Name: surface tension in drops and bubbles
Uploaded: 2023-05-16T08:18:41.000Z
Duration: 1 min 13 s
Channel: JoVE

Uma gota líquida pode ser considerada esférica, ignorando o efeito da gravidade. Os dois hemisférios da gota se atraem devido à tensão superficial. Além disso, as forças devidas à pressão do líquido interno e do ar externo atuam nos hemisférios.
No equilíbrio, a magnitude das forças internas e externas se equilibram. Reescrever essa expressão indica um excesso de pressão dentro da gota de líquido.
Para gotas de líquidos diferentes com o mesmo raio, o excesso de pressão é maior para o líquido com maior tensão superficial. No entanto, se o raio diminuir, o excesso de pressão aumenta.
O cenário permanece inalterado no caso de bolhas de ar dentro de um líquido, onde a pressão dentro das bolhas é maior do que a pressão no líquido.
No caso de uma bolha de sabão, a pressão contida na espessura da bolha é maior que a pressão do ar externo e menor que a pressão do ar dentro da superfície. 
A adição dessas expressões dá o excesso de pressão dentro de uma bolha de sabão.

<ol>
	<li>Verma, H.C. (2008). Conceitos de Física Parte I, Quarta Edição. pág. 286-28</li>
</ol>

pressão excessiva dentro de uma gota e uma bolha

A forma de uma pequena gota de líquido pode ser considerada esférica, desprezando o efeito da gravidade. Essa gota pode ser considerada como duas gotas hemisféricas iguais juntas devido à tensão superficial. As forças atuando na gota esférica são devidas à pressão do líquido dentro da gota, a pressão devido ao ar fora da gota e a força devido à tensão superficial atuando nas duas gotas hemisféricas.

<img alt="Equation1" src="/files/ftp_upload/14715/14715_Equation_1v2.svg" style="text-align: center; height:20px;" />

onde γ corresponde à tensão superficial. Utilizando a informação de que a força por unidade de comprimento é a tensão superficial, obtemos a força atuando no diâmetro. A diferença entre a pressão dentro e fora da gota em relação à sua área superficial fornece as forças de pressão resultantes atuando na gota. No equilíbrio, as forças internas e externas se equilibram, indicando que a pressão dentro da superfície líquida é maior do que a pressão externa.

<img alt="Equation2" src="/files/ftp_upload/14715/14715_Equation_2v2.svg" style="text-align: center; height: 40px;" />

No caso de uma bolha de ar dentro de um líquido, essa condição permanece inalterada, e a pressão dentro da bolha de ar é maior do que a pressão no líquido circundante. A diferença de pressão através dessa interface ar-líquido é proporcional à curvatura da interface, o que, por sua vez determina o tamanho da bolha.

Uma visão transversal de uma bolha de sabão apresenta duas superfícies: uma em contato com o ar dentro da bolha e a outra em contato com o ar fora da bolha. A pressão dentro da bolha é maior do que a pressão do ar fora da superfície. Além disso, a pressão dentro da bolha é menor do que a pressão do ar dentro da superfície pela mesma quantidade. Resolvendo essas duas condições, obtemos a relação de Young-Laplace para a bolha de sabão.

<img alt="Equation3" src="/files/ftp_upload/14715/14715_Equation_3v2.svg" style="text-align: center; height: 40px;" />

Pressão Excessiva Dentro de uma Gota e uma Bolha

A forma de uma pequena gota de líquido pode ser considerada esférica, negligenciando o efeito da gravidade. Essa queda pode ainda ser considerada como duas ...

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excess-pressure-inside-a-drop-and-a-bubble

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Fluid Mechanics

Mecânica dos Fluidos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Excess Pressure Inside a Drop and a Bubble

surface tension in drops and bubbles

Surface tension sets the pressure difference in small drops and bubbles. For a tiny liquid drop, gravity can be neglected, so the drop is treated as spherical. It can also be viewed as two equal hemispherical drops joined together by surface tension.

The forces on the drop come from three sources. The liquid inside pushes outward, the air outside pushes inward, and surface tension acts along the diameter between the two hemispheres. Since surface tension is force per unit length, it creates a force that must balance the pressure forces on the drop’s surface area.

At equilibrium, the inward and outward forces balance. This balance shows that the pressure inside the liquid surface is greater than the external pressure. The same idea applies to an air bubble inside a liquid, where the pressure inside the bubble is greater than the pressure in the surrounding liquid.

The pressure difference across the air-liquid interface depends on the curvature of the interface. That curvature also affects the size of the bubble. A soap bubble has two surfaces, one touching the air inside and one touching the air outside. The pressure inside the bubble is greater than the air pressure outside the outer surface, and it is lower than the air pressure inside the inner surface by the same amount. Solving these two conditions gives the Young-Laplace relation for a soap bubble.

