# Surface Tension Definition and its Formula

## 1. What is Surface Tension

Surface Tension Definition: Surface tension is the force acting along the surface of a liquid, causing the liquid to behave like a stretched elastic skin. We can also define it as the force per unit length acting on the surface at right angles to one side of a line drawn on the surface. Hence, it’s the property of a liquid in which the surface acts as though it’s covered with elastic skin.

The formula for surface tension is γ = F / L. Where γ = surface tension, F is the force, and L is the length. The si unit of surface tension is Newton per meter.

Additionally, we can say that it is a result of the cohesive forces between the molecules of the liquid. Consequently, because of this effect, they will refuse to separate from each other. Surface tension arises when the surface of a liquid interacts with another phase, which can be another liquid or even a solid. The defining characteristic of this phenomenon is the tendency of liquids to acquire the least possible surface area. This behaviour results in the liquid’s surface acting as an elastic sheet, a feature that sets the stage for numerous intriguing observations.

## 2. Surface Tension Formula

The formula for calculating surface tension is in force per unit length. Hence we can write the formula as

Surface Tension (S) = Force (F) / Length (L)

S = F / L

We need to also know that the S.I unit of the surface tension is in Newton per meter (Nm-1). Another unit for this force is dynes per centimeter (dyn/cm). We also have erg/cm2, and Joules per meter square (J/m2)

We can equally write surface tension equation as

S = (1/2) (F / L)

## 3. Surface Tension In Our Dialy Lives

Many of the everyday observations, show that the surface of a liquid behaves as it were a stretched elastic skin. For example, close a tap of a water but not very tight. Now observe the drops of the water from the tap. You will see the water forming slowly as it comes out from the tap. Therefore, as the water is coming out from the tap. It will appear to be making a bubble (in the form of balloon or elastic skin or bag). Hence, the elastic bag supports the weight of the water until the spherical drop of water falls on the floor.

This force is due to the attraction between the same molecules (cohesive force). Therefore, it makes the surface of the liquid to behave like a stretched elastic sheet. Thanks to this type of a force, insects can comfortably float (walk) on a water. When insects walk on a water. The surface they currently occupy will behave like an elastic skin. You will see the stretch on the surface.

### a. Everyday Observations: Glass of Water and Broken Thermometer:

Surface tension becomes particularly evident when you observe how liquid behaves in everyday scenarios. Filling a glass with water to its brim allows for the addition of a few more drops before it overflows, defying gravity and our expectations. Similarly, a broken thermometer releases a small pool of mercury that exhibits peculiar characteristics due to surface tension. The captivating nature of these observations lies in the fact that they provide tangible evidence of an otherwise imperceptible force at work.

### b. Significance of Surface Tension in Nature:

Surface tension is a fundamental force that influences numerous natural phenomena. It’s responsible for the behavior of liquid droplets, the floating of small objects on the surface of water, and even the formation of bubbles. Understanding surface tension allows us to appreciate the intricacies of our world and can be applied in diverse fields, from biology to materials science.

## 4. Surface Tension Definition: Explanation

Surface tension is a physical phenomenon that results from the cohesive forces between the molecules of a liquid at the interface between the liquid and another medium, such as air or another liquid. It is a fundamental physical phenomenon that plays a crucial role in many aspects of our lives. These roles ranges from the behavior of fluids to the way our bodies function.

Therefore, these cohesive forces make the surface of the liquid to contract and form a thin, elastic layer. The layer is known as the surface film or surface skin. We should also know that this layer behaves as if it were a stretched membrane. Hence, when you place an object on it, it is capable of supporting that object. It can also resist deformation from external forces.

The magnitude of the surface tension of a liquid depends on various factors. These factors depends on

1. The nature of the liquid,
2. Temperature, and
3. The presence of impurities or dissolved substances.

The study of surface tension has applications in many fields, including physics, chemistry, materials science, and engineering. For example, it is a fundamental factor in determining the behavior of fluids in:

1. Capillary tubes,
2. The formation of drops and bubbles
3. Wetting of surfaces, and
4. Stability of emulsions and foams.

