Surface Tension and Viscosity: Two Properties, One Cause
Both measure intermolecular forces, which is why they usually rise and fall together and why both fall with temperature.
Surface tension
A molecule inside a liquid is surrounded on all sides and its attractions balance. A molecule at the surface has neighbours only below and beside it, so there is a net inward pull. Creating new surface therefore requires work, and surface tension is that work per unit area.
The consequence is that a liquid minimises its surface area, which is why free droplets are spherical — a sphere has the smallest surface for a given volume.
Capillary action
A liquid rises in a narrow tube when it wets the walls, because adhesion to the wall exceeds cohesion within the liquid. The rise continues until the weight of the raised column balances the upward force.
The rise is inversely proportional to the tube radius, so narrower tubes give greater rise. Where the liquid does not wet the walls the contact angle exceeds ninety degrees, the cosine is negative, and the liquid is depressed instead — which is why mercury falls in a glass capillary.
The shape of the meniscus follows from the same comparison: concave where adhesion dominates, convex where cohesion does.
Viscosity
Viscosity measures resistance to flow, and it arises because adjacent layers of liquid moving at different speeds exert drag on one another. Stronger intermolecular forces mean more drag and higher viscosity.
Temperature dependence
Liquid viscosity decreases with temperature, because faster-moving molecules escape one another's attraction more easily. The dependence is approximately exponential, with a form resembling the Arrhenius equation.
Measurement
| Property | Method | Principle |
|---|---|---|
| Surface tension | Capillary rise | Height of rise in a tube of known radius |
| Surface tension | Drop weight | Mass of a drop detaching from a tip |
| Viscosity | Ostwald viscometer | Time for a fixed volume to flow through a capillary |
| Viscosity | Falling sphere | Terminal velocity of a sphere through the liquid |
The Ostwald method is comparative: the flow time is measured for the unknown and for a reference liquid in the same instrument, and the viscosities are in the ratio of the times multiplied by the ratio of densities. Because it is comparative, the instrument dimensions need never be known.
Surfactants
A surfactant has a hydrophilic head and a hydrophobic tail, so it accumulates at the surface with the tail pointing out of the water. This disrupts the surface layer and lowers the surface tension substantially.
Above a certain concentration, adding more surfactant no longer lowers surface tension because the surface is saturated; the additional molecules form micelles in the bulk instead. That concentration is the critical micelle concentration, and it shows as a sharp change of slope in several measured properties plotted against concentration.
Detecting the critical micelle concentration from such a break is a standard experimental question.
Frequently asked questions
Why are droplets spherical?
Because a sphere has the minimum surface area for a given volume, and surface tension drives the liquid to minimise surface area.
Why does mercury fall in a glass capillary rather than rise?
Because cohesion within mercury exceeds adhesion to glass, so the contact angle exceeds ninety degrees and the capillary force acts downward.
Why do gas and liquid viscosity respond oppositely to temperature?
Because the mechanisms differ. Liquid viscosity comes from intermolecular attraction, which weakens on heating; gas viscosity comes from momentum transfer, which increases with molecular speed.
What is the critical micelle concentration?
The concentration above which added surfactant forms micelles rather than accumulating at the surface, because the surface is already saturated.
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