11. Capillary Rise Method — Surface Tension of a Liquid¶
Module
Fluid Properties: Viscosity & Surface Tension · Module 3
Try it live
Explore this on the interactive simulator with real-time sliders and graphs: 🔬 Launch in Simulator
Aim¶
To determine the surface tension of a liquid by measuring the height to which it rises in a capillary tube of known bore.
Theoretical Background¶
The surface of a liquid behaves as though covered by a thin, stretched elastic membrane under tension, because molecules at the surface experience a net inward force from their neighbours below (there being no liquid molecules above to balance the attraction) — this surface tension is what makes small drops nearly spherical and allows some insects to walk on water.
When a narrow glass capillary tube is dipped vertically into a wetting liquid (one that makes an acute contact angle with glass, ideally close to zero, such as water), the liquid surface inside the tube curves into a concave meniscus. The surface tension acting all around the circumference of this curved meniscus produces a net upward force on the liquid column, pulling it up the tube until this force is exactly balanced by the weight of the raised liquid column.
Equating the upward pull (surface tension × circumference × cosine of the contact angle) to the weight of the raised column (cross-sectional area × height × density × g) gives a simple relation between the rise height, the tube's bore, and the surface tension — showing that narrower tubes produce a proportionately greater rise, which is why the effect is called capillarity (from the Latin for 'hair-like').
Because the rise height is inversely proportional to the tube radius, this experiment is most cleanly performed with several capillaries of different, precisely known bores, so that a graph of h against 1/r gives a straight line whose slope directly yields the surface tension, independent of any single, possibly imprecise measurement of r.
Governing Formulas¶
Height of capillary rise (contact angle ≈ 0, fully wetting liquid):
Surface tension:
where \(r\) is the internal radius of the capillary and \(\rho\) the density of the liquid.
Simulator Controls¶
| Control | Symbol | Range | Unit |
|---|---|---|---|
| Capillary radius | r | 0.10 – 1.00 | mm |
| Liquid (density) | ρ | 780 – 1300 | kg/m³ |
Readouts:
| Quantity | Symbol | Unit |
|---|---|---|
| Height of capillary rise | h | cm |
Procedure¶
- Launch the Capillary Rise panel; select a liquid and note its density.
- Vary the capillary radius r over the available range and record the height of rise h shown on the readout for each capillary.
- Plot h against 1/r and verify that the points lie on a straight line through the origin.
- Repeat with a different liquid and compare the slope of the resulting graph.
- Calculate the surface tension T from the slope of the h vs 1/r graph, using the known ρ.
Observation Table¶
Table: Height of capillary rise for capillaries of decreasing bore
| S. No. | r (mm) | 1/r (mm⁻¹) | ρ (kg/m³) | Rise height h (cm) |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 |
Graph¶
Plot Rise height, h (y-axis) against 1/r (x-axis).
Expected trend: a straight line through the origin (h ∝ 1/r).
h vs 1/r, expected to be a straight line through the origin; slope = 2T/ρg
Calculation¶
- Compute the slope of the h vs 1/r graph: slope = 2T/(ρg).
- Rearrange to find T = ρg × slope / 2, using the known ρ.
- Repeat for a second liquid as a cross-check and compare the two computed surface tensions against their expected relative order.
Result¶
Table: Surface tension of the liquid(s) studied
| Liquid | ρ (kg/m³) | Slope (cm·mm) | T (dyne/cm) |
|---|---|---|---|
| 1 | |||
| 2 |
Maximum Permissible Error¶
Both h and r are lengths measured with a travelling microscope, so their combined fractional error is usually small — but the meniscus curvature must be read to the same point (bottom of meniscus) consistently to avoid a systematic bias.
Precautions¶
- Use a clean, grease-free capillary and liquid; even trace contamination changes the contact angle and surface tension significantly.
- Ensure the capillary is held exactly vertical, since any tilt increases the effective rise height along the tube without a corresponding increase in vertical height.
- Read the bottom of the concave meniscus with a travelling microscope, focusing precisely rather than estimating by eye.
Self-Check Quiz¶
1. If the capillary radius r is halved (all else fixed), the height of capillary rise h:
- A) Halves
- B) Doubles
- C) Stays the same
- D) Quadruples
Answer: B — h ∝ 1/r, so halving the radius doubles the rise height — narrower tubes produce proportionately taller rises.
2. Capillary rise occurs because:
- A) The liquid is boiling
- B) Surface tension acting around the curved meniscus produces a net upward force that lifts the liquid column until balanced by its weight
- C) Gravity pulls the liquid upward in narrow tubes
- D) Air pressure inside the tube is higher than outside
Answer: B — The curved surface (meniscus) under tension pulls the liquid up the tube; equilibrium is reached when this pull exactly balances the weight of the raised column.
3. A liquid that does not wet glass (contact angle greater than 90°, such as mercury) will, in a capillary tube, show:
- A) The same rise as water
- B) A depression (fall) below the level outside the tube
- C) No change in level at all
- D) An enormously larger rise than water
Answer: B — For a non-wetting liquid the meniscus curves the opposite way (convex), and the surface-tension force pulls the liquid down inside the tube relative to the level outside — mercury famously shows capillary depression.
Viva-Voce Questions¶
- Why does a wetting liquid rise in a capillary tube while a non-wetting liquid (like mercury) is depressed?
- Derive, in outline, the relation h = 2T/(rρg) by balancing forces on the raised liquid column.
- Why is it advantageous to use several capillaries of different bore and plot h vs 1/r, rather than relying on a single measurement?
- What effect would a greasy or contaminated capillary have on the observed rise, and why?
- How does temperature generally affect the surface tension of a liquid?
- Why must the capillary be held exactly vertical during the measurement?