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surfaceTensionV2

# surfaceTensionV2 - MECH 314 Introduction to Fluid Mechanics...

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MECH 314 Introduction to Fluid Mechanics February 19, 2009 American University of Beirut, Spring 2009 Handout # 3 Surface Tension (version 0) Surface tension gives rise to various familiar phenomena in liquid behavior such as the formation and rise of soap bubbles, liquid level in a capillary tube rising above that of the pool in which the tube is placed, the breakup of a jet of water into droplets. Surface tension physics is currently being employed in some very exciting technologies such as ink jet printing and drug delivery. What gives rise to surface tension? Whenever there is an interface between a liquid and a gas or a liquid and a solid, the liquid atoms close the interface experience uneven attractive forces. For example, in a liquid-gas interface shown in Figure 1, the liquid molecules at the interface experiences stronger attractive forces from the liquid molecules neighboring them that from neighboring gas molecules. As a result the liquid molecules at the interface are attracted inward and normal to the interface. This uneven force distribution causes the interface to experience tension and the surface of the liquid behaves as if it were in tension like a stretched membrane. Gas Liquid Figure 1: Attractive forces on molecules in the liquid interior and at the liquid-gas inter- face. From energy consideration, the liquid molecules near the surface have higher energy than those in the interior since work must be done to bring a molecule from the interior to the surface. Since the free energy of a system always tends to a minimum, the interface must tend to a minimum, i.e. contract. For a system that is capable of undergoing pressure-volume work and surface tension- interface area work, Gibb’s equation is dE = T dS - p dV + γ dA (1) 1

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where surface tension, γ , is defined as γ = " ∂E ∂A # S,V and A is the interface area. Surface tension, having the units of force per unit length (or energy per unit area) may also be defined in terms of the change in Helmholtz free energy with the interface area. If the system is kept at constant temperature, volume, and interface area, then Δ E = Q , which together with the second law Δ S Q T , results in Δ E - T Δ S 0 So for systems kept at constant temperature, volume, and interface area, the quantity H E - TS , called the Helmholtz free energy , obeys the inequality Δ H 0 stating that the Helmoltz free energy for such systems decreases (for irreversible process), or stays the same (for reversible process). Combining H E - TS and Gibbs equation (1), one gets dH = dE - T dS - S dT = - S dT - p dV + γ dA leading to γ = " ∂H ∂A # T,V stating that the surface tension, for constant temperature and volume, is the change in Helmholtz free energy resulting form an infinitesimal change in interface area. Note that
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surfaceTensionV2 - MECH 314 Introduction to Fluid Mechanics...

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