88.2 Surface phenomenon of liquid Out-class reading Levine p. 387-390 13.2 Curved interfaces
§8.2 Surface phenomenon of liquid Out-class reading: Levine p. 387-390 13.2 Curved interfaces
88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure l Curved liquid surface drop Convex surface Concave surfa In graduated cylinder
8.2.2 Curved surface and additional pressure drop 1. Curved liquid surface In graduated cylinder Convex surface Concave surface §8.2 Surface phenomenon of liquid
88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure Convex surface Concave surface pex Pe ex pin=pex + Ap Pin=pax+△p Ap additional pressure For convex surface: Ap>0 For concave surface: Ap <0
p additional pressure Convex surface Concave surface For convex surface: p>0 For concave surface: p < 0 p p p in ex = + pex 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid
88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure Pm=P+△n(4p+c)ld=odA A=4r ex Ap= o8Ttrdr 2o 20 To increase the volume(dn of liquid at p Ap Laplace equation Ap+ dp
( ) p dp dV dA + = pex p p p in ex = +Δ To increase the volume (dV) of liquid at pex = p + dp dA p dV = 3 3 4 V = r 2 A = 4r 2 p r = 2 8 2 4 rdr p r dr r = = Laplace equation pin 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid
88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure For curved surface: 20 Ap p- For convex surface, r>0, Ap>0, point to Laplace-Young equation the interior of liquid; ris the radius of curvature For concave surface, 0, Ap <0, point to the gaseous phase; For plane e surface, r-)00, 4→0,Pax=Pin
1 2 1 1 p r r = + For curved surface: Laplace-Young equation r is the radius of curvature. For convex surface, r > 0, p > 0, point to the interior of liquid; For concave surface, r<0, p < 0, point to the gaseous phase; For plane surface, r →, p → 0, pex = pin, 2 p r = 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid