Where do capillary phenomena occur in nature? Wetting and capillarity

Capillarity (from lat. Capillaris - hair) - physical phenomenon, which consists in the ability of liquids to change the level in tubes, narrow channels of arbitrary shape, and porous bodies. A rise in liquid occurs in cases where channels are wetted by liquids, for example, water in glass tubes, sand, soil, etc. A decrease in liquid occurs in tubes and channels that are not wetted by liquid, for example, mercury in a glass tube. The life activity of animals and plants, chemical technologies, and everyday phenomena (for example, lifting kerosene along the wick in a kerosene lamp, wiping hands with a towel) are based on capillarity. Soil capillarity is determined by the rate at which water rises in the soil and depends on the size of the spaces between soil particles. Capillaries are thin tubes, as well as the thinnest vessels in the human body and other animals.

The curvature of the liquid meniscus is especially well observed in thin tubes called capillaries. If a capillary is lowered into a vessel with liquid, the walls of which are wetted by the liquid, then the liquid rises along the capillary to a certain height h(Fig. 50.1). This is explained by the fact that the curvature of the liquid surface causes additional molecular pressure. If the surface is convex and has a spherical shape, then the additional pressure will be

Figure 50.1

In the case of a convex meniscus (r > 0), the total pressure is greater than atmospheric pressure and the liquid descends through the capillary. If the meniscus is concave (r< 0), суммарное давление меньше атмосферного и жидкость поднимается по капилляру. Жидкость поднимается (или опускается) до тех пор, пока гидростатическое давление р = ρqh столба жидкости высотой h не компенсирует добавочное (Лапласовское) давление р л. (Лаплас установил зависимость этого давления от формы мениска.) В этом случае

where ρ is the density of the liquid; g is the acceleration of gravity, r is the radius of the capillary, R is the radius of curvature of the meniscus.

Height of rise (depth of descent) of liquid in the capillary:

.

§ 51. The phenomenon of capillarity in everyday life, nature and technology

The phenomenon of capillarity in everyday life plays a huge role in a wide variety of processes occurring in nature. For example, the penetration of moisture from the soil into plants, stems and leaves is due to capillarity. Plant cells form capillary channels, and the smaller the radius of the capillary, the higher the liquid rises through it. The blood circulation process is also associated with capillarity. Blood vessels are capillaries.

Soil capillarity is especially important. Through the smallest vessels, moisture from the depths is mixed to the surface of the soil. If they want to reduce the evaporation of moisture, then the soil is loosened, destroying the capillaries. In order to increase the flow of moisture from the depths, the soil is rolled, increasing the number of capillary channels. In technology, capillary phenomena are of great importance in drying processes and in construction.

§ 52. Pressure under a curved surface of a liquid

A spherical convex surface produces additional pressure on the liquid caused by internal tension forces directed into the liquid, R is the radius of the sphere. If the surface of a liquid is concave, then the resulting force of surface tension is directed out of the liquid and the pressure inside the liquid.

Excessive pressure inside a soap bubble radius R caused by the action of both surface layers of a thin spherical soap film:

Figure 52.1

In the general case, excess pressure for an arbitrary liquid surface is described by Laplace’s formula:

, (52.1)

where and are the radii of curvature of any two mutually perpendicular sections of the liquid surface at a given point.

The radius of curvature is positive if the center of curvature of the corresponding section is inside the fluid, and negative if the center of curvature is outside the fluid.

Lesson objectives:

• study of the most important phenomena and properties of nature - wetting, non-wetting, capillary phenomena.

Lesson objectives:

Educational: deepening into the phenomena of wetting and non-wetting, as well as the capillarity of liquids, to learn the scope of their application;

Developmental: to develop in students creative thinking and speech;

Key terms:

Wetting is a surface phenomenon that consists in the interaction of the surface solid(other liquid) with liquid.

Contact angle (shows the degree of wetting)- this is the angle formed by tangent planes to the interfacial surfaces that limit the wetting liquid, while the vertex of the angle lies on the dividing line of the three phases.

The video shows the capillary flow of liquid

Curvature of the surface leads to the appearance of additional capillary pressure in the liquid Dp, the value of which is related to the average curvature r of the surface by the Laplace equation: Dp = p1 – p2 = 2s12/r, where (s12 is the surface tension at the interface of two media; p1 and p2 are the pressure in liquid 1 and medium 2 in contact with it.

