Angle of Contact

Angle of Contact

Introduction: have you seen surface of the water in a glass? the surface is having concave surface. Whenever a liquid is placed in a container , the surface of the liquid may be concave or convex. The shape of the surface is determined by a important parameter called as Angle of contact. We will study this topic in  detail in this section.

Fig1. Angle of contact

Angle of contact : Angle between the tangent drawn on solid and liquid surface in contact is called as Angle of contact.

Figure  shows angle of contact between liquid and solid interface.

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Shape of a meniscus

1) Concave meniscus : The shape of the meniscus depends upon the direction of resultant force in the system which is in contact. The fig2 below shows concave meniscus.

Figure 2. Concave meniscus

Consider a container filled with liquid in it. Let us study the portion shown with dotted line in the fig 2 above.
Consider a  molecule M on the surface of the liquid which is in contact with container. There exist a adhesive force on the molecule due to solid surface. This adhesive force AM acting on the molecule is perpendicular to the surface since the surface is vertical and acts towards the solid. The cohesive force MN which is  at an angle of 45० with both liquid and solid surface acts toward liquid. The adhesive force is much larger than the cohesive force, thus according to parallelogram law of vector addition the resultant force MR is towards solid. For equilibrium, the surface of the liquid or tangent MT must be  perpendicular to the resultant force. Thus the surface near the contact moves up in order to adjust itself perpendicular to the resultant force. Hence the surface looks concave.

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2) Convex meniscus : The shape of the meniscus depends upon the direction of resultant force in the system which is in contact. The fig3 below shows convex meniscus.

Figure 3. Convex  meniscus

Consider a  molecule M on the surface of the liquid which is in contact with container. There exist a adhesive force on the molecule due to solid surface. This adhesive force AM acting on the molecule is perpendicular to the surface since the surface is vertical and acts towards the solid. The cohesive force MN  acts toward liquid. AS the magnitude of  cohesive force is much larger than the adhesive force, the resultant force MR is inside the  liquid  according to parallelogram law of vector addition .For equilibrium, the surface of the liquid or tangent MT must be  perpendicular to the resultant force. Thus the surface near the contact adjust itself perpendicular to the resultant force. Hence the surface looks convex.

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3)Zero angle of contact : The shape of the meniscus depends upon the direction of resultant force in the system which is in contact. The fig4 below shows zero angle of contact.

Figure 4. zero angle of contact

Consider a  molecule M on the surface of the liquid (pure liquid) which is in contact with container. There exist a adhesive force on the molecule due to solid surface. This adhesive force AM acting on the molecule is perpendicular to the surface since the surface is vertical and acts towards the solid. The cohesive force is negligible. AS the  cohesive force is negligible the adhesive force is  the resultant force MR which is inside the  solid .For equilibrium, the surface of the liquid or tangent MT must be  perpendicular to the resultant force. Thus the surface near the contact adjust itself perpendicular to the resultant force. The angle  of contact is 0.(The tangent on the solid and liquid surface in contact overlap on each other , thus angle is zero)

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4)Angle of contact 90० : The shape of the meniscus depends upon the direction of resultant force in the system which is in contact. The fig5 below shows angle of contact 90० .

Fig5. Angle of contact 90० 

Consider a  molecule M on the surface of the liquid (hypothetical) which is in contact with container. Consider a  molecule M on the surface of the liquid which is in contact with container. There exist a adhesive force on the molecule due to solid surface. This adhesive force AM acting on the molecule is perpendicular to the surface since the surface is vertical and acts towards the solid. The cohesive force MN which is  at an angle of 45० with both liquid and solid surface acts toward liquid, thus the resultant force MR is exactly vertically . For equilibrium, the surface of the liquid  must be  perpendicular to the resultant force. Thus the surface near the contact adjust itself perpendicular to the resultant force. Hence the surface looks plane.

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Condition for concavity and convexity  

Below fig is a part of fig 5 above, 

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 Related Topic :  Mechanical Properties of fluid      Pressure due to liquid column     Absolute and gauge pressure  Hydrostatic Paradox       Pascal's Law        Measurement of pressure         Surface Tension Surface Energy         Angle of contact          Capillary Action            Motion in a fluid                    Critical velocity and Reynold's Number                      Viscosity                 Stokes' Law            Terminal velocity                 Equation of continuity                  Bernoulli Equation          Speed of Efflux    Ventury Tube

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