Capillary phenomena, surface phenomena at the boundary of a liquid with another medium, associated with the curvature of its surface. The curvature of the liquid surface at the boundary with the gas phase occurs as a result of the action of the surface tension of the liquid, which tends to reduce the interface and give the limited volume of liquid the shape of a ball. Since the sphere has a minimum surface area for a given volume, this shape corresponds to the minimum surface energy of the liquid, i.e. its stable equilibrium state. In the case of sufficiently large masses of liquid, the effect of surface tension is compensated by gravity, so a low-viscosity liquid quickly takes the form of a vessel in which it is poured, and it is free. the surface appears almost flat.
In the absence of gravity or in the case of very small masses, the liquid always takes on a spherical shape (drop), the curvature of the surface of which determines many things. properties of a substance. Therefore, capillary phenomena are pronounced and play a significant role in conditions of weightlessness, during the crushing of a liquid in a gaseous medium (or spraying a gas into a liquid) and the formation of systems consisting of many drops or bubbles (emulsions, aerosols, foams), during the emergence of a new phase of liquid droplets during the condensation of vapors, vapor bubbles during boiling, crystallization nuclei. When a liquid comes into contact with condensed bodies (another liquid or a solid body), the curvature of the interface occurs as a result of the action of interfacial tension.
In the case of wetting, for example, when a liquid comes into contact with a solid vessel wall, the attractive forces acting between the molecules of the solid and the liquid cause it to rise along the vessel wall, as a result of which the portion of the liquid surface adjacent to the wall takes a concave shape. In narrow channels, for example, cylindrical capillaries, a concave meniscus is formed - a completely curved liquid surface (Fig. 1).
Rice. 1. Capillary elevation h liquid wetting the walls of a capillary of radius r; q - contact angle of wetting.
capillary pressure.
Since the forces of surface (interfacial) tension are directed tangentially to the surface of the liquid, the curvature of the latter leads to the appearance of a component directed inside the volume of the liquid. As a result, capillary pressure arises, the value of which Dp is related to the average radius of curvature of the surface r 0 by the Laplace equation:
Dp = p 1 - p 2 \u003d 2s 12 / r 0, (1)
where p 1 and p 2 - pressure in liquid 1 and neighboring phase 2 (gas or liquid), s 12 - surface (interfacial) tension.
If the liquid surface is concave (r 0< 0), давление в ней оказывается пониженным по сравнению с давлением в соседней фазе p 1 < р 2 и Dp < 0. Для выпуклых поверхностей (r 0 >0) the sign of Dp is reversed. The negative capillary pressure that occurs when the walls of the capillary are wetted by liquid leads to the fact that the liquid will be sucked into the capillary until the weight of the liquid column height h will not balance the pressure drop Dp. In a state of equilibrium, the height of the capillary rise is determined by the Jurin formula:
where r 1 and r 2 are the densities of liquid 1 and medium 2, g is the acceleration of gravity, r is the radius of the capillary, q is the wetting angle. For liquids that do not wet the capillary walls, cos q< 0, что приводит к опусканию жидкости в капилляре ниже уровня плоской поверхности (h < 0).
From expression (2) follows the definition of the capillary constant of the liquid A= 1/2 . It has the dimension of length and characterizes the linear size Z[A, at which capillary phenomena become significant So, for water at 20 ° C a = 0.38 cm. In weak gravity (g: 0), the value A increases. In the area of particle contact, capillary condensation leads to contraction of particles under the action of reduced pressure Dp< 0.
Kelvin equation.
The curvature of the liquid surface leads to a change in the equilibrium vapor pressure above it R compared to saturated steam pressure ps above a flat surface at the same temperature T. These changes are described by the Kelvin equation:
where is the molar volume of the liquid, R is the gas constant. The decrease or increase in vapor pressure depends on the sign of the curvature of the surface: over convex surfaces (r 0 > 0) p > p s ; over concave (r 0< 0) R< р s . . So, above the drops, the vapor pressure is increased; in bubbles, on the contrary, it is lowered.
Based on the Kelvin equation, the filling of capillaries or porous bodies is calculated at capillary condensation. Since the values R are different for particles of different sizes or for surface areas with depressions and protrusions, equation (3) also determines the direction of the transfer of matter in the process of transition of the system to an equilibrium state. This leads, in particular, to the fact that relatively large drops or particles grow due to the evaporation (dissolution) of smaller ones, and surface irregularities of non-crystalline bodies are smoothed out due to the dissolution of protrusions and healing of depressions. Noticeable differences in vapor pressure and solubility occur only at sufficiently small r 0 (for water, for example, at r 0. Therefore, the Kelvin equation is often used to characterize the state of colloidal systems and porous bodies and processes in them.
Rice. 2. Fluid displacement by length l in a capillary of radius r; q - contact angle.
capillary impregnation.
