surface tension

[biǎo miàn zhāng lì]

Physical concepts

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Surface tension refers to liquid Tension acting on any boundary line along the surface due to unbalanced molecular gravity in the surface layer^[4] 。^[5]

The water drops condensed on the leaves in the morning and the water drops slowly falling from the faucet are formed under the effect of surface tension. In addition, Water strider The reason why we can stand on the water surface is also due to the effect of surface tension^[1] 。^[4]

Chinese name: surface tension
Foreign name: surface tension
influence factor: Nature and temperature of liquid

Definition: Liquids such as water will produce forces to minimize the surface
Example: Spherical droplets, ripples, etc
Field: Mathematical Science

catalog

nine Spherical droplet
ten Ripple

brief introduction

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Liquids are cohesive and adsorptive, both of which are manifestations of molecular gravity. Cohesion enables liquid to resist tensile force, while adsorption enables liquid to adhere to other objects^[2] 。

Surface tension phenomenon (2 sheets)

At the boundary between liquid and gas, that is, the liquid surface and the interface between two immiscible liquids, extremely small tension is generated due to the attraction between molecules. Suppose there is a film layer on the surface, which bears the tensile force of the surface. This tension of the liquid is called surface tension^[2] 。

Because the surface tension only exists on the free surface of the liquid or at the interface between two immiscible liquids Surface tension coefficient σ To measure its size. σ It refers to the value of tensile force per unit length on the surface, in N/m. The surface tension of various liquids covers a wide range, and its value decreases slightly with the increase of temperature^[2] 。

In our daily life, the phenomenon that water drops hang on the branches after rain, and the water surface is slightly higher than the mouth of the cup without spilling is the result of surface tension^[2] 。

The surface tension coefficient of a liquid is a property of the liquid itself, which is mainly determined by the liquid itself. The surface tension coefficient of inorganic liquid is much larger than that of organic liquid, which means that the surface tension coefficient of liquid is related to the type of liquid. The surface tension coefficient of water is 72.8mN/m (20 ℃). The surface tension coefficient of known organic liquids is less than that of water, including nitrogen 、 oxygen The surface tension coefficient of organic liquids containing F 、 Si The liquid surface tension coefficient of is the smallest. Aqueous solution: if it contains inorganic salts, the surface tension is greater than that of water; Containing organic matter, the surface tension is smaller than that of water.^[6]

calculation

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If the surface tension is required, an arbitrary area element can be drawn on the liquid surface. Let each side length of this area element be l , the horizontal tension of other parts of the surface on each side is F , so the surface tension σ For:

The surface tension is perpendicular to the periphery of this area, and its size is expressed in dynes per centimeter (1 dyne/cm=10 -3 N/m) Therefore, the dimension of surface tension is MT -2 。

size

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At room temperature (about 20 ℃), the surface tension of most liquids is within the range of 20~40 dynes/cm, but there are others larger than that, for example, the surface tension of water is 72 dynes/cm; The surface tension of mercury is 470 dyne/cm. liquid metal The surface tension of liquid copper at 1131 ℃ is 1103 dynes/cm. Some elements are gaseous at room temperature, but their surface tension is very small when they are liquid at low temperature. For example, the surface tension of 4.3 liquid helium is only 0.098 dyne/cm, and that of 90.2 liquid hydrogen is 0.2 dyne/cm. Theoretical analysis also points out that for the same liquid, the surface tension will decrease when the temperature rises.

influence factor

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The direction of surface tension is tangent to the liquid surface and perpendicular to the boundary line of any two parts of the liquid surface. The surface tension is only related to the nature and temperature of the liquid. In general, the higher the temperature, the smaller the surface tension. In addition, impurities will also significantly change the surface tension of the liquid. For example, clean water has a large surface tension, while the surface tension of water stained with soap liquid is relatively small, that is, the surface of clean water has a greater shrinkage trend^[3] 。

Formation mechanism

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Compare the force of molecule A in the liquid with that of molecule B on the liquid surface. Take the effective force path of molecular force as the radius to make a sphere with molecule A as the center (Figure 1), then all molecules that have an effect on molecule A are within the sphere. Choose a longer time T (is the average time between two collisions of molecules). Due to symmetry, the resultant force of each molecule on A during this period is equal to zero. One part of the spherical surface centered on molecule B is in the liquid and the other part is outside the liquid surface. The molecular density of this part is far less than that of the liquid part. If the effect of these molecules on B is ignored, then due to symmetry, CC' and DD' The total force of all molecular forces between is equal to zero; The effective force on B is determined by DD' The downward resultant force generated by all the following molecules. Since every molecule within the boundary is subject to the resultant force pointing to the interior of the liquid, these molecules have a downward trend towards the interior of the liquid. At the same time, there is a lateral attraction between molecules, that is, there is a tendency to shrink the surface as much as possible. In this case, the surface of the fluid seems to be covered with an elastic film outside a solid with a surface area larger than that of the fluid.

