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Related Concept Videos

Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
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...
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.
Viscosity of Fluid01:19

Viscosity of Fluid

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.
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...
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...

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Variable thickness model for fluid films under large displacement.

Pavel Grinfeld1

  • 1Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19105, USA.

Physical Review Letters
|January 15, 2011
PubMed
Summary

This study introduces dynamic nonlinear equations for thin fluid films, revealing dynamic thickening phenomena consistent with experimental observations under large deformations. The findings highlight the role of internal energy functions in capturing diverse fluid film behaviors.

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Area of Science:

  • Fluid dynamics
  • Nonlinear physics
  • Materials science

Background:

  • Understanding the behavior of thin fluid films under large deformations is crucial for various scientific and engineering applications.
  • Existing models may not fully capture the complex dynamic phenomena observed in experiments.

Purpose of the Study:

  • To develop and analyze dynamic nonlinear equations for free thin fluid films.
  • To explain experimental observations, such as dynamic thickening, in fluid films undergoing large deformations.

Main Methods:

  • Formulation of a two-dimensional model for thin fluid films.
  • Representation of film thickness using two-dimensional density (ρ).
  • Numerical solutions of the derived dynamic nonlinear equations.

Main Results:

  • The numerical solutions exhibit features consistent with experimental data for fluid films under large deformations.
  • Dynamic thickening was observed in the simulations.
  • Demonstration that a suitable internal energy function e(ρ) can capture a wide range of effects.

Conclusions:

  • The proposed dynamic nonlinear equations provide a robust framework for studying thin fluid films.
  • The model successfully explains dynamic thickening and other complex behaviors.
  • Internal energy functions are key to accurately modeling diverse fluid film dynamics.