The decrease in pressure under the concave menisci is one of the reasons for the capillary movement of the liquid towards the menisci with a smaller radius of curvature. A special case of this is the impregnation of porous bodies - the spontaneous absorption of liquids into lyophilic pores and capillaries (Fig. 2). Speed v the movement of the meniscus in a horizontally located capillary (or in a very thin vertical capillary, when the influence of gravity is small) is determined by the Poiseuille equation:
Where l is the length of the absorbed liquid section, h is its viscosity, Dp is the pressure drop in the section l, equal to the capillary pressure of the meniscus: Dp = - 2s 12 cos q/r. If the contact angle q does not depend on the speed v, it is possible to calculate the amount of absorbed liquid during the time t from the ratio:
l(t) = (rts 12 cos q/2h) l/2 . (5)
If q is a function v, That l And v associated with more complex relationships.
Equations (4) and (5) are used to calculate the impregnation rate when treating wood with antiseptics, dyeing fabrics, applying catalysts to porous carriers, leaching and diffusion extraction of valuable rock components, etc. To speed up the impregnation, surfactants are often used that improve wetting by reducing contact angle q. One of the options for capillary impregnation is the displacement of one liquid from a porous medium by another, which does not mix with the first and better wetting the surface of the pores. This is the basis, for example, of methods for extracting residual oil from reservoirs with aqueous solutions of surfactants, and methods of mercury porosimetry. Capillary absorption of solutions into pores and displacement of immiscible liquids from pores, accompanied by adsorption and diffusion of components, are considered by physicochemical hydrodynamics.
In addition to the described equilibrium states of a liquid and its movement in pores and capillaries, the equilibrium states of very small volumes of a liquid, in particular, thin layers and films, are also referred to as capillary phenomena. These capillary phenomena are often referred to as type II capillary phenomena. They are characterized, for example, by the dependence of the surface tension of the liquid on the radius of the drops and by the linear tension. Capillary phenomena were first studied by Leonardo da Vinci (1561), B. Pascal (17th century), and J. Jurin (18th century) in experiments with capillary tubes. The theory of capillary phenomena was developed in the works of P. Laplace (1806), T. Jung (1804), A. Yu. Davydov (1851), J. W. Gibbs (1876), I. S. Gromeka (1879, 1886). The beginning of the development of the theory of capillary phenomena of the second kind was laid by the works of B. V. Deryagin and L. M. Shcherbakov.
When wetting, surface curvature occurs, which changes the properties of the surface layer. The existence of an excess of free energy near a curved surface leads to the so-called capillary phenomena - very peculiar and important.
Let us first conduct a qualitative consideration on the example of a soap bubble. If, in the process of blowing the bubble, we open the end of the tube, 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, in order to maintain the equilibrium state of the soap bubble, it is necessary that the pressure inside was greater than the outside. If, at the same time, a tube is connected to a monometer, then a certain level difference is recorded on it - an excess pressure DP in the volumetric phase of the gas from the concave side of the bubble surface.
Let us establish a quantitative relationship between DP and the surface curvature radius 1/r between two bulk phases that are in equilibrium and separated by a spherical surface. (for example, a gas bubble in a liquid or a drop of liquid in a 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. Variations in the surface ds and volume dV are possible in the equilibrium state. Let V increase by dV and s by ds. Then:
dF = - P 1 dV 1 - P 2 dV 2 + sds.
In the state of equilibrium dF = 0. Taking into account the fact that dV 1 = dV 2 , we find:
P 1 - P 2 \u003d s ds / dV.
Thus P 1 > P 2 . Given that V 1 = 4/3 p r 3 , where r is the radius of curvature, we get:
Substitution gives Laplace's equation:
P 1 - P 2 \u003d 2s / r. (1)
More generally, for an ellipsoid of revolution with principal radii of curvature r 1 and r 2 , Laplace's law is formulated:
P 1 - P 2 \u003d 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 the Laplace law, which is the basis of the theories of capillary phenomena. The equation shows that the pressure difference in 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 water drop 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 with vapor, is 15 atm higher than in the vapor phase. It must be remembered that, regardless of the state of aggregation of the phases, in a state of equilibrium, the pressure on the concave side of the surface is always greater than on the convex one. The equation provides the basis for experimental measurement of s by the method of the highest 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 fluid-containing
In narrow vessels, in which the distance between the walls is commensurate with the radius of curvature of the liquid surface. Curvature results from the interaction of the fluid with the walls of the vessel. The specificity of the 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 of wetting.
Let us consider the position of liquid levels in two capillaries, one of which has a lyophilic surface and therefore its walls are wetted, while the other has a lyophilized surface and is not wetted. In the first capillary, the surface has a negative curvature. The additional Laplace pressure tends to stretch the liquid. (pressure is directed towards the center of curvature). The pressure below the surface is lower than the pressure at the flat surface. As a result, a buoyant force arises that lifts the liquid in the capillary until the weight of the column balances the acting force. In the second capillary, the surface curvature is positive, the additional pressure is directed into the liquid, as a result, the liquid in the capillary descends.
