Liquid

Cavitation in water from a boat propeller

Quantities of liquids are measured in units of volume. These include the SI unit cubic metre (m³) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm³ = 1 L = 0.001 m³), and the cubic centimetre, also called millilitre (1 cm³ = 1 mL = 0.001 L = 10⁻⁶ m³).[13]

The volume of a quantity of liquid is fixed by its temperature and pressure. Liquids generally expand when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception.[14]

On the other hand, liquids have little compressibility. Water, for example, will compress by only 46.4 parts per million for every unit increase in atmospheric pressure (bar).[15] At around 4000 bar (400 megapascals or 58,000 psi) of pressure at room temperature water experiences only an 11% decrease in volume.[16] Incompressibility makes liquids suitable for transmitting hydraulic power, because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression.[17]

However, the negligible compressibility does lead to other phenomena. The banging of pipes, called water hammer, occurs when a valve is suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon caused by liquid's incompressibility is cavitation. Because liquids have little elasticity they can literally be pulled apart in areas of high turbulence or dramatic change in direction, such as the trailing edge of a boat propeller or a sharp corner in a pipe. A liquid in an area of low pressure (vacuum) vaporizes and forms bubbles, which then collapse as they enter high pressure areas. This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface.[18]

In a gravitational field, liquids exert pressure on the sides of a container as well as on anything within the liquid itself. This pressure is transmitted in all directions and increases with depth. If a liquid is at rest in a uniform gravitational field, the pressure ${\displaystyle p}$ at depth ${\displaystyle z}$ is given by[19]

${\displaystyle p=p_{0}+\rho gz\,}$

where:

${\displaystyle p_{0}\,}$ is the pressure at the surface

${\displaystyle \rho \,}$ is the density of the liquid, assumed uniform with depth

${\displaystyle g\,}$ is the gravitational acceleration

For a body of water open to the air, ${\displaystyle p_{0}}$ would be the atmospheric pressure.

Static liquids in uniform gravitational fields also exhibit the phenomenon of buoyancy, where objects immersed in the liquid experience a net force due to the pressure variation with depth. The magnitude of the force is equal to the weight of the liquid displaced by the object, and the direction of the force depends on the average density of the immersed object. If the density is smaller than that of the liquid, the buoyant force points upward and the object floats, whereas if the density is larger, the buoyant force points downward and the object sinks. This is known as Archimedes' principle.[20]

Surface waves in water

Unless the volume of a liquid exactly matches the volume of its container, one or more surfaces are observed. The presence of a surface introduces new phenomena which are not present in a bulk liquid. This is because a molecule at a surface possesses bonds with other liquid molecules only on the inner side of the surface, which implies a net force pulling surface molecules inward. Equivalently, this force can be described in terms of energy: there is a fixed amount of energy associated with forming a surface of a given area. This quantity is a material property called the surface tension, in units of energy per unit area (SI units: J/m²). Liquids with strong intermolecular forces tend to have large surface tensions.[21]

A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical drops and bubbles unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including surface waves, capillary action, wetting, and ripples. In liquids under nanoscale confinement, surface effects can play a dominating role since – compared with a macroscopic sample of liquid – a much greater fraction of molecules are located near a surface.

The surface tension of a liquid directly affects its wettability. Most common liquids have tensions ranging in the tens of mJ/m², so droplets of oil, water, or glue can easily merge and adhere to other surfaces, whereas liquid metals such as mercury may have tensions ranging in the hundreds of mJ/m², thus droplets do not combine easily and surfaces may only wet under specific conditions.

The surface tensions of common liquids occupy a relatively narrow range of values when exposed to changing conditions such as temperature, which contrasts strongly with the enormous variation seen in other mechanical properties, such as viscosity.[22]

A simulation of viscosity. The fluid on the left has a lower viscosity and Newtonian behavior while the liquid on the right has higher viscosity and non-Newtonian behavior.

An important physical property characterizing the flow of liquids is viscosity. Intuitively, viscosity describes the resistance of a liquid to flow.

More technically, viscosity measures the resistance of a liquid to deformation at a given rate, such as when it is being sheared at finite velocity.[23] A specific example is a liquid flowing through a pipe: in this case the liquid undergoes shear deformation since it flows more slowly near the walls of the pipe than near the center. As a result, it exhibits viscous resistance to flow. In order to maintain flow, an external force must be applied, such as a pressure difference between the ends of the pipe.

