Capillarity

Force of Cohesion and Adhesion

Cohesion force is an attraction force between molecules in a similar substance, while an attraction force between molecules of an unequal substance is called the Adhesion Force. For example, we pour water into a glass. Cohesion occurs when water molecules attract each other, while adhesion occurs when water molecules and glass molecules pull each other.

Contact angle

Before learning the concept of Capillarity, we first understand how the influence of adhesion force and cohesion force on capillarity. For example, we review the liquid in a glass. When the cohesion force of the liquid molecule is stronger than the adhesion force (the pulling force between the liquid molecules and the glass molecule) the liquid surface will form an upward curve. An example of this case is when the water is in a glass. Usually, it is said that water soaks the surface of the glass. Conversely, if the adhesion force is stronger, then the surface of the liquid will curve downward. For example when mercury is in a glass.

Capillarity 1The angle formed by the curve is called the contact angle. When the fluid cohesion force is higher than the adhesion force, the contact angle formed is generally smaller than 90o (figure a). Conversely, if the adhesion force is higher than the fluid cohesion style, the contact angle formed is greater than 90o (figure b). Adhesion forces and cohesion forces are theoretically difficult to calculate, but contact angles can be measured. What does it have to do with capillarity?

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Capillarity concept

If the fluid cohesion force is greater than the adhesion force, the liquid surface will curl upwards. When we insert a thin tube or pipe (a pipe whose diameter is smaller than the container), the liquid in the container rises through the pipe column. This is because the force of the total surface tension along the tube wall works upward. The maximum height that a liquid can achieve is when the surface tension force is equal to the weight of the liquid in the pipe. So, the liquid is only able to rise to a height where the surface tension force is balanced with the weight of the liquid in the pipe.

Capillarity 2Capillarity 3Conversely, if the adhesion force is greater than the fluid cohesion force, the surface of the liquid will curve downward. When we insert a thin tube or pipe (a pipe with a smaller diameter than the container), it will form a lower part of the liquid (see picture below).

This effect is known as the capillary, and the thin pipe is called the capillary tube. Keep in mind that our smallest blood vessels can also be called capillary pipes because blood circulation in small blood vessels also occurs due to the effects of capillarity. Likewise, the phenomenon of rising melting of wax or kerosene through the axis. Also, capillarity is also believed to play an essential role in the passage of water and nutritious substances from the roots to the leaves through the xylem vessels. If there is no capillarity, the soil surface will dry immediately after rain. Another significant effect of capillarity is the retention of water in the gaps between soil particles.

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Capillarity equation

How can we determine the height of the water rising through the capillary pipe column? The liquid rise in the capillary pipe column which has a radius r up to the height h. The force acting in holding the liquid at height h is the component of the surface tension force in the vertical direction: F cos θ.

The top of the capillary tube is open so that there is atmospheric pressure on the surface of the liquid. The length of the touch surface between the liquid and the pipe is 2πr (circumference). Thus, the magnitude of the surface tension force of the vertical components that work along the contact surface are:

Capillarity 5

F = Surface tension force, γ = Surface tension, r = radius of the capillary tube, θ = Contact angle

If the curved upward surface is ignored, the volume of liquid in the pipe is:

Fluid volume = the surface area of pipe x-height of the liquid

V = A h

V = (π r2) h

If the vertical component of the Surface Tension Force is balanced with the weight of the liquid column in the capillary tube, then the liquid cannot rise again. In other words, the liquid will reach its maximum height, if the vertical component of the surface tension force is balanced with the weight of the liquid as high as h. The vertical component of the surface tension force is:

F = γ 2 π r cos θ

While the weight of the liquid in the capillary pipe is:

w = m g

w = ρ V g

w = ρ ( π r2 h ) g

When the liquid reaches its maximum height (h), the vertical component of the surface tension force must equal the weight of the liquid in the capillary tube. Mathematically, written:

Capillarity 6

This is the equation we are looking for. If you want to determine the height of the liquid column, please use this equation.

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