Applications Wetting can explain the use of detergents, the fact why hands that are covered in oil or grease are easier to wash off with gasoline than with water, as well as why geese come out dry from water, etc. The explanation of capillary phenomena occurs in the movement of water in plants and capillaries. And also when cultivating the soil. For example: preserving moisture by loosening, etc., destroying capillaries. And also the capillary phenomenon can explain electrical and nuclear phenomena, allows you to detect cracks with an opening of 1 micron, which cannot be seen with the naked eye.

Conclusions.

We live in the world of the most amazing phenomena nature. There are a lot of them. We encounter them every day without thinking about the essence. But man, as an intelligent phenomenon, must understand the essence of these phenomena. Such phenomena as wetting and non-wetting, capillary phenomenon are very widespread in technology and nature. They are indispensable in everyday life and in solving scientific and technical problems. This knowledge gives us answers to many questions. For example, why a drop appears in free flight or why planets and stars have a spherical shape; some solid bodies are well wetted by liquid, while others are not. Why can capillary phenomena absorb nutrients, moisture from the soil of plant roots, or why blood circulation in animal organisms is based on capillary phenomena, etc.

Control block:

1.What is a capillary?

2.How to recognize wetting and non-wetting?

3.Give an example of wetting.

4.What is capillary phenomenon?

5.Give an example of non-wetting.

Homework.

Robot progress

1.Place drops of water and oil on glass, aluminum, copper, paraffin plates.

2. Sketch the shapes of the drops.

3.Look at the drops and draw conclusions about the relationship between the molecules of a solid and a liquid.

4. Enter these results into a table.

5.Add a little olive oil to the mixture of water and sparta using a syringe.

6.Pass a wire through the center of the oil ball and rotate it.

7.Notice how the shape of the drop changes.

8.Draw conclusions about the shape of the liquid surface.

The film of water that is on the surface provides support for many organisms when moving. It is observed in small insects and arachnids. The most famous to us are water striders, which rest on the water only with the end segments of their widely spaced legs. The foot, which is covered with a waxy coating, is not wetted by water. The surface layer of water bends under the pressure of the foot, and small depressions are formed. (Figure 6) The feathers and down of waterfowl are always richly lubricated with fatty secretions of special glands. This explains their waterproofness. A thick layer of air, which is located between the feathers of a duck and is not displaced from there by water, not only protects the duck from heat loss, but also greatly increases its reserve of buoyancy.

The existence of wetting and contact angle leads to curvature of the liquid surface near the walls of the vessel. If the liquid wets the walls, the surface has a concave shape; if it does not, it is convex. This kind of curved surface of a liquid is called a meniscus. (Fig. 10.11)

Wetting	Non-wetting

Under a curved surface in a capillary, the pressure will differ from the pressure under a flat surface by the amount
. Between the liquid in the capillary and in a wide vessel such a level difference is established so that hydrostatic pressure
balanced capillary pressure
. In the case of a spherical meniscus

. The radius of curvature of the meniscus can be expressed through the contact angle and capillary radius r
, Then
,

In case of wetting
And height of liquid rise in a capillary the larger the smaller the capillary radiusr .

The capillary phenomenon takes an exceptional role in human life. The supply of moisture to plants and trees occurs precisely with the help of capillaries, which are found in every plant. Capillary phenomena can also play a negative role. For example, in construction. The need to waterproof building foundations is caused by capillary phenomena.

Questions for self-control

1. Describe the liquid state in comparison with crystals and gases.

2.What is long-range and short-range order?

3.What does the radial distribution function allow you to do? Draw it for crystals, liquids and gases.

4.What is surface tension coefficient?

6.What is wetting? What is a measure of wetting? Give examples of processes that require good wetting.

7.What determines the height of the liquid rising in the capillary?

Lecture No. 5 (11)

Properties of solids

1. Amorphous and crystalline bodies. Structure and types of crystals. De

defects in crystals.

2. Mechanical properties of crystals. Mechanism of plastic deformation

tions. Elastic tensile deformation. Hooke's law.

Amorphous and crystalline bodies.

In amorphous bodies exists close order arrangement of atoms. Crystals have in a long way arrangement of atoms. Amorphous body isotropic, crystalline – anisotropic.

