Why does water rise in a capillary tube but mercury falls?

The sign of the rise is set by the angle of contact θ through cos θ in h = 2S cosθ/(ρgr). Water wets glass, so θ is acute (cos θ positive) and the meniscus is concave — water rises. Mercury does not wet glass, so θ is obtuse (about 140°, cos θ negative) and the meniscus is convex — mercury is pushed down below the outside level, a capillary depression.

Does capillary rise depend on the radius of the tube?

Yes. The rise is inversely proportional to the tube radius, h ∝ 1/r, because h = 2S cosθ/(ρgr). Halving the bore doubles the rise; a hair-thin tube gives a very large rise. This is why thin xylem vessels and the fine pores of blotting paper lift water effectively.

What happens if the capillary tube is shorter than the calculated rise?

The liquid does not overflow or fountain out of the top. Once the column reaches the open end it can rise no further, so the radius of curvature of the meniscus increases (the meniscus flattens) until 2S cosθ/R balances the available column height. The product hR stays constant; only R adjusts. Liquid spilling from a short capillary is a classic NEET distractor.

Is capillary action caused by surface tension or by adhesion?

Both, working together. Adhesion versus cohesion fixes the angle of contact and hence whether the meniscus is concave or convex. Surface tension acting across the curved meniscus then creates the pressure difference 2S cosθ/r that drives the column up or down. NCERT states the rise is 'due to surface tension'; the angle of contact only decides its direction and size.

How does kerosene rise in a lantern wick?

The wick is a bundle of fine fibres with countless narrow channels between them, acting as a mesh of capillaries. Kerosene wets the fibres (small angle of contact), so by capillary action it climbs the channels against gravity and feeds the flame continuously. The same mechanism lifts water through soil, cloth and the stems of plants.

Why does capillary rise decrease as temperature increases?

Surface tension S falls as temperature rises, and since h = 2S cosθ/(ρgr), a smaller S gives a smaller rise. The density ρ also drops slightly with temperature, but the dominant effect is the fall in surface tension, so warm liquids climb less than cold ones in the same tube.

Capillary Action — NEET Physics

What capillarity is

When a tube of very small bore — a capillary, from the Latin capilla meaning hair — is dipped into a liquid, the liquid level inside the tube settles either above or below the level outside. NCERT and NIOS both define the phenomenon plainly: the rise or depression of a liquid in an open tube of small cross-section is capillary action, or capillarity. Water in glass rises; mercury in glass falls. The narrower the tube, the larger the effect.

The cause is not a new force. It is surface tension acting across the curved liquid surface inside the tube. A curved interface carries a pressure difference between its two sides, and that pressure difference is what drives the liquid column up or holds it down. Everything in this topic follows from one equation for the meniscus and one balance of pressures.

Capillary rise of water. Water wets glass, the angle of contact θ is acute, the meniscus is concave, and the column rises a height $h$ above the outside level. (After NCERT Fig. 9.19.)

Angle of contact and the meniscus

The angle of contact $\theta$ is the angle between the tangent to the liquid surface at the point of contact and the solid wall, measured inside the liquid (NCERT §9.6.3). It is fixed by the competition between cohesion (liquid–liquid attraction) and adhesion (liquid–solid attraction), and it decides the shape of the meniscus.

When adhesion dominates, the liquid wets the wall, climbs slightly at the edges, and the meniscus is concave with an acute $\theta$ — this is water on clean glass. When cohesion dominates, the liquid pulls away from the wall, the meniscus is convex, and $\theta$ is obtuse — this is mercury on glass, near $140^\circ$. The two regimes set the two outcomes of capillarity.

Liquid–solid pair	Dominant force	Angle of contact $\theta$	Meniscus	Effect in capillary
Water on clean glass	Adhesion > cohesion	Acute (near $0^\circ$ for very clean glass)	Concave	Rise
Kerosene / detergent water	Strong adhesion	Small acute	Concave	Strong rise (wets, spreads)
Pure water on waxy leaf	Cohesion > adhesion	Obtuse	Convex (beads up)	Does not wet
Mercury on glass	Cohesion > adhesion	Obtuse ($\approx 140^\circ$)	Convex	Depression (fall)

This is why wetting agents such as soaps and detergents lower the angle of contact: a smaller $\theta$ lets the liquid penetrate fibres and fine pores, while water-proofing agents do the opposite, raising $\theta$ so water beads off the surface (NCERT §9.6.3).