## 5. Causes and Fundamentals of Surface Tension

### a. Attraction of Liquid Particles:

At the core of surface tension lies the attraction between liquid particles. These particles exhibit a cohesive force, drawing them together within the liquid. Along the surface, these particles are pulled toward the rest of the liquid, creating the tension we observe. This cohesive force is instrumental in minimizing the surface area.

### b. Role of Interactions with Solid, Liquid, or Gas:

Surface tension is not solely dependent on the forces of attraction between liquid particles. It also hinges on the forces of attraction with solid, liquid, or gas substances in contact with the liquid. This multifaceted interplay adds complexity to the surface tension phenomenon, making it an intriguing field of study that extends beyond the liquid phase.

### c. The Concept of Surface Energy:

The energy responsible for the surface tension phenomenon is akin to the work required to remove the surface layer of molecules in a unit area. This concept is fundamental to understanding surface tension’s impact and how it contributes to the overall behaviour of liquids.

## 6. Surface Tension Definition: Measurement

We use a tensiometer to measure the surface tension of a liquid. We have different types of tensiometers which are:

1. Drop volume tensiometer
2. Force tensiometer
3. Spinning drop tensiometer
4. Bubble pressure tensiometer

This brings us to three methods for measuring surface tension:

1. Wilhelmy plate method
2. Du nouy ring method
3. Optical method

## 7. Measurement and Units of Surface Tension

### a. Surface Tension Units: Dynes/cm and Newton per Meter (N/m):

Surface tension is typically quantified in two main units: dynes/cm and Newton per Meter (N/m). Dynes/cm represent the force in dynes required to break a film of length 1 cm, providing a practical measurement of surface tension. Newton per Meter is the SI unit, expressing surface tension as the force required to break a film of length 1 meter. These units are essential for understanding and comparing surface tension values across different liquids.

### b. Mathematical Expression: Tension (T) = Force (F) / Length (L):

Mathematically, surface tension can be expressed through a straightforward formula: Tension (T) equals the force (F) per unit length (L). This equation provides a clear and quantifiable relationship between the fundamental parameters of surface tension.

### c. Dimensional Formula of Surface Tension (MT-2):

The dimensional formula of surface tension is MT-2. This succinct expression encapsulates the fundamental dimensions of mass (M) and time (T), providing a comprehensive understanding of surface tension’s physical characteristics.

## 8. Examples of Surface Tension in Nature

### a. Water Striders: Walking on Water:

In biology, water striders, small insects with negligible weight, appear to defy gravity as they effortlessly walk on the water’s surface. This remarkable feat is a testament to the power of surface tension, which supports their diminutive weight and prevents them from sinking into the water. Understanding this behaviour allows us to appreciate the intricate adaptations of creatures in their natural habitats.

### b. Rainproof Tents: Bridging Water’s Pores:

The concept of surface tension extends beyond the realm of insects. In everyday life, rainproof tents rely on the surface tension of water to bridge the pores in their material. By forming a barrier against water infiltration, this application of surface tension showcases its practical importance in materials science.

### c. Clinical Tests for Jaundice:

Surface tension finds applications in clinical diagnostics, where it is employed in tests for conditions like jaundice. The behavior of blood components in the presence of reagents with specific surface tension properties aids in diagnosing health issues, highlighting surface tension’s role in medical science.

### d. Cleaning with Soaps and Detergents:

The use of soaps and detergents for cleaning is a common practice that capitalizes on surface tension. These cleaning agents lower the surface tension of water, allowing it to penetrate fabrics and surfaces more effectively. By reducing surface tension, soaps and detergents enable thorough cleaning processes and illustrate the practical implications of this force.

### e. Round Bubbles: Wall Tension and Liquid Droplet Shapes:

Surface tension is instrumental in the formation of round bubbles. It provides the necessary wall tension that shapes these delicate structures. The role of surface tension in the formation and stability of bubbles demonstrates its importance in everyday phenomena, from dishwashing to the visual arts.