During cooling and heating, the temperature versus time curves are different for amorphous and crystalline bodies. For amorphous bodies, the transition from liquid to solid can be tens of degrees. For crystals, the melting point is constant. There may be cases when the same substance, depending on the cooling conditions, can be obtained in both a crystalline and an amorphous solid state. For example, glass very slow cooling melt can crystallize. In this case, reflection and scattering of light will occur at the boundaries of the small crystals formed, and the crystallized glass loses its transparency.

Crystal lattice. The main property of crystals is the regularity of the arrangement of atoms in them. The set of points at which atoms (more precisely, atomic nuclei) are located is spoken of as crystal lattice, and the points themselves are called lattice nodes.

The main characteristic of the crystal lattice is spatial periodicity its structure: the crystal seems to consist of repeating parts(cells).

We can break the crystal lattice into exactly identical parallelepipeds containing the same number of equally spaced atoms. The crystal represents set of parallelepipeds, parallel shifted relative to each other. If you move the crystal lattice parallel to itself by a distance of the length of the edge, then the lattice will align with itself. These offsets are called broadcasts, and the symmetry of the lattice with respect to these displacements is said to be translational symmetry(parallel translation, rotation about an axis, mirror reflection, etc.).

If there is an atom at the vertex of any elementary cell, then the same atoms must obviously be located at all other vertices of this and other cells. A collection of identical and identically located atoms is called Bravais lattice of this crystal. She imagines crystal lattice skeleton, personifying its entire translational symmetry, i.e. all its periodicity.

Classification of different types of crystal symmetry is based primarily on classification different types of Bravais gratings.

The most symmetrical Bravais lattice is a lattice having the symmetry Cuba(cubic system). There are three different

Bravais lattices related to the cubic system: simple
	body-centered(in the center of the cube there is an atom), face-centered (except for the atoms at the vertices - there is also an atom in

centers of all their faces). In addition to cubic, there are tetragonal, rhombic, monoclinic and others (we will not consider).

The Bravais lattice, generally speaking, does not include all the atoms in the crystal. Real crystal lattice can be represented as a collection of several Bravais lattices pushed into one another.

Physical types of crystals.

Based on the type of particles from which the crystal lattice is built, and the nature of the interaction forces between them, ionic, atomic, metallic and molecular crystals are distinguished.

1. Ionic crystals. Positive and negative ions are located alternately at the nodes of the crystal lattice. These ions are attracted to each other by electrostatic (Coulomb) forces. Example: Rock salt grid
(Fig. 11.1).

2. Atomic crystals. Typical representatives are graphite and diamond. Connection between atoms - covalent. In this case, each of the valence electrons is included in an electron pair that connects this atom with one of its neighbors.

3. Metal crystals. The gratings consist of positively charged ions, between which are “free” electrons. These electrons are “collectivized” and can be considered as a kind of “electron gas”. Electrons play the role of “cement”, holding the “+” ions, otherwise the lattice would disintegrate. Ions hold electrons within the lattice.

4. Molecular crystals. An example is ice. There are molecules in the nodes, which are interconnected by van der Waals forces, i.e. forces interaction molecular electric dipoles.

There can be several types of bonds at the same time (for example, in graphite - covalent, metallic and van der Waals).

Defects in crystals.

In real crystal lattices there is deviations from the ideal arrangement of atoms in the lattices we have considered so far. All such deviations are called lattice defects.

Point defects- those in which short-range order is disrupted:

1 – absence of an atom at any site (vacancy) (Fig. 11.2);
2 – replacement of one’s own atom with “strangers” (Fig. 11.3);
3 – introduction of one’s own atom or someone else’s into the interstitial space (Fig. 11.4)

Another type of defect is dislocations– linear defects of the crystal lattice, violating the correct alternation of atomic planes. They disrupt long-range order, distorting its entire structure. They play an important role in the mechanical properties of solids. The simplest types of dislocations are edge and screw. In the case of an edge dislocation, an extra crystalline plane is pushed between adjacent layers of atoms (Fig. 11.5).

In the case of a screw dislocation, part of the crystal lattice is shifted relative to another (Fig. 11.6)

Mechanical properties of crystals.

Mechanism of plastic deformation. The basis of plastic deformation of metals is movement of dislocations. The essence of plastic deformation is shear, as a result of which one part of the crystal is displaced relative to another due to the sliding of dislocations. In Fig. 11.7 (a, b, c) shows the movement of an edge dislocation with the formation unit shift steps.

