Why Aren't Pressure Differences Included in Capillary Filling Dynamics?

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    Capillary Dynamics
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Discussion Overview

The discussion revolves around the dynamics of capillary filling, specifically questioning why pressure differences are not included in the equations that describe this phenomenon, such as the Lucas-Washburn equation. Participants explore the implications of pressure differences in both dynamic and static contexts.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the omission of pressure differences in the Lucas-Washburn equation, particularly in the context of equilibrium height (Jurin's height).
  • Another participant points out that while Laplace pressure can be computed for a static system, its role in dynamic equations remains unclear.
  • A participant asserts that the force due to pressure difference acts downward in the case of water rising due to capillary action.
  • In contrast, another participant argues that the gravitational force acts downward while surface tension opposes it, suggesting a more complex interaction.
  • One participant claims that the pressure difference is indeed accounted for in the equation, noting that the pressure below the meniscus is less than atmospheric pressure, which facilitates fluid movement up the capillary.
  • This participant compares the situation to sucking on a straw, indicating a balance of pressures that leads to the formulation of the Lucas-Washburn equation.

Areas of Agreement / Disagreement

Participants express differing views on the role of pressure differences in capillary dynamics. Some argue that it is not included in the dynamic equations, while others contend that it is implicitly accounted for. The discussion remains unresolved regarding the exact treatment of pressure differences in the context of capillary filling.

Contextual Notes

Participants have not reached a consensus on how pressure differences should be integrated into the dynamics of capillary filling, and there are varying interpretations of the forces at play.

Rishav Roy
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When we write the equation for expressing the dynamics of capillary filling, why don't we include the effects of pressure difference?
 
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What equation?
 
m(d^2x/dt^2)=-mg+(wetted perimeter)*surface tension-viscous forces.
This is the Lucas -Washburn equation.
Even during finding the equilibrium height (Jurin's height) at which the movement of fluid stops, we equate the gravitational forces to the surface tension forces, without considering the pressure difference. Why is that?
 
Last edited:
What pressure difference?
 
Sorry for the late reply.
Coming to the question, we can compute a pressure difference between the two sides of a meniscus (Laplace pressure) due to the presence of a curvature. but this computation is done when the system is static. But when we write equations describing the dynamics (Lucas-Washburn equations mentioned in my previous reply), why don't we include the force due to this pressure-difference?
 
What direction does this force act?
 
Consider a simple case of water rising up due to capillary action. Then this force due to pressure difference acts in the downward direction.
 
No. mg acts in the downward direction. Surface tension at the perimeter of the meniscus opposes that force.
 
The pressure difference actually is taken into account in the equation. The pressure in the fluid immediately below the meniscus is less than atmospheric. So the atmospheric pressure pushing down on the fluid in the bath forces fluid up the capillary. It's like sucking on a straw. If you combine the Laplace relationship with the hydrostatic balance on the fluid, the atmospheric pressures cancel, and you are left with the Lucas Washburn equation, sans the acceleration term and the viscous term.

Chet
 

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