Physics · Ch 7 — Properties of Matter
Surface Tension by capillary rise method
Surface Tension by capillary rise method
SURFACE TENSION BY THE CAPILLARY RISE METHOD. The fundamental cause of a liquid rising up a narrow tube is the pressure difference across the curved liquid-air interface (the influence of gravity on the shape of that interface itself is ignored); this capillary rise is more pronounced the finer the tube. Consider a capillary tube of radius r held vertically in a beaker of water, with the water risen to a height h inside the tube above the level outside. The surface-tension force acts along the tangent to the curved meniscus at the point of contact with the tube's wall, all around the circle of contact; resolving this force into a horizontal component (which cancels around the full circle) and a vertical component (which acts upward all the way around the circumference ), the TOTAL upward force supporting the raised liquid column is . This upward force must support the WEIGHT of the liquid column of height h that has risen inside the tube (for a very fine tube, the small extra volume in the curved meniscus at the top can be neglected compared to the volume of the cylindrical column below it): . Solving for T gives the SURFACE TENSION BY CAPILLARY RISE: . Equivalently, solving fo …
What this figure shows. A capillary tube of radius r held vertically in a beaker of liquid shows the liquid risen to height h inside the narrow tube above the liquid level in the beaker, with a curved meniscus (concave, contact angle theta) at the top of the risen column. The surface-tension force T acts along the tangent to the meniscus at the wall of the tube, all around its circumference, and is resolved into a horizontal component T sin(theta) and a vertical component T cos(theta) that acts upward all around the circle of contact -- summing this vertical component around the full circumference (2pir) gives the total upwa …
Worked out. Water rises to a height of 2.0 cm in a given capillary tube; using the inverse proportionality h times r = constant, a second capillary tube with one-third the radius of the first is shown to give a water rise of 6.0 x 10^-2 m (6 cm), a direct numerical illustration that halving or thirding the bore of a capillary triples or otherwise scales up the height the liquid …
Worked out. Mercury has an angle of contact of 140 degrees with soda-lime glass; for a narrow glass capillary of radius 2 mm, using the surface tension of mercury (T = 0.456 N per metre) and its density (13.6 x 10^3 kg per cubic metre) in the capillary-rise formula with cos(140 degrees) approximately -0.766 gives a NEGATIVE height of about -2.62 x 10^-3 m, confirming that mercury is depressed (pushed down) inside the glass capillary rather than rising, exactly as expec …