Curved surfaces The minimization of the surface area of a liquid may result in the formation of a curved surface,as in a bubble.We shall now see that there are two consequences of curvature,and hence of the surface tension,that are relevant to the properties of liquids. One is that the vapour pressure of a liquid depends on the curvature of its surface.The other is the capillary rise (or fall)of liquids in narrow tubes. PDF文件使用"pdfFactory Pro”试用版本创建fm,fineprint.com,cn
Curved surfaces The minimization of the surface area of a liquid may result in the formation of a curved surface, as in a bubble. We shall now see that there are two consequences of curvature, and hence of the surface tension, that are relevant to the properties of liquids. One is that the vapour pressure of a liquid depends on the curvature of its surface. The other is the capillary rise (or fall) of liquids in narrow tubes. PDF 文件使用 "pdfFactory Pro" 试用版本创建 fwww.fineprint.com.cn
Laplace equation △P=Pin-Pout Protruding surface:AP>0 Concave surface:△P<o p 液 液 PDF文件使用"pdfFactory Pro”试用版本创建m,fineprint.com,cn
Laplace equation DP=Pin-Pout Protruding surface: DP>0 Concave surface: DP<0 PDF 文件使用 "pdfFactory Pro" 试用版本创建 ÿwww.fineprint.com.cn Ì
Laplace equation △P=2yr This simple relation is the Laplace equation.r is the radius of curvature. The Laplace equation shows that the difference in pressure decreases to zero as the radius of curvature becomes infinite.Small cavities have small radii of curvature,so the pressure difference across their surface is quite large. PDF文件使用"pdfFactory Pro”试用版本创建fm,fineprint.com,cn
DP=2γ/r Laplace equation This simple relation is the Laplace equation. r is the radius of curvature. The Laplace equation shows that the difference in pressure decreases to zero as the radius of curvature becomes infinite.Small cavities have small radii of curvature, so the pressure difference across their surface is quite large. PDF 文件使用 "pdfFactory Pro" 试用版本创建 ÿwww.fineprint.com.cn f
Discussion .Protruding surface r>0 AP=Pin-Pout=2y/r>0 .Concave surface r<0 AP=Pin-Pout=2y/r<0 Flat surface r=o△P=0 .Bubbles in the air have two surfaces (one on each side of the film),so,AP=4y/r The direction of AP always point at the center of curved surface. PDF文件使用"pdfFactory Pro”试用版本创建酸能.fineprint.com.cn
Discussion •Protruding surface r>0 DP=Pin-Pout=2γ/r>0 •Concave surface r<0 DP=Pin-Pout=2γ/r<0 •Flat surface r=¥ DP=0 •Bubbles in the air have two surfaces (one on each side of the film) , so, DP=4γ/r The direction of DP always point at the center of curved surface. PDF 文件使用 "pdfFactory Pro" 试用版本创建 駿ÿ www.fineprint.com.cn