At equilibrium, the Laplacian pressure is equal to the hydrostatic pressure of a liquid column of height h:
DP \u003d ± 2s / r \u003d (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 meniscus radius.
In order to relate the height of the capillary rise to the wetting characteristic, we express the meniscus radius in terms of the wetting angle Q and the radius of the capillary r 0. It is clear that r 0 = r cosQ, the height of the capillary rise is expressed as (Jurin's formula):
h \u003d 2scosQ / 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.
A number of well-known phenomena and processes are explained by the capillary rise of liquids: the impregnation of paper and fabrics is due to the capillary rise of liquid in the pores. The water resistance 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 vegetation cover of the Earth, 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 (lay waterproofing), etc.
Thermodynamic reactivity (t.r.s.).
It characterizes the ability of a substance to go into some other state, for example, into another phase, to enter into a chemical reaction. It indicates the remoteness of the given system from the state of equilibrium under given conditions. T.r.s. is determined by chemical affinity, which can be expressed as 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 the phase or chemical equilibrium.
The corresponding increase 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 \u003d ± 2 s V mol / r (3)
The equations show that the increase in reactivity due to a change in dispersion is proportional to the curvature of the surface, or dispersion.
If we consider the transition of a substance from a condensed phase to a gaseous one, 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 \u003d RT ln (p d / p s) (4), where p d and p s are the saturated vapor pressure over curved and even surfaces.
Substituting (4) into (3) we get: ln (p d / p s) = ±2 s V mol /RT r
The ratio is called the Kelvin-Thomson equation. It follows from this equation that with a positive curvature, the saturated vapor pressure over a curved surface will be the greater, the greater the curvature, i.e. smaller droplet radius. For example, for a drop of water with a radius of 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 makes it possible 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 that occurs in capillaries during wetting, an inverse relationship is obtained: the saturated vapor pressure over the curved surface (above the drop) decreases with increasing curvature (with decreasing capillary radius). Thus, if the liquid wets the capillary, then the vapor condensation in the capillary occurs at a lower pressure than on a flat surface. This is why the Kelvin equations are often referred to as the capillary condensation equation.
Let us consider the influence 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 a different dispersed state, similarly 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 a substance in a finely dispersed state and the solubility in equilibrium with large particles of this substance
For an electrolyte that dissociates in solution into n ions, we can write (neglecting the activity coefficients):
ln(a d /a s) \u003d n ln (c d /c s) \u003d ±2 s V mol /RT r, where a d and a s are the electrolyte activities in solutions saturated with respect to in the highly dispersed y and coarsely dispersed state. The equations show that with increasing dispersion, the solubility increases, or the chemical potential of the particles of the disperse system is 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 an irregular shape with positive and negative curvature and are in a saturated solution, then the areas with positive curvature will dissolve, and those with negative curvature will grow. As a result, the particles of the dissolved substance eventually acquire a well-defined shape corresponding to the equilibrium state.
The degree of dispersion can also affect the equilibrium of a chemical reaction: - DG 0 d \u003d RT ln (K d / K), where DG 0 d is the increment in chemical affinity due to dispersion, K d and K are the equilibrium constants of reactions involving dispersed and non-dispersed substances .
With an increase in 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 dispersity of the initial calcium carbonate shifts the equilibrium to the right, and the pressure of carbon dioxide over the system increases. Increasing the dispersion of calcium oxide leads to the opposite result.
For the same reason, with an increase in dispersion, the bond of crystallization water with the substance is weakened. So Al 2 O 3 macrocrystal. 3 H 2 O gives up water at 473 K, while in a precipitate of particles of colloidal size, the crystalline hydrate decomposes at 373 K. Gold does not interact with hydrochloric acid, and colloidal gold dissolves in it. Coarse sulfur does not significantly interact with silver salts, and colloidal sulfur forms silver sulfide.
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Introduction
In this age of high technology, the natural sciences are becoming increasingly important in people's lives. People of the 21st century produce super-efficient computers, smartphones, and study the world around us deeper and deeper. I think that people are preparing for a new scientific and technological revolution that will change our future in a fundamental way. But no one knows when these changes will take place. Each person with his work can bring this day closer.
This research work is my small contribution to the development of physics.
This research work is devoted to the currently topical topic "Capillary phenomena". In life, we often deal with bodies pierced by many small channels (paper, yarn, leather, various building materials, soil, wood). Coming into contact with water or other liquids, such bodies very often absorb them. This project shows the importance of capillaries in the life of living and non-living organisms.
The purpose of the research work: to substantiate from the point of view of physics the cause of the movement of liquid through capillaries, to identify the features of capillary phenomena.
Object of study: the property of liquids, being absorbed, rise or fall through the capillaries.
Subject of research: capillary phenomena in animate and inanimate nature.
