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Related Concept Videos

Conditions of Equilibrium01:28

Conditions of Equilibrium

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Equilibrium refers to a state where a rigid body is not subjected to any translational or rotational motion. This state is achieved when the force and couple acting on a rigid body equal zero. When the system of external forces results in a net effect equivalent to zero, the rigid body is considered to be in equilibrium.
Internal forces are not considered for conditions of equilibrium because they occur in equal and opposite pairs within the body, effectively canceling each other. As a result,...
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Dynamic Equilibrium02:20

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Free Energy and Equilibrium02:56

Free Energy and Equilibrium

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The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
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Equilibrium Conditions for a Particle01:23

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
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Calculating the Equilibrium Constant02:46

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The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
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Measurement of the Rheology of Crude Oil in Equilibrium with CO2 at Reservoir Conditions
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Measurement of the Rheology of Crude Oil in Equilibrium with CO2 at Reservoir Conditions

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Equilibrium Droplets on Deformable Substrates: Equilibrium Conditions.

Nektaria Koursari1, Gulraiz Ahmed2, Victor M Starov1

  • 1Department of Chemical Engineering , Loughborough University , Loughborough , Leicestershire LE11 3TU , U.K.

Langmuir : the ACS Journal of Surfaces and Colloids
|April 21, 2018
PubMed
Summary
This summary is machine-generated.

This study verifies Jacobi's condition for droplet equilibrium on deformable substrates, proving that derived profiles minimize excess free energy. This ensures accurate modeling of droplet-substrate systems.

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Area of Science:

  • Physics
  • Materials Science
  • Surface Science

Background:

  • Droplet behavior on deformable substrates is crucial in various applications.
  • Previous models often lacked rigorous proof of equilibrium stability.
  • Ensuring minimum excess free energy is key for true equilibrium.

Purpose of the Study:

  • To rigorously verify equilibrium conditions for droplets on deformable substrates.
  • To confirm that derived profiles represent a true minimum of excess free energy.
  • To validate the application of Jacobi's sufficient condition in such systems.

Main Methods:

  • Investigation of equilibrium conditions using Jacobi's sufficient condition.
  • Analysis of necessary conditions: vanishing first variation and positive second variation of free energy.
  • Application to a simplified model with linear disjoining/conjoining pressure.

Main Results:

  • The deduced droplet and substrate profiles satisfy Jacobi's condition.
  • For the first time, the validity of Jacobi's condition is demonstrated for droplet-substrate equilibrium.
  • The results confirm a true minimum of excess free energy for the system.

Conclusions:

  • The developed model accurately predicts equilibrium droplet profiles on deformable substrates.
  • Jacobi's condition provides a robust verification of thermodynamic equilibrium.
  • This work sets a precedent for validating equilibrium models in surface science.