Comparison of capillary rise on Cosmic bodies

COMPARISON OF CAPILLARY RISE ON COSMIC BODIES

INTRODUCTION

Capillarity or capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces. When a capillary tube is inserted into a beaker containing liquid, the level of liquid in the capillary tend to rise or fall depending on the angle of contact between liquid and the tube wall. We intend to study only the rise of liquid in a capillary tube. Since the liquid rises against gravity, the extent to which it can rise also directly depends on the local acceleration due to gravity. We thus intend to compare the capillary rise on each cosmic body such as the Moon, Earth, Jupiter, Sun and Neutron Star.

ASSUMPTIONS

1. The local acceleration due to gravity is constant and not varying continuously

2. The angle of contact is always acute

3. The liquid is free from impurities

4. Temperature of the liquid is constant

5. The capillary is indestructible

6. Space time distortion does not impede capillary motion

CALCULATION

Consider a liquid [pure water] of density ‘ρ’ in a glass beaker with an inverted glass capillary tube inserted in a beaker as shown in figure.1. Let ‘r’ be the radius of the capillary tube, ‘θ’ be the angle of contact between pure water and the wall of capillary tube and ‘T’ be the surface tension of water.

The equation for capillary rise ‘h’ in the tube is given by,

h – Capillary rise in the tube (m)

T – Surface tension of water [T = 7.28*10^-2 N/m]

θ – Angle of contact between pure water and glass tube [θ = 0°]

ρ – Density of water [ρ = 1000 Kg/m³]

r – Radius of capillary tube [r = 1.5 *10^-3 m]

g – Acceleration due to gravity on a cosmic body [m/s²]

As discussed in the previous posts, the capillary rise of water is different for each planet or star since the rise is inversely proportional to the acceleration due to gravity. The capillary rise of water on each cosmic body is given in table.1

	COSMIC BODY	CAPILLARY RISE [m]
1	Moon	5.99E-02
2	Earth	9.90E-03
3	Jupiter	3.96E-03
4	Sun	3.55E-04
5	Neutron Star	1.39E-14

            Table.1 Capillary rise of water on each cosmic body

GRAPH

The acceleration due to gravity is plotted against the capillary rise on each cosmic body:

This graph allows us to study the effect of acceleration due to gravity on the capillary rise in each cosmic body. The maximum capillary rise is on Moon where the acceleration due to gravity is less while the minimum capillary rise is on Neutron star. Practically, the observable difference in capillary rise between Sun and Neutron star is negligible.

CONCLUSION

Thus the effect of acceleration due to gravity on capillary rise was successfully studied