Fig. 1 Force state of molecules on fluid surface layer

Laplace formula

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The length of the inspected side is ds one 、ds two If its curvature is not equal to zero, then the surface tension T The resultant force of shall have a component in the normal direction of the surface, and the pressure difference on both sides of the surface shall be balanced with it. The relationship between differential pressure and surface tension is as follows Laplace formula give:

Fig. 2 Surface Tension and Pressure on Curved Surface

Where P one 、 P two Is the pressure on both sides of the surface; R one 、 R two Is the radius of curvature in any two orthogonal directions on the surface. Pressure on concave surface P one Always greater than the pressure on the convex face P two 。

contact angle

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In the case where the boundary surfaces of the three mediums intersect at a point (for example, a drop of mercury stops on the desktop), the contact line is subject to the surface tension of three different boundary interfaces (Figure 3). Since the contact line has no mass, it is necessary to maintain balance in all directions that can move freely. The component of the resultant force of surface tension in these directions must be equal to zero, which requires that the three boundary surfaces intersect at a certain angle. If| σ twelve |Ratio| σ twenty-three |And| σ thirty-one |If the sum of is even larger, the balance is impossible. For example, when gasoline drops on the water surface, because the surface tension of air and water is greater than the sum of the surface tension of the other two oil surfaces, the three mediums cannot be in equilibrium, and gasoline will spread on the whole water surface until the thickness of the oil layer reaches the molecular size. If medium 3 is melted fat, when it is placed between air and water, it will form the shape of a thin convex lens (such as a fat ball floating on vegetable soup).

If one of the three mediums is a solid (usually the boundary of the solid is a plane), only the contact line parallel to the solid wall can move freely, and the balance equation in this direction can be obtained (Fig. 3b):

Figure 3 Balance at Three Medium Contact Line

Where θ It is called contact angle. If medium 2 is air, medium 3 is liquid, and θ<π /2, the solid is said to be hydrophilic to the liquid; If θ>π /2, the solid is said to hate the liquid. θ The smaller the liquid, the higher the degree of infiltration of the solid.

Capillary phenomenon

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When a thin pipe is inserted into the liquid, the liquid will climb or fall in the pipe due to the surface tension on the contact surface of liquid, gas and solid. set up r Is the inner radius of the tube, and the liquid surface in the tube is approximately regarded as a spherical cap (Figure 4). In case of pipe wall infiltration, the resultant force of surface tension is:

It shall be balanced with the weight of the liquid higher than the pipe:

Where h Is the liquid level; ρ Is the density of the liquid; g yes Gravitational acceleration ； σ = σ twenty-three 。 Thus

The above formula can also be determined by Laplace formula Export, note in formula (1)

Fig. 4 Fluid climb in capillary tube

so r Smaller h The larger. Therefore, only when the pipe diameter is very small can the water resist gravity and climb higher in the pipe. This explains the water absorption of absorbent paper. When the free liquid surface bulges in the middle, it does not rise, but drops below the liquid level outside the pipe. Capillary action is also an important factor affecting the flow of groundwater or oil in porous media (see Seepage Mechanics).

Spherical droplet

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Spherical droplet

The mercury drops on the glass plate are basically spherical, because all the molecules in the thin layer on the outer surface of the mercury drops are in a high potential state. The calculation shows that if the total potential energy of the molecule is minimized, the surface must be spherical. If we try to eliminate the influence of gravity, for example, put the liquid drop in another liquid with the same specific gravity and no chemical reaction with the liquid drop, or fall freely in a vacuum, or in the environment of weightless satellites and rockets, the liquid drop will appear ideal spherical. Spherical soap bubbles and dewdrops on lotus leaves can also be explained in the same way.

Ripple

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Surface tension sometimes plays an important role in the movement of liquids. For example, the ripples generated when the breeze sweeps over the water surface are water waves whose surface tension plays a major role.

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