Capillary rise on Black Hole

CAPILLARY RISE ON SURFACE OF BLACK HOLE

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 determine the extent of capillary rise by a liquid on the surface of Black hole.

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 tube is indestructible

6. Space time deformation has no effect on capillarity phenomenon

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.

Fig .1 Capillarity

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 event horizon of Black hole [g = ꝏ m/s²]

Substituting the constants in equation (1),

The cohesive and adhesive forces of liquid cannot overcome the extreme gravitational pull of a black hole, hence the capillary rise is zero.

CONCLUSION

We thus determined the capillary rise of water on the surface of Black hole. It is interesting to note that the capillary rise does not depend on the length of the capillary tube.