bubbles in viscous liquids form surface domes.
  • Unlike soap bubbles, these domes collapse slowly under gravity.
  • This collapse leads to a unique wavy or rippling structure.

Purpose of the Study:

  • To investigate the physics behind the slow collapse and rippling of air bubbles in viscous liquids.
  • To formulate a theoretical model for the onset and growth of surface corrugations.
  • To establish a quantitative relationship between bubble properties and ripple formation.

Main Methods:

  • Theoretical modeling of fluid sheet dynamics.
  • Analysis of the interplay between gravitational and bending forces.
  • Experimental observation of bubble behavior in viscous fluids.

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Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
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Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Related Experiment Videos

Last Updated: Jul 13, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
08:19

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Main Results:

  • A theory for the onset of surface rippling in viscous sheets was developed.
  • The growth of corrugations is governed by a balance of gravitational and bending forces.
  • A quantitative expression for the number of ripples was derived and experimentally validated.

Conclusions:

  • The rippling effect in viscous fluid sheets is primarily a geometric phenomenon.
  • The derived theory and ripple number expression show wide applicability across various fluid properties and scales.
  • Experimental results strongly support the theoretical predictions for ripple formation.