- To study theoretical material about the properties of a liquid.
- Familiarize yourself with the material on capillary phenomena.
- Conduct a series of experiments to determine the cause of the rise of fluid in the capillaries.
- Summarize the material studied during the work and formulate a conclusion.
Before proceeding to the study of capillary phenomena, it is necessary to get acquainted with the properties of the liquid, which play a significant role in capillary phenomena.
Surface tension
The term "surface tension" itself implies that the substance at the surface is in a "tight", that is, stressed state, which is explained by the action of a force called internal pressure. It pulls molecules into the liquid in a direction perpendicular to its surface. Thus, molecules located in the inner layers of a substance experience, on average, the same attraction in all directions from the surrounding molecules; the molecules of the surface layer are subjected to unequal attraction from the side of the inner layers of substances and from the side bordering the surface layer of the medium. For example, at the liquid-air interface, the liquid molecules located in the surface layer are more strongly attracted from the neighboring molecules of the inner layers of the liquid than from the air molecules. This is the reason for the difference in the properties of the surface layer of the liquid from the properties of its internal volumes.
Internal pressure causes the molecules located on the surface of the liquid to be drawn inward and thereby tends to reduce the surface to a minimum under given conditions. The force acting per unit length of the interface, causing the contraction of the surface of the liquid, is called the surface tension force or simply surface tension σ.
The surface tension of various liquids is not the same, it depends on their molar volume, the polarity of the molecules, the ability of the molecules to form hydrogen bonds with each other, etc.
As the temperature increases, the surface tension decreases linearly. The surface tension of a liquid is also influenced by the impurities present in it. Substances that reduce surface tension are called surface active agents (surfactants). In relation to water, surfactants are petroleum products, alcohols, ether, soap, and other liquid and solid substances. Some substances increase surface tension. Impurities of salts and sugar, for example.
This is explained by MKT. If the forces of attraction between the molecules of the liquid itself are greater than the forces of attraction between the molecules of the surfactant and the liquid, then the liquid molecules go inward from the surface layer, and the surfactant molecules are forced out to the surface. It is obvious that the salt and sugar molecules will be drawn into the liquid, and the water molecules will be pushed to the surface. Thus, surface tension, the basic concept of the physics and chemistry of surface phenomena, is one of the most important characteristics in practical terms as well. It should be noted that any serious scientific research in the field of physics of heterogeneous systems requires the measurement of surface tension. The history of experimental methods for determining surface tension, dating back more than two centuries, has gone from simple and crude methods to precision methods that allow finding surface tension with an accuracy of hundredths of a percent. Interest in this problem has especially increased in recent decades in connection with man's spacewalk, the development of industrial structure, where capillary forces in various devices often play a decisive role.
One such method for determining surface tension is based on raising a wetting liquid between two glass plates. They should be lowered into a vessel with water and gradually brought together parallel to each other. Water will begin to rise between the plates - it will be drawn in by the surface tension force, which was mentioned above. It is easy to calculate the coefficient of surface tension σ by the height of the rise of water y and the gap between the plates d.
Surface tension force F= 2σ L, Where L- the length of the plate (the deuce appeared due to the fact that water is in contact with both plates). This force holds the layer of water mass m = ρ Ldu, where ρ is the density of water. Thus, 2σ L = ρ Ldug. From here we can find the coefficient of surface tension σ = 1/2(ρ gdu). (1) But it’s more interesting to do this: squeeze the plates together at one end, and leave a small gap at the other.
The water will rise and form a surprisingly regular surface between the plates. The section of this surface by a vertical plane is a hyperbola. To prove it, it suffices to substitute a new expression for the gap in a given place in formula (1) instead of d. From the similarity of the corresponding triangles (see Fig. 2) d = D (x/L). Here D- clearance at the end L is the length of the plate, and x- the distance from the place of contact of the plates to the place where the gap and the height of the level are determined. Thus, σ = 1/2(ρ gu)D(x/L), or at= 2σ L/ρ gD(1/ X). (2) Equation (2) is indeed a hyperbolic equation.
Wetting and non-wetting
For a detailed study of capillary phenomena, one should also consider some molecular phenomena that are found on the three-phase boundary of the coexistence of solid, liquid, gaseous phases, in particular, the contact of a liquid with a solid body is considered. If the adhesion forces between the molecules of a liquid are greater than between the molecules of a solid body, then the liquid tends to reduce the boundary (area) of its contact with the solid body, retreating from it if possible. A drop of such a liquid on a horizontal surface of a solid will take the form of an oblate ball. In this case, the liquid is called non-wetting the solid. The angle θ formed by the surface of a solid body and the tangent to the surface of the liquid is called the edge angle. For non-wetting θ > 90°. In this case, a solid surface that is not wetted by a liquid is called hydrophobic, or oleophilic. If the adhesion forces between the molecules of the liquid are less than between the molecules of the liquid and the solid, then the liquid tends to increase the boundary of contact with the solid. In this case, the liquid is called wetting the solid; contact angle θ< 90°. Поверхность же будет носить название гидрофильная. Случай, когда θ = 180°, называется полным несмачиванием. Однако это практически никогда не наблюдается, так как между молекулами жидкости и твёрдого тела всегда действуют силы притяжения. При θ = 0° наблюдается полное смачивание: жидкость растекается по всей поверхности твёрдого тела. Полное смачивание или полное несмачиваение являются крайними случаями. Между ними в зависимости от соотношения молекулярных сил промежуточное положение занимают переходные случаи неполного смачивания.
