Effective viscosity of dilute bacterial suspensions: a two-dimensional model
Brian M Haines1, Igor S Aronson, Leonid Berlyand
1Department of Mathematics, Pennsylvania State University, 418 McAllister Building, University Park, PA 16802, USA.
Physical Biology
|November 26, 2008
Summary
This study explores suspensions of self-propelled particles in 2D hydrodynamics. Researchers derived a formula for effective viscosity, including a new term explaining reduced viscosity in active suspensions.
Area of Science:
- Fluid dynamics
- Soft matter physics
- Statistical mechanics
Background:
- Understanding the rheology of active matter is crucial.
- Previous models for passive suspensions do not fully explain active systems.
Purpose of the Study:
- To develop a theoretical framework for the effective viscosity of active suspensions.
- To identify the contribution of self-propulsion to suspension rheology.
Main Methods:
- Utilizing two-dimensional (2D) Stokesean hydrodynamics.
- Deriving analytical formulas for effective viscosity at low concentrations.
Main Results:
- Obtained a formula for effective viscosity including Einstein's terms for passive suspensions.
- Introduced a novel term dependent on particle properties, explaining decreased viscosity in active systems.
Conclusions:
- Self-propulsion significantly alters the effective viscosity of suspensions.
- The derived formula accurately predicts experimental observations of reduced viscosity in active suspensions.
Related Concept Videos
01:27Viscosity
Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.Newton's law of viscosity states that the viscous force on a faster-moving...
01:17Viscosity
When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
The SI unit of viscosity is...
The SI unit of viscosity is...
01:19Viscosity 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.
01:30Typical 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.
01:20Stokes' 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 for low Reynolds...
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...
01:09Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...