Laws of Motion

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Computer illustrations to the laws of motion 3 (of 3)

Rising bubbles in a viscous liquid

The simulation shows bubbles that rise in a viscous liquid. The motion of the bubble is governed by the buoyancy force and the opposing force of viscous friction which is proportional to the velocity. At the first moment after the bubble tears off the bottom, the frictional force is zero (because the bubble starts from rest with zero velocity), and the acceleration is maximal. However, the increasing speed causes the gradual growth of the opposing frictional force, and eventually this downward force balances the upward buoyant force: The bubble's upward motion becomes uniform.

Examples:

1. Three bubbles of different size starting simultaneously. In this example we can easily compare the motion of bubbles of different sizes. The buoyancy force is proportional to the volume of the bubble, while the frictional force is proportional to its diameter. Hence the final upward velocity is proportional to the diameter squared -- large bubbles float upward faster than small ones. The time needed for the velocity to establish is also proportional to the diameter squared -- a small bubble reaches the constant speed much faster than a large one. (Click also here to see the applet.)

2. Chaotic formation of bubbles. In this example a bubble appears at the bottom of the cubic vessel at an arbitrary moment, and gradually grows being held there by the surface tension. The bubble remains at the bottom until the growing buoyancy force overcomes the surface tension. Then the bubble rises with an upward acceleration, whose value gradually diminishes due to the increasing frictional force. After some time the bubble rises uniformly (in case it has not reached the surface by this time). The lapse of time after which the accelerated motion transforms into the uniform one, as well as the final speed gained by the bubble, depend on the size of the bubble. The whole process reminds the first stage of boiling. (Click also here to see the applet.)

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Eugene Butikov personal page | Overview | Previous section

Computer illustrations to the laws of motion 3 (of 3)