Wettability and non-wettability are relative concepts: a liquid that wets one solid may not wet another. For example, water wets glass but does not wet paraffin; Mercury does not wet glass, but it wets copper.
Wetting is usually interpreted as the result of the action of surface tension forces. Let the surface tension at the air-liquid boundary be σ 1.2, at the liquid-solid boundary σ 1.3, and at the air-solid boundary σ 2.3.
Three forces act per unit length of the wetting perimeter, numerically equal to σ 1.2, σ 2.3, σ 1.3, directed tangentially to the corresponding interfaces. In the case of equilibrium, all forces must balance each other. The forces σ 2.3 and σ 1.3 act in the plane of the surface of a solid body, the force σ 1.2 is directed to the surface at an angle θ.
The equilibrium condition for the interfacial surfaces has the following form:
The value of cosθ is usually called wetting and denoted by the letter B.
The condition of the surface has a certain effect on wetting. The wettability changes dramatically already in the presence of a monomolecular layer of hydrocarbons. The latter are always present in the atmosphere in sufficient quantities. The surface microrelief also has a certain effect on wetting. However, to date, a single regularity of the influence of the roughness of any surface on its wetting by any liquid has not yet been revealed. For example, the Wenzel-Deryagin equation cosθ = x cosθ0 connects the contact angles of the liquid on rough (θ) and smooth (θ 0) surfaces with the ratio x of the area of the true surface of the rough body to its projection onto the plane. However, in practice this equation is not always observed. Thus, according to this equation, in the case of wetting (θ<90) шераховатость должна приводить к понижению краевого угла (т.е. к большей гидрофильности), а в случае θ >90 - to its increase (i.e. to greater hydrophobicity). Proceeding from this, as a rule, information is given on the effect of roughness on wetting.
According to many authors, the rate of spreading of a liquid on a rough surface is lower due to the fact that during spreading, the liquid experiences a delaying effect of the encountered bumps (ridges) of roughness. It should be noted that it is the rate of change in the diameter of a spot formed by a strictly dosed drop of liquid deposited on a clean surface of a material that is used as the main characteristic of wetting in capillaries. Its value depends both on surface phenomena and on the viscosity of the liquid, its density, and volatility.
It is obvious that a more viscous liquid with other identical properties spreads over the surface longer and therefore flows more slowly through the capillary channel.
Capillary phenomena
Capillary phenomena, a set of phenomena caused by surface tension at the interface of immiscible media (in liquid-liquid, liquid-gas or vapor systems) in the presence of surface curvature. A special case of surface phenomena.
Having studied in detail the forces underlying capillary phenomena, it is worth going directly to the capillaries. Thus, it can be experimentally observed that a wetting liquid (for example, water in a glass tube) rises through the capillary. In this case, the smaller the capillary radius, the higher the liquid rises in it. A liquid that does not wet the capillary walls (for example, mercury with a glass tube) falls below the liquid level in a wide vessel. So why does the wetting liquid rise through the capillary, while the non-wetting liquid descends?
It is not difficult to notice that the surface of the liquid is somewhat curved directly at the walls of the vessel. If the liquid molecules in contact with the vessel wall interact with the molecules of the solid body more than between themselves, in this case the liquid tends to increase the area of contact with the solid body (wetting liquid). In this case, the surface of the liquid bends down and is said to wet the walls of the vessel in which it is located. If the molecules of the liquid interact with each other more strongly than with the molecules of the walls of the vessel, then the liquid tends to reduce the area of contact with the solid body, its surface curves upward. In this case, one speaks of non-wetting of the walls of the vessel by the liquid.
In narrow tubes, the diameter of which is fractions of a millimeter, the curved edges of the liquid cover the entire surface layer, and the entire surface of the liquid in such tubes has a shape resembling a hemisphere. This is the so-called meniscus. It can be concave, which is observed in the case of wetting, and convex when not wetted. The radius of curvature of the liquid surface is of the same order as the radius of the tube. The wetting and non-wetting phenomena in this case are also characterized by the contact angle θ between the wetted surface of the capillary tube and the meniscus at the points of their contact.
