Related Experiment Video
Updated: Feb 22, 2026
11:51
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
9.2K
Motion of a Rigid Cylinder Between Parallel Plates in Stokes Flow: Part 1: Motion in A Quiescent Fluid and
1Creare Inc., P.O. Box 71, Hanover, NH 03755, U.S.A.
Computers & Fluids
|September 26, 2017
Summary
This study models rigid circular cylinder motion in a channel using a numerical scheme for Stokes equations. It reveals unique force and velocity patterns for particles, differing from spherical counterparts.
Area of Science:
- Fluid dynamics
- Computational mechanics
- Rheology
Background:
- Stokes flow in confined geometries is crucial for microfluidics and biomechanics.
- Understanding particle motion near boundaries requires advanced numerical methods.
- Previous models often simplify particle shape or boundary conditions.
Purpose of the Study:
- To apply a general numerical scheme to solve 2D Stokes equations for a circular cylinder between parallel boundaries.
- To calculate the resistance matrix coefficients for cylinder motion (translation and rotation).
- To analyze the translational and angular velocities of a free-settling cylinder under gravity.
Main Methods:
- Utilized numerically generated boundary-conforming coordinates to simplify the flow domain.
- Solved transformed Stokes equations in vorticity-stream function form on a uniform grid.
- Employed an iterative algorithm to compute forces, torques, and velocities.
Main Results:
- Calculated resistance matrix coefficients for various cylinder radii and positions.
- Identified a force minimum between the centerline and wall, and a maximum on the centerline for parallel translation.
- Observed distinct translational and angular velocity profiles for settling cylinders, differing from rolling particles.
Conclusions:
- Cylindrical particle behavior in a channel differs qualitatively from spherical particles due to distinct flow patterns.
- The motion of a spherical particle in a tube shares similarities with a cylinder in a plane channel.
- The numerical scheme provides accurate solutions for complex Stokes flow problems involving confined particles.
Related Concept Videos
01:17Steady, Laminar Flow Between Parallel Plates
915
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.
915
01:23Steady, Laminar Flow in Circular Tubes
1.2K
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
1.2K
01:22Couette Flow
1.2K
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
1.2K
01:20Stokes' Law
3.0K
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
3.0K
01:02Fluid Pressure over Flat Plate of Variable Width
2.2K
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...
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...
2.2K
01:28Navier–Stokes Equations
2.4K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.4K