## 9. The Science Behind Surface Tension

### a. Intermolecular Forces – Van der Waals Force:

The science of surface tension delves into the intricacies of intermolecular forces, including the Van der Waals force. These forces play a pivotal role in drawing liquid particles together, creating the cohesive strength that underlies surface tension. Understanding the nature of intermolecular forces is central to comprehending the driving factors behind surface tension.

### b. Exploring the Relationship Between Forces and Length:

Surface tension hinges on the relationship between forces and length. As we explore this connection, we gain insight into how different forces act on liquid surfaces, creating tension along specific lengths. This exploration is a key element in unraveling the mysteries of surface tension.

## 10. How Does Surface Tension Work?

Surface tension is due to intermolecular forces, which are the attractive forces between molecules. These forces are stronger between like molecules than between unlike molecules. Thus, they create a cohesive force at the surface of a liquid.

At the surface of a liquid, the molecules are more strongly attracted to each other than they are to the air above the surface. Therefore, it makes the surface of the liquid to behave like a stretched elastic sheet. Consequently, this behavior is the reason why it resists penetration by objects and why it can form droplets.

## 11. Molecular Explanation of Surface Tension

The cohesive forces between the molecules of a liquid are responsible for a stretched elastic skin of the liquid. These forces are due to the presence of intermolecular forces. The intermolecular forces responsible are van der Waals forces and hydrogen bonds. They cause the molecules to come together. This attraction creates a net inward force on the surface molecules. Subsequently, it pulls them towards the bulk of the liquid. Hence, it makes the surface to act as if it is a stretched elastic membrane.

The strength of the cohesive forces between the molecules of the liquid determines the magnitude of the stretched elastic skin of a liquid, with stronger forces resulting in higher surface tension.

## 12. Methods of Surface Tension Measurement

### a. Spinning Drop Method:

The spinning drop method is one of the techniques used to measure surface tension. It involves the rotation of a drop of liquid to determine its surface tension properties, providing valuable insights into the nature of the liquid’s surface.

### b. Pendant Drop Method:

In the pendant drop method, a drop of liquid is suspended from a solid object. By studying the shape of the pendant drop, researchers can gather data on surface tension and use it for various scientific applications.

The Du Noüy–Padday method relies on the use of a precision instrument known as a Du Noüy ring. This method offers a straightforward approach to measuring surface tension, making it a valuable tool in laboratories.

### d. Du Noüy Ring Method:

The Du Noüy ring method, a variant of the Du Noüy–Padday method, involves using a carefully designed ring to study the surface tension of a liquid. Its simplicity and accuracy contribute to its widespread use in scientific research.

### e. Wilhelmy Plate Method:

The Wilhelmy plate method employs a thin flat plate that is immersed in a liquid to measure surface tension. By assessing the liquid’s interaction with the plate, researchers can gain valuable data on surface tension properties.

### f. Pendant Drop Method:

The pendant drop method, as previously mentioned, involves suspending a drop of liquid from a solid object. This technique offers a practical and versatile approach to surface tension measurement.

### g. Stalagmometric Method:

The stalagmometric method focuses on the use of capillary tubes to measure surface tension. By observing the meniscus in these tubes, researchers can determine surface tension values with precision.

### h. Capillary Rise Method:

Capillary rise is another phenomenon closely related to surface tension. This method explores the rise of liquids in narrow tubes, shedding light on surface tension and its impact on capillary action.

### i. Bubble Pressure Method:

The bubble pressure method assesses the pressure within gas bubbles formed within a liquid. This method provides valuable insights into the surface tension properties of the surrounding liquid.

### j. Resonant Oscillations of Liquid Drops:

Resonant oscillations of liquid drops offer a unique perspective on surface tension. By studying the frequency of these oscillations, researchers can glean information about the liquid’s surface properties.