Under a concave meniscus of the wetting liquid, the pressure is less than under a flat surface. Therefore, the liquid in a narrow tube (capillary) rises until the hydrostatic pressure of the liquid raised in the capillary at the level of a flat surface compensates for the pressure difference. Under a convex meniscus of a nonwetting liquid, the pressure is greater than under a flat surface, and this leads to a sinking of the nonwetting liquid.
The presence of surface tension forces and the curvature of the liquid surface in a capillary tube is responsible for the additional pressure under the curved surface, called the Laplace pressure: ∆ p= ± 2σ / R.
The sign of the capillary pressure ("plus" or "minus") depends on the sign of the curvature. The center of curvature of a convex surface is inside the corresponding phase. Convex surfaces have positive curvature, concave surfaces have negative curvature.
Thus, the equilibrium condition for a liquid in a capillary tube is determined by the equality
p 0 = p 0 – (2σ / R) + ρ gh (1)
where ρ is the liquid density, h is the height of its rise in the tube, p 0 - atmospheric pressure.
From this expression it follows that h= 2σ /ρ gR. (2)
We transform the resulting formula by expressing the radius of curvature R meniscus through the radius of the capillary tube r.
From fig. 6.18 it follows that r = R cosθ . Substituting (1) into (2), we get: h= 2σ cosθ /ρ gr.
The resulting formula, which determines the height of the rise of a liquid in a capillary tube, is called the Jurin formula. Obviously, the smaller the radius of the tube, the higher the liquid rises in it. In addition, the height of the rise increases with the increase in the coefficient of surface tension of the liquid.
The rise of the wetting liquid through the capillary can be explained in another way. As mentioned earlier, under the action of surface tension forces, the surface of the liquid tends to shrink. As a result, the surface of the concave meniscus tends to straighten and become flat. At the same time, it pulls the particles of the liquid lying under it, and the liquid rises up the capillary. But the surface of a liquid in a narrow tube cannot remain flat; it must have the shape of a concave meniscus. As soon as the given surface takes the form of a meniscus in the new position, it will again tend to contract, and so on. As a result of these reasons, the wetting liquid rises through the capillary. The uplift will stop when the force of gravity Fgravity of the lifted liquid column, which pulls the surface down, balances the resultant force F of the surface tension forces directed tangentially to each point on the surface.
Along the circumference of contact of the liquid surface with the capillary wall, a surface tension force acts equal to the product of the surface tension coefficient and the circumference: 2σπ r, Where r is the capillary radius.
The force of gravity acting on the lifted fluid is
F strand = mg = ρ Vg = ρπ r^2hg
where ρ is the liquid density; h is the height of the liquid column in the capillary; g- arrangement of gravity.
The liquid rise stops when F strand = F or ρπ r^2hg= 2σπ r. Hence the height of the rise of the liquid in the capillary h= 2σ /ρ gR.
In the case of a non-wetting liquid, the latter, seeking to reduce its surface, will sink down, pushing the liquid out of the capillary.
The derived formula is also applicable to a non-wetting liquid. In this case h is the height of the liquid in the capillary.
Capillary phenomena in nature
Capillary phenomena are also very common in nature and are often used in practical human activities. Wood, paper, leather, brick and many other objects around us have capillaries. Through the capillaries, water rises along the stems of plants and is absorbed into the towel when we dry ourselves with it. Rising water through the smallest holes in a piece of sugar, taking blood from a finger are also examples of capillary phenomena.
The human circulatory system, starting with very thick vessels, ends with a very extensive network of the thinnest capillaries. May be of interest, for example, such data. The cross-sectional area of the aorta is 8 cm 2 . The diameter of a blood capillary can be 50 times smaller than the diameter of a human hair with a length of 0.5 mm. There are about 160 billion capillaries in the adult human body. Their total length reaches 80 thousand km.
Through the numerous capillaries present in the soil, water from the deep layers rises to the surface and evaporates intensively. To slow down the process of moisture loss, capillaries are destroyed by loosening the soil with the help of harrows, cultivators, rippers.
Practical part
Take a glass tube with a very small inner diameter ( d < l мм), так называемый капилляр. Опустим один из концов капилляра в сосуд с водой -вода поднимется выше уровня воды в сосуде. Поверхностное натяжение способно поднимать жидкость на сравнительно большую высоту.
The rise of a liquid due to the action of the forces of the surface tension of water can be observed in a simple experiment. Take a clean rag and dip one end of it into a glass of water, and hang the other out over the edge of the glass. Water will begin to rise through the pores of the fabric, similar to capillary tubes, and soak the entire cloth. Excess water will drip from the hanging end (see photo 2).
If you take a light-colored fabric for the experiment, then the photo shows very poorly how the water spreads through the fabric. Also keep in mind that not all fabrics will have excess water dripping from the hanging end. I have done this experiment twice. The first time we used a light fabric (cotton jersey); water dripped very well from the hanging end. The second time they used a dark fabric (knitwear made of mixed fibers - cotton and synthetics); it was clearly visible how the water spreads over the fabric, but the drops from the hanging end did not drip.
