Lecture.Packet.4.Wetting - CEE 440 © 2011 Charles J Werth...

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Unformatted text preview: CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 1 3.3 INTERFACIAL TENSION, CONTACT ANGLE, AND DENSITY Interfacial tension ( γ ab , a is one phase and b is another) can be thought of as the force per unit length (or energy per unit area) acting at a liquid- liquid or liquid-solid interface. Interfacial tension - arises because of unbalanced cohesional forces on molecules at the interface. The tension causes the interface between the two fluids to contract and form an area that is as small as possible. If one phase is liquid and the other vapor, then we use the term surface tension denoted by γ . e.g. Water bugs, rain drops, Goretex, oil slick CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 2 Consider a soap film stretched across a wire frame with one movable side. The work done in extending the movable member dx is: L Work = Δ E = γ dA= γ L dx (3.58) Δ E = change in energy γ = surface tension (force/length = N/m; energy/area = J/m 2 ) L = length (m) dA = change in area (m 2 ) dx = change in length CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 3 Alternatively we could think of an expanding soap bubble: The free energy of the soap bubble surface is initially: If the radius of the soap bubble is increased by dR, then the final free energy is: R dR the surface tension of the soap film results in stable, spherical bubble E init = ______ γ (3.59) E final = 4 π (R+dR) 2 γ (3.60) 4 π R 2 CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 4 It follows that the change in surface free energy or the work required to expand the soap bubble is: Since increasing the soap bubble radius increases the surface free energy, the tendency to do so must be balanced by a pressure difference across the film Δ P. Hence, fluid on the concave side of the interface (i.e., inside the soap bubble) is at a higher pressure. Work = Δ E = E final – E init = (4 π γ R 2 + 8 π γ R dR + 4 π γ dR 2 ) – 4 π γ R 2 (3.61) Δ E = 8 π γ R dR + 4 π γ dR 2 (3.62) ~ 8 π γ R dR CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 5 The work against this pressure difference is given as follows: This work equals the work required to expand the bubble by dR. So as the bubble gets larger the pressure difference decreases and vice versa. This example also demonstrates that interfacial tension results in curved surfaces between phases. Work = Δ E = Δ P * Area * Distance Distance = R final – R init = R + dR – R = dR (3.63) Δ E = Δ P 4 π R 2 dR (3.64) Δ P 4 π R 2 dR = 8 π γ R dR (3.65) Rearranging: Δ P = 2 γ / R (Young-Laplace Equation) (3.66) CEE 440 © 2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved. 6 Consider the following configuration: What happens when valve 1 and valve 2 are...
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Lecture.Packet.4.Wetting - CEE 440 © 2011 Charles J Werth...

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