### k. Sessile Drop Method:

The sessile drop method involves analyzing a drop of liquid on a solid surface. By observing the shape and behaviour of the drop, scientists can infer surface tension characteristics.

## 13. Surface Tension Definition: Effects

Surface tension has several effects on the behavior of liquids. For instance, it causes liquids to form droplets. These are spherical in shape due to the minimization of the surface area. Therefore, the spherical shape of droplets is due to the balance between the stretched elastic skin of the liquid and the hydrostatic pressure.

It also affects the wetting of a solid surface by a liquid. When the cohesive forces between the liquid molecules are stronger than the adhesive forces between the liquid and the solid. The liquid forms a droplet on the surface of the solid. On the other hand, if the adhesive forces are stronger. The liquid spreads over the surface, forming a thin film.

## 14. Surfactants

We use surfactants (molecules) to lower the surface tension of a liquid. They are amphiphilic molecules, which means they have both hydrophobic and hydrophilic regions. The hydrophobic region is attracted to non-polar molecules, while the hydrophilic region is attracted to polar molecules.

When you add it to a liquid. Surfactant molecules align themselves at the surface, with their hydrophobic regions in the liquid and their hydrophilic regions in the air. This alignment reduces the cohesive forces between the liquid molecules.

## 15. Surface Curvature and Pressure

We can describe the curvature of the surface by the radius of curvature. It is the radius of the circle that best fits the surface at a given point. Laplace equation describes the relationship between the surface tension, curvature, and pressure.

The surface curvature of a liquid interface refers to the curvature of the liquid’s surface at a given point. A liquid interface can have different curvatures at different points, and the curvature can change depending on the surrounding environment.

Surface pressure, on the other hand, refers to the force per unit length that acts on a liquid surface. This pressure is caused by the stretched elastic skin of the liquid and is directed perpendicular to the facet. It is directly proportional to the surface tension and inversely proportional to the radius of curvature of the surface.

Mathematically, the relationship between surface tension, surface pressure, and surface curvature can be expressed using the Laplace-Young equation:

ΔP = S(1/R1 + 1/R2)

where

S = Surface tension

ΔP is the pressure difference across the interface

R1 and R2 are the principal radii of curvature at the interface.

The Laplace-Young equation states that the pressure difference across a curved interface is proportional to the surface tension and the sum of the inverse radii of curvature.

This equation explains why small bubbles have higher internal pressure than large bubbles. This is because the radius of curvature of a small bubble is smaller than that of a large bubble. Hence, the pressure difference across the interface causes the bubble to expand or contract until the internal and external pressures are equal.

## 16. Force Due to Surface Tension

When we consider a small segment of the liquid surface with length L. The cohesive forces between the molecules of the liquid cause a net inward force on this segment. This force is directed tangentially along the surface and is perpendicular to the length of the segment.

The formula for force due to surface tension is F = γL,

This coefficient (γ) represents the amount of energy required to increase the surface area of the liquid by one unit.

If the surface area of the liquid changes by a small amount dA. Then the work done is given by

dW = FdA.

This work represents the energy required to increase the surface area of the liquid by dA, and is equal to γdA.

This force plays an important role in many natural and technological processes. We have roles like the formation of droplets, the behavior of bubbles, and the adhesion of materials. Understanding its mathematical expression helps in designing and optimizing these processes.

## 17. How to Calculate Surface Tension

### a. Practical Calculation Example:

Calculating surface tension is a practical application of the mathematical expression Tension (T) = Force (F) / Length (L). By working through a real-world example, we can see how these components come together to quantify the surface tension of a given liquid.

### b. Force and Length Parameters:

Surface tension calculations rely on two fundamental parameters: force (F) and length (L). These parameters serve as the building blocks for understanding and quantifying surface tension in a tangible way.

## 18. Wider Applications of Surface Tension

The study of a stretched elastic skin of a liquid has many practical applications in daily activities. One of these applications is capillary action (Capillarity). This is because it plays a key role in the transport of water in plants. It is also important in the absorption of liquids in paper towels and sponges.