Note that in reality the atoms jump to new positions in small groups one at a time. This alternate movement of atoms can be represented as the movement of a dislocation. Dislocations cause that plastic deformation of real crystals occurs under the influence of stresses several orders of magnitude lower than those calculated for ideal crystals. But if the dislocation density and impurity concentration are high, then this leads to strong deceleration of dislocations and cessation of their movement. As a result, paradoxically, the strength of the material increases.

Tensile strain. Hooke's law.

The nature of the change in the forces connecting atoms in a solid depending on the distance between them is qualitatively the same as in gases and liquids (Fig. 11.8). If to the rod length and cross section apply force
(Fig. 11.9), then under the influence of this force the rod will lengthen by a certain amount
. At the same time the distances between neighboring atoms along the axis of the rod will increase by a certain amount
(Fig. 11.8). Lengthening the entire chain of atoms
associated with
obvious relation:

(*) (Where – distance between neighboring atoms at ). When atoms are displaced from their equilibrium positions, attractive forces arise between them , and increases with increasing :

When wetting, surface curvature occurs, changing the properties of the surface layer. The existence of excess free energy at a curved surface leads to so-called capillary phenomena - very unique and important.

Let us first carry out a qualitative examination using the example of a soap bubble. If we open the end of the tube in the process of blowing a bubble, we will see that the bubble located at its end will decrease in size and be drawn into the tube. Since the air from the open end communicated with the atmosphere, to maintain the equilibrium state of the soap bubble, it was necessary that the pressure inside be greater than the outside. If you connect the tube to a monometer, then a certain level difference is recorded on it - excess pressure DP in the volumetric phase of the gas on the concave side of the bubble surface.

Let us establish a quantitative relationship between DP and the radius of curvature of the surface 1/r between two volumetric phases that are in a state of equilibrium and separated by a spherical surface. (for example, a gas bubble in a liquid or a drop of liquid in the vapor phase). To do this, we use the general thermodynamic expression for free energy under the condition T = const and the absence of transfer of matter from one phase to another dn i = 0. In a state of equilibrium, variations in the surface ds and volume dV are possible. Let V increase by dV and s by ds. Then:

dF = - P 1 dV 1 - P 2 dV 2 + sds.

In equilibrium, dF = 0. Taking into account the fact that dV 1 = dV 2, we find:

P 1 - P 2 = s ds/dV.

So P 1 > P 2 . Considering that V 1 = 4/3 p r 3, where r is the radius of curvature, we obtain:

Substitution gives Laplace's equation:

P 1 - P 2 = 2s/r. (1)

In a more general case, for an ellipsoid of revolution with main radii of curvature r 1 and r 2, Laplace’s law is formulated:

P 1 - P 2 = s/(1/R 1 - 1/R 2).

For r 1 = r 2 we obtain (1), for r 1 = r 2 = ¥ (plane) P 1 = P 2 .

The difference DP is called capillary pressure. Let us consider the physical meaning and consequences of Laplace's law, which is the basis of theories of capillary phenomena. The equation shows that the pressure difference in the bulk phases increases with increasing s and with decreasing radius of curvature. Thus, the higher the dispersion, the greater the internal pressure of a liquid with a spherical surface. For example, for a drop of water in the vapor phase at r = 10 -5 cm, DP = 2. 73. 10 5 dynes/cm 2 » 15 at. Thus, the pressure inside the drop compared to the steam is 15 atm higher than in the steam phase. It must be remembered that regardless of state of aggregation phases, in a state of equilibrium, the pressure on the concave side of the surface is always greater than on the convex side. Uranium provides the basis for the experimental measurement of s by the method of maximum bubble pressure. One of the most important consequences of the existence of capillary pressure is the rise of liquid in the capillary.

Capillary phenomena are observed in liquid-containing

In narrow vessels in which the distance between the walls is commensurate with the radius of curvature of the liquid surface. Curvature occurs as a result of the interaction of the liquid with the walls of the vessel. The specific behavior of a liquid in capillary vessels depends on whether the liquid wets or does not wet the walls of the vessel, more precisely on the value of the contact angle.