The rise of liquid through the capillaries occurs when the forces of attraction of the molecules of the liquid to each other are less than the forces of their attraction to the molecules of the solid. In this case, the liquid is said to wet the solid.
If you take a not very thin tube, fill it with water and close the lower end of the tube with your finger, you can see that the water level in the tube is concave (Fig. 9).
This is the result of the fact that water molecules are more strongly attracted to the molecules of the walls of the vessel than to each other.
Not all liquids and not in any tubes "cling" to the walls. It also happens that the liquid in the capillary falls below the level in a wide vessel, while its surface is convex. Such a liquid is said to not wet the surface of a solid. The attraction of liquid molecules to each other is stronger than to the molecules of the walls of the vessel. This is how, for example, mercury behaves in a glass capillary. (Fig.10)
Conclusion
So, in the course of this work, I made sure that:
- Capillary phenomena play an important role in nature.
- The rise of the liquid in the capillary continues until the force of gravity acting on the liquid column in the capillary becomes equal in absolute value to the resulting force.
- The wetting liquid in the capillaries rises, and the non-wetting liquid falls down.
- The height of the rise of the liquid in the capillary is directly proportional to its surface tension and inversely proportional to the radius of the capillary channel and the density of the liquid.
Among the processes that can be explained with the help of surface tension and wetting of liquids, it is worth highlighting capillary phenomena. Physics is a mysterious and extraordinary science, without which life on Earth would be impossible. Let's look at the most striking example of this important discipline.
In life practice, such processes, interesting from the point of view of physics, as capillary phenomena, are quite common. The thing is that in everyday life we are surrounded by many bodies that easily absorb liquid. The reason for this is their porous structure and the elementary laws of physics, and the result is capillary phenomena.
Narrow tubes
A capillary is a very narrow tube in which the liquid behaves in a particular way. There are many examples of such vessels in nature - capillaries of the circulatory system, porous bodies, soil, plants, etc.
The capillary phenomenon is the rise or fall of liquids through narrow tubes. Such processes are observed in the natural channels of humans, plants and other bodies, as well as in special narrow glass vessels. The picture shows that different water levels have been established in the communicating tubes of different thicknesses. It is noted that the thinner the vessel, the higher the water level.
These phenomena underlie the absorbent properties of the towel, the nutrition of plants, the movement of ink along the rod, and many other processes.
Capillary phenomena in nature
The process described above is extremely important for the maintenance of plant life. The soil is quite loose, there are gaps between its particles, which are a capillary network. Water rises through these channels, nourishing the root system of plants with moisture and all the necessary substances.
Through the same capillaries, the liquid actively evaporates, so it is necessary to plow the land, which will destroy the channels and retain nutrients. Conversely, the pressed earth will evaporate moisture faster. This is due to the importance of plowing the land to retain subsoil fluid.
In plants, the capillary system ensures the rise of moisture from small roots to the uppermost parts, and through the leaves it evaporates into the external environment.
Surface tension and wetting
The question of the behavior of liquids in vessels is based on such physical processes as surface tension and wetting. The capillary phenomena caused by them are studied in a complex.
Under the action of the force of surface tension, the wetting liquid in the capillaries is above the level at which it should be according to the law of communicating vessels. Conversely, a non-wetting substance is located below this level.
So, water in a glass tube (wetting liquid) rises to the greater height, the thinner the vessel. On the contrary, mercury in a glass tube (non-wetting liquid) falls the lower, the thinner this container is. In addition, as indicated in the picture, the wetting liquid forms a concave meniscus shape, while the non-wetting liquid forms a convex one.
wetting
This is a phenomenon that occurs at the boundary where a liquid comes into contact with a solid (another liquid, gases). It arises due to the special interaction of molecules at the boundary of their contact.
Complete wetting means that the drop spreads over the surface of the solid, and non-wetting transforms it into a sphere. In practice, one or another degree of wetting is most often encountered, rather than extreme options.
Surface tension force
The surface of the drop has a spherical shape and the reason for this is the law acting on liquids - surface tension.
Capillary phenomena are due to the fact that the concave side of the liquid in the tube tends to straighten to a flat state due to surface tension forces. This is accompanied by the fact that the outer particles drag the bodies below them upwards, and the substance rises up the tube. However, the liquid in the capillary cannot assume the flat shape of the surface, and this rising process continues until a certain point of equilibrium. To calculate the height to which a column of water will rise (fall), you need to use the formulas that will be presented below.
Calculation of the height of the rise of the water column
The moment of stopping the rise of water in a narrow tube occurs when the force of gravity Р the weight of the substance balances the force of surface tension F. This moment determines the height of the rise of the liquid. Capillary phenomena are caused by two multidirectional forces:
- the force of gravity P strand causes the liquid to sink down;
- surface tension F pushes the water up.
The surface tension force acting along the circle where the liquid comes into contact with the walls of the tube is equal to:
where r is the radius of the tube.
