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Stokes' Law

Stokes' Law

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...

Colloids and Suspensions

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Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles visible to the naked eye or seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. The suspended particles in a suspension settle out after some time of mixing. The separation of particles from a suspension is...

Colloids

Colloids

Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles that are visible to the naked eye or can be seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. On the other hand, a solution is a homogeneous mixture in which no settling occurs and in which the dissolved...

Newtonian Fluid: Problem Solving

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...

Steady, Laminar Flow Between Parallel Plates

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 Fluid

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.

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Related Experiment Video

Updated: Dec 9, 2025

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Orientation dependent Stokes drag in a colloidal liquid crystal.

A A Verhoeff¹, J van Rijssel¹, V W A de Villeneuve¹

¹Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands. a.a.verhoeff@uu.nl.

|September 10, 2020

Summary

Researchers measured direction-dependent Stokes drag in colloidal rod liquid crystals. They found drag along the director is twice that perpendicular, revealing unique viscoelastic properties.

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Area of Science:

Physics
Materials Science
Colloid Science

Background:

Stokes drag is crucial for microscale phenomena like Brownian motion and suspension rheology.
Nematic liquid crystals exhibit complex viscoelastic behavior due to viscous and elastic forces.

Purpose of the Study:

To measure the direction-dependent Stokes drag on a sphere in a nematic liquid crystal of colloidal rods.
To investigate the influence of director orientation on drag forces in this unique material system.

Main Methods:

Utilized combined fluorescence confocal microscopy and polarization microscopy to track a sedimenting sphere.
Quantified the drag experienced by the sphere as it moved parallel and perpendicular to the director.

Main Results:

The Stokes drag for motion parallel to the director was found to be twice as large as for motion perpendicular to the director.
This anisotropy in drag highlights the significant role of the liquid crystal's structure.

Conclusions:

The study provides the first measurement of direction-dependent Stokes drag in a colloidal liquid crystal.
The findings underscore the interplay between viscous and elastic forces, revealing the distinct viscoelastic properties of these materials.