Let us consider the position of the liquid levels in two capillaries, one of which has a lyophilic surface and therefore its walls are wetted, and the other has a lyophobic surface and is not wetted. In the first capillary the surface has negative curvature. Additional Laplace pressure tends to stretch the liquid. (pressure is directed towards the center of curvature). The pressure under the surface is lower than the pressure at the flat surface. As a result, a buoyant force arises, lifting the liquid in the capillary until the weight of the column balances the acting force. In the second capillary, the curvature of the surface is positive, additional pressure is directed into the liquid, as a result, the liquid in the capillary descends.

At equilibrium, the Laplace pressure is equal to the hydrostatic pressure of a liquid column of height h:

DP = ± 2s/r = (r - r o) gh, where r, r o are the densities of the liquid and gas phase, g is the acceleration of gravity, r is the radius of the meniscus.

In order to relate the height of the capillary rise to the wetting characteristic, the radius of the meniscus will be expressed in terms of the wetting angle Q and the capillary radius r 0. It is clear that r 0 = r cosQ, the height of the capillary rise will be expressed in the form (Jurin’s formula):

h = 2sсosQ / r 0 (r - r 0)g

In the absence of wetting Q>90 0 , сosQ< 0, уровень жидкости опускается на величину h. При полном смачивании Q = 0, сosQ = 1, в этом случае радиус мениска равен радиусу капилляра. Измерение высоты капиллярного поднятия лежит в основе одного из наиболее точных методов определения поверхностного натяжения жидкостей.

The capillary rise of liquids explains a number of well-known phenomena and processes: the impregnation of paper and fabrics is caused by the capillary rise of liquid in the pores. The waterproofness of fabrics is ensured by their hydrophobicity - a consequence of negative capillary rise. The rise of water from the soil occurs due to the structure of the soil and ensures the existence of the Earth's vegetation, the rise of water from the soil along the trunks of plants occurs due to the fibrous structure of wood, the process of blood circulation in the blood vessels, the rise of moisture in the walls of the building (waterproofing is laid), etc.

Thermodynamic reactivity (t.r.s.).

Characterizes the ability of a substance to transform into some other state, for example into another phase, or enter into a chemical reaction. It indicates the distance of a given system from the state of equilibrium under given conditions. T.r.s. is determined by chemical affinity, which can be expressed by a change in the Gibbs energy or a difference in chemical potentials.

R.s depends on the degree of dispersion of the substance. A change in the degree of dispersion can lead to a shift in phase or chemical equilibrium.

The corresponding increment in the Gibbs energy dG d (due to a change in dispersion) can be represented as a combined equation of the first and second laws of thermodynamics: dG d = -S dT + V dp

For an individual substance V =V mol and at T = const we have: dG d = V mol dp or DG d = V mol Dp

Substituting the Laplace relation into this equation, we obtain dG d = s V mol ds/dV

for spherical curvature: dG d =±2 s V mol /r (3)

The equations show that the increment reactivity, caused by a change in dispersion, is proportional to the curvature of the surface, or dispersion.

If the transition of a substance from the condensed phase to the gaseous phase is considered, then the Gibbs energy can be expressed in terms of vapor pressure, taking it as ideal. Then the additional change in the Gibbs energy associated with the change in dispersion is:

dG d = RT ln (p d / p s) (4), where p d and p s - pressure saturated steam over curved and flat surfaces.

Substituting (4) into (3) we obtain: ln (p d / p s) = ±2 s V mol /RT r

The relationship is called the Kelvin-Thomson equation. From this equation it follows that with positive curvature, the saturated vapor pressure over a curved surface will be greater, the greater the curvature, i.e. smaller radius of the drop. For example, for a drop of water with a radius r = 10 -5 cm (s = 73, V mol = 18) p d / p s = 0.01, i.e. 1%. This consequence of the Kelvin-Thomson law allows us to predict the phenomenon of isotremic distillation, which consists in the evaporation of the smallest drops and the condensation of vapor on larger drops and on a flat surface.

With negative curvature, which occurs in capillaries during wetting, an inverse relationship is obtained: the saturated vapor pressure above the curved surface (above the drop) decreases with increasing curvature (with decreasing capillary radius). Thus, if a liquid wets a capillary, then condensation of vapors in the capillary occurs at lower pressure than on a flat surface. This is why Kelvin's equations are often called the equation of capillary condensation.

