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Related Concept Videos

Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
Concept of Pressure at a Point01:15

Concept of Pressure at a Point

The concept of pressure at a point in a fluid establishes that pressure within a fluid is uniform in all directions at a specific location. This uniformity occurs because fluid molecules exert force evenly across any point due to their random motion and continuous collisions within the fluid. Pressure at a point is determined by the surrounding fluid molecules and is influenced by factors like depth and density, rather than by shape or orientation.
In a fluid at rest, pressure acts equally in...
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
The resultant force...
Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
Pressure Variation in a Fluid at Rest01:11

Pressure Variation in a Fluid at Rest

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.
When measuring pressure at two different levels within the fluid, the difference in pressure...

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Related Experiment Video

Updated: Jun 25, 2026

Fabrication of Large-area Free-standing Ultrathin Polymer Films
10:08

Fabrication of Large-area Free-standing Ultrathin Polymer Films

Published on: June 3, 2015

Disjoining pressure for nonuniform thin films.

Bing Dai1, L Gary Leal, Antonio Redondo

  • 1Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

This study derives a new formula for disjoining pressure in nonuniform thin films, accounting for van der Waals forces. The findings extend classical models to complex film geometries, crucial for nanoscale fluid dynamics.

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Published on: July 28, 2020

Area of Science:

  • Fluid dynamics
  • Surface science
  • Colloid and interface science

Background:

  • Van der Waals forces significantly influence thin film dynamics.
  • The concept of disjoining pressure is typically limited to parallel interfaces.
  • Existing models struggle with nonuniform film thicknesses.

Purpose of the Study:

  • To derive a generalized formula for disjoining pressure in nonuniform thin films.
  • To extend the applicability of disjoining pressure to complex film geometries.
  • To incorporate molecular-scale effects into thin film pressure calculations.

Main Methods:

  • Minimization of total Helmholtz free energy for thin films on substrates.
  • Derivation of disjoining pressure formula for nonuniform thickness.
  • Comparison with augmented Young-Laplace equation and classical Lifshitz expression.

Main Results:

  • A novel formula for disjoining pressure in nonuniform films is derived: Pi=-A_{123}(4-3h_{x};{2}+3hh_{xx})/24pih;{3}.
  • The formula reduces to the classical Lifshitz expression for parallel interfaces.
  • The importance of molecular size (steric effects) is highlighted for nanoscale films.

Conclusions:

  • The derived formula accurately describes disjoining pressure in nonuniform thin films.
  • This work provides a more robust theoretical framework for understanding van der Waals forces in complex fluid interfaces.
  • Future applications may require accounting for steric effects in nanoscale film dynamics.