Jurin's law — the ascent formula

Consider a vertical capillary of internal radius $r$ dipped in a liquid of surface tension $S$, density $\rho$, and angle of contact $\theta$. The meniscus is a section of a sphere of radius $R$, and simple geometry gives $R = r/\cos\theta$. The pressure just below a concave meniscus is less than the pressure just above it by

$$ (P_i - P_o) = \frac{2S}{R} = \frac{2S\cos\theta}{r}. $$

Take two points at the same horizontal level: A just below the meniscus inside the tube and B on the free surface outside (NCERT §9.6.5). Points at the same level in a connected liquid must be at the same pressure, so the deficit below the meniscus is made up by a column of liquid of height $h$:

$$ h\,\rho g = (P_i - P_o) = \frac{2S\cos\theta}{r}. $$

Rearranging gives the ascent formula, also called Jurin's law:

$$ \boxed{\,h = \dfrac{2S\cos\theta}{\rho g r}\,} $$

Reading the formula

Each symbol pulls the rise in a definite direction. $h$ grows with the surface tension $S$ and with $\cos\theta$ (wetting), and shrinks as the density $\rho$, gravity $g$, and radius $r$ increase. The sign of $h$ is carried entirely by $\cos\theta$.

Factor	Effect on rise $h$	Reason
Surface tension $S$ ↑	$h$ increases ($h \propto S$)	Larger tension pulls a taller column
Angle of contact $\theta$ ↑	$h$ decreases ($\propto \cos\theta$); negative past $90^\circ$	Less wetting; obtuse $\theta$ flips sign to depression
Radius $r$ ↑	$h$ decreases ($h \propto 1/r$)	Wider bore, smaller pressure deficit
Density $\rho$ ↑	$h$ decreases ($h \propto 1/\rho$)	Heavier column for the same support
Temperature ↑	$h$ decreases	$S$ falls as temperature rises

NCERT notes the rise is "due to surface tension" and "is larger for a smaller $a$". For a fine capillary it is of the order of a few centimetres — using $S = 0.073~\text{N m}^{-1}$, $r = 0.05~\text{cm}$, $\theta \approx 0$, the formula returns $h \approx 2.98~\text{cm}$.

Rise versus depression

The single formula $h = \tfrac{2S\cos\theta}{\rho g r}$ covers both behaviours. Only the angle of contact changes. The two cases stand side by side below.

	Capillary rise (water)	Capillary depression (mercury)
Wetting	Liquid wets glass	Liquid does not wet glass
Angle of contact $\theta$	Acute ($\theta < 90^\circ$)	Obtuse ($\theta > 90^\circ$)
$\cos\theta$	Positive	Negative
Meniscus	Concave	Convex
Pressure below meniscus	Below atmospheric	Above atmospheric
Result	$h > 0$: liquid climbs	$h < 0$: liquid is pushed down

Capillary depression of mercury. Mercury does not wet glass, the angle of contact is obtuse, the meniscus is convex, and the column is pushed below the outside level by a depth $h$. With $\cos\theta < 0$ the ascent formula gives a negative $h$.

Why rise goes as 1/r

Of all the dependences in the ascent formula, NEET tests $h \propto 1/r$ most often. For a fixed liquid and tube material, $S$, $\theta$, $\rho$ and $g$ are constant, so

$$ h \propto \frac{1}{r} \qquad \Longrightarrow \qquad h_1 r_1 = h_2 r_2 = \text{constant}. $$

Halve the bore and the rise doubles; a hair-thin capillary lifts water a long way. There is a second, equally testable consequence. The mass of liquid raised is the weight supported by surface tension, and it scales the opposite way.

Force balance picture of $h \propto 1/r$. The upward pull $2\pi r S\cos\theta$ supports the column weight $\pi r^2 h \rho g$; equating gives $h = \tfrac{2S\cos\theta}{\rho g r}$, so doubling the radius halves the rise.