Let us consider the effect of particle dispersion on their solubility. Taking into account that the change in the Gibbs energy is expressed through the solubility of a substance in different dispersed states similar to relation (4), we obtain for non-electrolytes:

ln(c d /c a) = ±2 s V mol /RT r where c d and c a are the solubility of the substance in a highly dispersed state and the solubility at equilibrium with large particles of this substance

For an electrolyte that dissociates into n ions in solution, we can write (neglecting the activity coefficients):

ln(a d /a s) = n ln (c d /c s) = ±2 s V mol /RT r, where a d and a s are the activities of the electrolyte in solutions saturated with respect to the highly dispersed and coarsely dispersed state. The equations show that with increasing dispersion, solubility increases, or the chemical potential of particles disperse system greater than that of a large particle by 2 s V mol /r. At the same time, solubility depends on the sign of the surface curvature, which means that if the particles of a solid have irregular shape with positive and negative curvature and are in a saturated solution, then areas with positive curvature will dissolve, and areas with negative curvature will grow. As a result, the particles of the soluble substance acquire over time a completely definite shape that corresponds to the equilibrium state.

The degree of dispersion may also affect the equilibrium chemical reaction: - DG 0 d = RT ln (K d / K), where DG 0 d is the increase in chemical affinity due to dispersity, K d and K are the equilibrium constants of reactions involving dispersed and non-dispersed substances.

With increasing dispersion, the activity of the components increases, and in accordance with this, the chemical equilibrium constant changes in one direction or another, depending on the degree of dispersion of the starting substances and reaction products. For example, for the decomposition reaction of calcium carbonate: CaCO 3 « CaO + CO 2

An increase in the dispersion of the initial calcium carbonate shifts the equilibrium to the right, and the pressure of carbon dioxide above the system increases. Increasing the dispersion of calcium oxide leads to the opposite result.

For the same reason, with increasing dispersion, the connection between the water of crystallization and the substance weakens. So a macrocrystal of Al 2 O 3. 3 H 2 O gives up water at 473 K, while in a precipitate of particles of colloidal sizes, the crystalline hydrate decomposes at 373 K. Gold does not interact with hydrochloric acid, and colloidal gold dissolves in it. Coarsely dispersed sulfur does not react noticeably with silver salts, and colloidal sulfur forms silver sulfide.

The curvature of the liquid surface at the edges of the vessel is especially clearly visible in narrow tubes, where the entire free surface of the liquid is curved. In tubes with a narrow cross-section, this surface is part of a sphere; it is called meniscus. A wetting liquid forms a concave meniscus (Fig. 1, a), while a non-wetting liquid forms a convex meniscus (Fig. 1, b).

Since the surface area of ​​the meniscus is greater than the cross-sectional area of ​​the tube, under the influence of molecular forces the curved surface of the liquid tends to straighten.

Surface tension forces create additional (Laplacian) pressure under the curved surface of the liquid.

For calculation overpressure Let us assume that the surface of the liquid has the shape of a sphere of radius R (Fig. 2.a), from which a spherical segment is mentally cut off, resting on a circle of radius .

Each infinitesimal element of the length of this contour is acted upon by a surface tension force tangent to the surface of the sphere, the modulus of which is . Let's decompose the vector into two force components. From Figure 2, a we see that the geometric sum of forces for two selected diametrically opposed elements is equal to zero. Therefore, the surface tension force is directed perpendicular to the section plane into the liquid (Fig. 2, c) and its modulus is equal to

The excess pressure created by this force

where is the area of ​​the base of the spherical segment. That's why

If the surface of the liquid is concave, then the surface tension force is directed out of the liquid (Fig. 2, b) and the pressure under the concave surface of the liquid is less than under the flat surface by the same amount. This formula determines the Laplace pressure for the case of a spherical free surface of the liquid. It is a special case of Laplace’s formula, which determines the excess pressure for an arbitrary liquid surface of double curvature:

where are the radii of curvature of any two mutually perpendicular normal sections surface of the liquid. The radius of curvature is positive if the center of curvature of the corresponding section is inside the fluid, and negative if the center of curvature is outside the fluid. For cylindrical surface excess pressure.

If you place a narrow tube ( capillary) one end into a liquid poured into a wide vessel, then due to the presence of the Laplace pressure force, the liquid in the capillary rises (if the liquid is wetting) or falls (if the liquid is non-wetting) (Fig. 3, a, b), since under the flat surface of the liquid in There is no excess pressure in a wide vessel.