Surface Tension in Drops and Bubbles

characteristics of fluids

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pascal's law

Pascal’s Principle in Static Fluids

Pascal’s principle explains how pressure changes move through a fluid that is not flowing. A fluid at rest is in static equilibrium. If the fluid is water, it is in hydrostatic equilibrium. In this state, the net force on any part of the fluid must be zero, or the fluid will begin to flow. Blaise Pascal described this idea in 1653 in Treatise on the Equilibrium of Liquids. He showed that when pressure changes in an enclosed fluid, that change is transmitted without loss through the fluid and...

application of pascal's law

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pressure gauges

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archimedes' principle

Buoyant Force from Fluid Pressure

Archimedes' principle explains buoyant force in a fluid. An upward buoyant force acts on an object that is partially or fully immersed in a fluid. This force is equal to the weight of the fluid displaced by the object. To see why an object floats, imagine removing a submerged object from the fluid. The space it occupied would be filled by fluid with weight w_fl. That weight is supported by the surrounding fluid, so the buoyant force must match the weight of the displaced fluid. The principle...

density and archimedes' principle

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excess pressure inside a drop and a bubble

Surface tension sets the pressure difference in small drops and bubbles. For a tiny liquid drop, gravity can be neglected, so the drop is treated as spherical. It can also be viewed as two equal hemispherical drops joined together by surface tension. The forces on the drop come from three sources. The liquid inside pushes outward, the air outside pushes inward, and surface tension acts along the diameter between the two hemispheres. Since surface tension is force per unit length, it creates a...

buoyancy

Buoyant Force in Sinking and Floating

Buoyant force explains why objects float, sink, or stay suspended in a fluid. A fluid can be a liquid or a gas, and every object placed in it experiences this upward force. A metal ball sinks, while a rubber ball floats. A submarine also changes its buoyancy to move up or down. The force comes from pressure changes in the fluid. Fluid pressure increases with depth because the weight of the fluid above also increases. That means the bottom of an object feels more pressure than the top. This...

contact angle

Wetting and Surface Curvature

Wetting and surface curvature describe how a liquid behaves where it meets a solid. When a solid is dipped into a liquid, the liquid surface can bend near the contact line. In some cases, the liquid rises along the solid. In others, the surface becomes convex or depressed near the solid. This behavior comes from cohesive and adhesive forces. Adhesive force is the attraction between molecules of different materials, such as a solid and a liquid. Cohesive force is the attraction between...

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rise of liquid in a capillary tube

Capillary Action in Thin Tubes

Capillary action explains why liquid can rise or fall in a very thin tube compared with the liquid around it. A capillary is a narrow cylindrical tube, and the effect becomes noticeable when it is dipped into a liquid. The movement happens because two forces act in opposite directions. Cohesive forces make liquid molecules stick to each other, so the liquid tends to hold together and form a rounded shape. Adhesive forces pull the liquid toward the walls of the container. In a narrow glass...

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laminar and turbulent flow

Fluid Motion Patterns in Air and Water

Fluid dynamics studies fluids in motion. Scientists often use velocity vectors to show fluid motion in places like meteorology. For example, wind in the atmosphere can be mapped with vectors that show the speed and direction of the wind at each point. Another way to show fluid motion is with a streamline. A streamline shows the path of a small volume of fluid as it flows. When the flow changes with time, the streamlines do not match the flow lines. The fluid velocity is always tangential to...

equation of continuity

Fluid Flow in Narrowing Pipes

Fluid flow in a pipe is described by flow rate and average speed. Flow rate, or volume flow rate, is the amount of fluid that passes a point through an area in a given time. It depends on both how fast the fluid moves and the size and shape of the conduit. For a river or pipe, a greater speed usually means a greater flow rate. A larger cross-sectional area also increases flow rate. That is why the same fluid can move differently through conduits of different sizes. The relationship becomes...

bernoulli's equation

Fluid Pressure and Speed in Motion

Bernoulli's equation connects fluid pressure with fluid speed. It helps explain why moving fluids can create pressure changes in everyday situations. One example is when two trains pass each other quickly and seem to pull inward. The same effect can happen when two cars pass each other at high speed. As the air between the trains or cars speeds up, its pressure drops. The air on the outside stays at atmospheric pressure. That pressure difference creates a net inward force on the vehicles.

bernoulli's principle

Fluid Pressure and Speed Changes

Bernoulli's equation links fluid pressure and fluid speed in a static, incompressible fluid. For horizontal flow, where gravitational energy density stays constant, the equation is especially useful. In that setting, the result is known as Bernoulli's principle. Bernoulli's principle says that fluid pressure drops when speed increases, and pressure rises when speed decreases. This pressure-speed relationship helps explain how moving fluids behave in simple flow situations. It also provides a...

bernoulli's principle: applications

Bernoulli's Principle in Fluid Devices

Bernoulli's principle helps explain how many fluid devices work when the fluid moves at a constant height. It is useful for devices that use fast flow to create low pressure and for devices that measure fluid speed. Some devices use this pressure change to pull one fluid into another. These are called entrainment devices. A Bunsen burner uses an adjustable gas nozzle to entrain air for proper combustion. An atomizer uses a squeeze bulb to make a jet of air that pulls perfume drops into the...

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energy conservation and bernoulli's equation

energy-conservation-and-bernoulli-s-equation

Bernoulli’s Equation in Streamlined Flow

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow. The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per...

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viscosity

Viscosity and How Fluids Flow

Viscosity describes how easily a fluid flows. Water moves quickly, while honey and maple syrup flow slowly and stick to a surface. That difference comes from fluid friction between liquid layers and between a fluid and the material around it. In this example, water has a lower viscosity than honey and maple syrup. Viscosity is measured in newton-second per meter squared (N·s/m2) or pascal-second (Pa·s). It also changes with temperature and can differ from one fluid to another by several orders...

poiseuille's law and reynolds number

Fluid Resistance, Viscosity, and Flow Regime

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

stokes' law

Terminal Velocity in a Viscous Fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature. For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the...

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key terms and concepts

Learn how surface tension creates pressure differences in small liquid drops, air bubbles, and soap bubbles, and how curvature leads to the Young-Laplace relation.

Surface Tension in Drops and Bubbles | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

Surface Tension in Drops and Bubbles

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