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Related Concept Videos

Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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,...
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...
Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
Poiseuille's Law and Reynolds Number01:10

Poiseuille's Law and Reynolds Number

Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:

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High Speed Droplet-based Delivery System for Passive Pumping in Microfluidic Devices
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Published on: September 2, 2009

Directed flow in nonadiabatic stochastic pumps.

Saar Rahav1, Jordan Horowitz, Christopher Jarzynski

  • 1Department of Chemistry, University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|October 15, 2008
PubMed
Summary

This study reveals how molecular machines operate using nonadiabatic parameter changes. A "no-pumping theorem" is derived for cyclic processes, with adiabatic limits yielding geometric expressions for pumped current.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Molecular Machines

Background:

  • Molecular machines are nanoscale devices that perform mechanical work.
  • Their operation can be influenced by external parameters and thermodynamic processes.
  • Understanding nonadiabatic variations is crucial for efficient molecular machine function.

Purpose of the Study:

  • To analyze the operational principles of molecular machines driven by nonadiabatic parameter variations.
  • To derive a formula for integrated flow between configurations.
  • To establish a
  • no-pumping theorem
  • for cyclic processes and explore adiabatic limits.

Main Methods:

  • Analysis of nonadiabatic dynamics in molecular systems.

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  • Derivation of a general formula for integrated flow.
  • Application of statistical mechanics to thermally activated transitions.
  • Investigation of the adiabatic limit for pumped current.

    • Main Results:

    • A formula for integrated flow between molecular configurations was derived.
    • A
    • no-pumping theorem
    • was established for cyclic processes involving thermally activated transitions.
    • In the adiabatic limit, the pumped current was shown to be a geometric expression.

    Conclusions:

    • Nonadiabatic parameter variations are key to molecular machine operation.
    • The derived
    • no-pumping theorem
    • provides fundamental insights into cyclic processes.
    • Geometric expressions accurately describe pumped current in the adiabatic limit, offering design principles for molecular devices.