The force of gravity acting on the liquid in the tube is:
P strand = ρπr2hg,
where ρ is the density of the liquid; h is the height of the liquid column in the tube;
So, the substance will stop rising, provided that P heavy \u003d F, which means that
ρπr 2 hg = σ2πr,
hence the height of the liquid in the tube is:
Similarly for a non-wetting liquid:
h is the drop height of the substance in the tube. As can be seen from the formulas, the height to which water rises in a narrow vessel (falls) is inversely proportional to the radius of the vessel and the density of the liquid. This applies to the wetting liquid and non-wetting. Under other conditions, a correction must be made for the shape of the meniscus, which will be presented in the next chapter.
Laplace pressure
As already noted, the liquid in narrow tubes behaves in such a way that one gets the impression of violating the law of communicating vessels. This fact always accompanies capillary phenomena. Physics explains this with the help of the Laplacian pressure, which is directed upwards with a wetting liquid. By lowering a very narrow tube into water, we observe how the liquid is drawn to a certain level h. According to the law of communicating vessels, it had to balance with the external water level.
This discrepancy is explained by the direction of the Laplacian pressure p l:
In this case, it is directed upwards. The water is drawn into the tube to the level where it balances with the hydrostatic pressure p g of the water column:
and if p l \u003d p g, then you can equate the two parts of the equation:
Now the height h is easy to derive as a formula:
When the wetting is complete, then the meniscus, which forms the concave surface of the water, has the shape of a hemisphere, where Ɵ=0. In this case, the radius of the sphere R will be equal to the inner radius of the capillary r. From here we get:
And in the case of incomplete wetting, when Ɵ≠0, the radius of the sphere can be calculated by the formula:
Then the required height, having a correction for the angle, will be equal to:
h=(2σ/pqr)cos Ɵ .
It can be seen from the presented equations that the height h is inversely proportional to the inner radius of the tube r. Water reaches its greatest height in vessels having the diameter of a human hair, which are called capillaries. As you know, the wetting liquid is drawn up, and the non-wetting liquid is pushed down.
An experiment can be made by taking communicating vessels, where one of them is wide and the other is very narrow. Pouring water into it, one can note a different level of liquid, and in the variant with a wetting substance, the level in a narrow tube is higher, and with a non-wetting one - lower.
Importance of capillary phenomena
Without capillary phenomena, the existence of living organisms is simply impossible. It is through the smallest vessels that the human body receives oxygen and nutrients. Plant roots are a network of capillaries that draw moisture from the ground to the topmost leaves.
Simple household cleaning is impossible without capillary phenomena, because according to this principle, the fabric absorbs water. The towel, the ink, the wick in the oil lamp, and many devices work on this basis. Capillary phenomena in technology play an important role in the drying of porous bodies and other processes.
Sometimes these same phenomena give undesirable consequences, for example, the pores of a brick absorb moisture. To avoid dampness of buildings under the influence of groundwater, it is necessary to protect the foundation with the help of waterproofing materials - bitumen, roofing felt or roofing felt.
Wetting clothes during rain, for example, trousers up to the knees from walking through puddles, is also due to capillary phenomena. There are many examples of this natural phenomenon around us.
Experiment with colors
Examples of capillary phenomena can be found in nature, especially when it comes to plants. Their trunks have many small vessels inside. You can experiment with coloring a flower in any bright color as a result of capillary phenomena.
You need to take brightly colored water and a white flower (or a leaf of Beijing cabbage, a stalk of celery) and put it in a glass with this liquid. After some time, on the leaves of Beijing cabbage, you can observe how the paint moves up. The color of the plant will gradually change according to the paint in which it is placed. This is due to the movement of the substance up the stems according to the laws that we have considered in this article.
Change the level in tubes, narrow channels of arbitrary shape, porous bodies. The rise of the liquid occurs when the channels are wetted with liquids, for example, water in glass tubes, sand, soil, etc. The decrease in liquid occurs in tubes and channels that are not wetted by liquid, for example, mercury in a glass tube.
On the basis of capillarity, the vital activity of animals and plants, chemical technologies, and everyday phenomena are based (for example, lifting kerosene along the wick in a kerosene lamp, wiping hands with a towel). Soil capillarity is determined by the rate at which water rises in the soil and depends on the size of the gaps between soil particles.
Thin tubes are called capillaries, as well as the thinnest vessels in the human body and other animals (see Capillary (biology)).
see also
Literature
- Prokhorenko P. P. Ultrasonic capillary effect / P. P. Prokhorenko, N. V. Dezhkunov, G. E. Konovalov; Ed. V. V. Klubovich. 135 p. Minsk: Science and Technology, 1981.
Links
- Gorin Yu. V. Index of physical effects and phenomena for use in solving inventive problems (TRIZ tool) // Chapter. 1.2 Surface tension of liquids. Capillarity.
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