Another example we can capitalize on is the formation and behavior of bubbles. The spherical shape of bubbles helps the surface of the bubble to contract and minimize its surface area.

Wetting and spreading are other important applications we need to consider. When a liquid comes into contact with a solid surface, it will either wet or not wet the surface. This is depending on the relative strengths of the adhesive and cohesive forces involved.

## 19. The Importance of Surface Tension

This type of force plays a crucial role in many aspects of our lives. It is what allows plants to transport water and nutrients through their stems and leaves. It enables insects to walk on water. When we look into medicine, we apply it to create microfluidic devices for drug delivery and to study the behavior of cells and proteins.

It is also responsible for the behavior of surfactants. As we earlier explained, they are molecules that reduce the surface tension of a liquid. Surfactants are found in many household products. These products can be detergents and soaps. We use them to enable more penetration in surfaces more easily.

## 20. Surface Tension Definition: Effects in Our Daily Lives

Surface tension plays a role in many everyday activities, from washing dishes to blowing bubbles. Soap and other cleaning agents can penetrate surfaces more easily and helps to remove dirt and grease.

Additionally, it allows droplets to form on surfaces. We can see these droplets in the dew that forms on grass in the morning. It is what allows inkjet printers to create sharp, precise images. It also enables the formation of bubbles in carbonated beverages.

## 21. Surface Tension Definition: Applications in Nature

Surface tension is essential to the functioning of many natural systems. In plants, it allows water and nutrients to be transported from the roots to the leaves through the stem. A quite obvious example is the one we mentioned earlier, where Insects are able to walk on water. Some species even use it to trap prey.

When we look into the behavior of marine organisms. We can see that the ocean allows the formation of waves. Therefore, it helps certain species to float on the surface of the water.

## 22. Applications in Science and Technology

It is an important factor in many scientific and technological applications. In materials science, we use it to study the behavior of materials at the nanoscale. In energy harvesting, we use it to maximize the efficiency of solar cells by optimizing the surface tension of the materials we use.

We also use it in the development of microfluidic devices. Which are used in a variety of applications, from drug delivery to lab-on-a-chip technology. Deeper research can help to create precise channels for the transport of fluids and particles at the micrometer scale.

## 23. Future Research

Research into the properties of this topic is ongoing, and there are many potential applications for this knowledge. One area of research is the development of new surfactants and other materials that can be used in a variety of industrial and biological processes.

Another area of research is in microfluidics. This is the study of fluids at the microscale. Hence, it can be used to control the behavior of fluids in microfluidic devices. This is because they have applications in fields such as medical diagnostics and drug delivery.

## 24. Frequently Asked Questions (FAQs)

Q: What is the difference between surface tension and viscosity?
A: Surface tension is the cohesive force that exists between molecules at the surface of a liquid, while viscosity is a measure of a liquid’s resistance to flow.

Q: How is surface tension measured?
A: It is measured in units of force per unit length. The unit is Newtons per meter or dynes per centimeter.

Q: What are some examples of how surface tension is used in everyday life?
A: We use it for washing dishes, blowing bubbles, and even in the formation of dew on grass.

Q: How does surface tension impact the behavior of insects on water?
A: It allow insects to walk on its surface by providing a supportive layer of cohesive molecules.

You may also like to read:

An object of mass 4 kg goes round a circle of radius 0.5 m

The amplitude of SHM y=2(sin5πt+√2cosπt) is

An object of mass 4 kg moves round a circle of radius 6m

How to Calculate Centripetal Acceleration

An object of weight 150 N moves with a speed of 4.5 m/s

How to Calculate Centripetal Force

Simple Harmonic Motion (SHM): Understanding the Basic Concepts

A stone of mass 500g tied to a rope 50 cm long

A Projectile is Launched at an Angle of 30

A body moves along a circular path

If a wheel 1.2m in diameter rotates at one revolution per second

## Source

American Physical Society