The weight of the supported column is $W = (\pi r^2 h)\rho g$. Substituting $h \propto 1/r$ gives $W \propto r$: the mass raised is directly proportional to the radius even though the height falls. Double the radius and the column is half as tall but holds twice the mass — exactly the NEET 2020 question solved below.

Worked example

Worked Example

A glass capillary of internal radius $0.2~\text{mm}$ is dipped vertically in water. Take surface tension $S = 0.072~\text{N m}^{-1}$, angle of contact $\theta = 0^\circ$, density $\rho = 1000~\text{kg m}^{-3}$ and $g = 10~\text{m s}^{-2}$. Find the height to which water rises.

Apply the ascent formula. With $\cos 0^\circ = 1$,

$$ h = \frac{2S\cos\theta}{\rho g r} = \frac{2 \times 0.072 \times 1}{1000 \times 10 \times 0.2\times10^{-3}}. $$

Evaluate. Numerator $= 0.144$. Denominator $= 1000 \times 10 \times 2\times10^{-4} = 2$. So $h = 0.144 / 2 = 0.072~\text{m} = 7.2~\text{cm}$.

Sanity check. A finer bore would lift water higher ($h\propto 1/r$); a wetting agent that keeps $\theta$ near zero keeps $\cos\theta\approx1$ and the rise maximal. If the same tube were dipped in mercury ($\theta\approx140^\circ$, $\rho\approx13600$), $\cos\theta$ turns negative and $h$ comes out negative — a depression of a few millimetres.

Foundation

The pressure-across-a-meniscus idea comes straight from surface tension and excess pressure — review it if the $2S/R$ term is unfamiliar.

Everyday and biological capillarity

Capillary action is one of the most visible surface-tension effects in nature. Wherever a wetting liquid meets a mesh of fine channels, it climbs.

Water in plants. Soil water rises through the innumerable narrow capillaries in the stems of plants and trees and reaches the branches and leaves (NIOS §9.6). The fine xylem vessels give a small $r$ and hence a large rise.
Blotting paper and cloth. Ink rises into the narrow air gaps of blotting paper, and water creeps up a wet cloth, both by capillary rise through fine pores.
The lamp wick. Kerosene wets the fibres of a lantern wick and climbs the capillary channels between them to feed the flame continuously.
Soil and farming. Farmers plough fields after rain to break the surface capillaries; this traps water in the soil instead of letting capillarity carry it to the surface to evaporate.
Mercury in a barometer. Because mercury depresses, a true mercury level reading must be corrected for the capillary fall in a narrow barometer tube.

Quick recap

Capillarity in one breath

Capillary action is the rise or depression of a liquid in a fine tube, caused by surface tension across a curved meniscus.
Ascent formula (Jurin's law): $h = \dfrac{2S\cos\theta}{\rho g r}$.
Acute $\theta$ (water, $\cos\theta>0$) gives a concave meniscus and a rise; obtuse $\theta$ (mercury, $\cos\theta<0$) gives a convex meniscus and a depression.
Rise is inversely proportional to radius, $h\propto 1/r$; the mass of liquid raised is proportional to radius, $m\propto r$.
A tube shorter than the calculated rise does not overflow — the meniscus flattens ($R$ increases) to balance.
Examples: water in plant stems, ink in blotting paper, kerosene in a wick; mercury depression in a barometer.

Factor	Effect on rise \(h\)	Reason
Surface tension \(S\) ↑	\(h\) increases (\(h \propto S\))	Larger tension pulls a taller column
Angle of contact \(\theta\) ↑	\(h\) decreases (\(\propto \cos\theta\)); negative past \(90^\circ\)	Less wetting; obtuse \(\theta\) flips sign to depression
Radius \(r\) ↑	\(h\) decreases (\(h \propto 1/r\))	Wider bore, smaller pressure deficit
Density \(\rho\) ↑	\(h\) decreases (\(h \propto 1/\rho\))	Heavier column for the same support
Temperature ↑	\(h\) decreases	\(S\) falls as temperature rises

Capillary Action