The viscosity of liquids decreases with increasing temperature.[24][25]

Precise control of viscosity is important in many applications, particularly the lubrication industry. One way to achieve such control is by blending two or more liquids of differing viscosities in precise ratios.[26] In addition, various additives exist which can modulate the temperature-dependence of the viscosity of lubricating oils. This capability is important since machinery often operate over a range of temperatures (see also viscosity index).[27]

The viscous behavior of a liquid can be either Newtonian or non-Newtonian. A Newtonian liquid exhibits a linear strain/stress curve, meaning its viscosity is independent of time, shear rate, or shear-rate history. Examples of Newtonian liquids include water, glycerin, motor oil, honey, or mercury. A non-Newtonian liquid is one where the viscosity is not independent of these factors and either thickens (increases in viscosity) or thins (decreases in viscosity) under shear. Examples of non-Newtonian liquids include ketchup, mayonnaise, hair gels, Play-Doh, or starch solutions.[28]

Confined liquids may exhibit different mechanical properties compared to bulk liquids. For example, liquids under sub-millimeter confinement (e.g. in the gap between rigid walls) exhibit a solid-like mechanical response and possess a surprisingly large low-frequency elastic shear modulus, which scales with the inverse cubic power of the confinement length.[29]

The speed of sound in a liquid is given by ${\displaystyle c={\sqrt {K/\rho }}}$ where ${\displaystyle K}$ is the bulk modulus of the liquid and ${\displaystyle \rho }$ the density. As an example, water has a bulk modulus of about 2.2 GPa and a density of 1000 kg/m³, which gives c = 1.5 km/s.[30]

A typical phase diagram. The dotted line gives the anomalous behaviour of water. The green lines show how the freezing point can vary with pressure, and the blue line shows how the boiling point can vary with pressure. The red line shows the boundary where sublimation or deposition can occur.

At a temperature below the boiling point, any matter in liquid form will evaporate until reaching equilibrium with the reverse process of condensation of its vapor. At this point the vapor will condense at the same rate as the liquid evaporates. Thus, a liquid cannot exist permanently if the evaporated liquid is continually removed.[31] A liquid at or above its boiling point will normally boil, though superheating can prevent this in certain circumstances.

At a temperature below the freezing point, a liquid will tend to crystallize, changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure, so unless supercooling occurs, the liquid will eventually completely crystallize. However, this is only true under constant pressure, so that (for example) water and ice in a closed, strong container might reach an equilibrium where both phases coexist. For the opposite transition from solid to liquid, see melting.

The phase diagram explains why liquids do not exist in space or any other vacuum. Since the pressure is zero (except on surfaces or interiors of planets and moons) water and other liquids exposed to space will either immediately boil or freeze depending on the temperature. In regions of space near the earth, water will freeze if the sun is not shining directly on it and vaporize (sublime) as soon as it is in sunlight. If water exists as ice on the moon, it can only exist in shadowed holes where the sun never shines and where the surrounding rock does not heat it up too much. At some point near the orbit of Saturn, the light from the sun is too faint to sublime ice to water vapor. This is evident from the longevity of the ice that composes Saturn's rings.[32]

Liquids can form solutions with gases, solids, and other liquids.

Two liquids are said to be miscible if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and ethanol (drinking alcohol) are miscible whereas water and gasoline are immiscible.[33] In some cases a mixture of otherwise immiscible liquids can be stabilized to form an emulsion, where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a surfactant in order to stabilize the droplets. A familiar example of an emulsion is mayonnaise, which consists of a mixture of water and oil that is stabilized by lecithin, a substance found in egg yolks.[34]

Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present.

In a liquid, atoms do not form a crystalline lattice, nor do they show any other form of long-range order. This is evidenced by the absence of Bragg peaks in X-ray and neutron diffraction. Under normal conditions, the diffraction pattern has circular symmetry, expressing the isotropy of the liquid. In radial direction, the diffraction intensity smoothly oscillates. This is usually described by the static structure factor S(q), with wavenumber q=(4π/λ)sin θ given by the wavelength λ of the probe (photon or neutron) and the Bragg angle θ. The oscillations of S(q) express the near order of the liquid, i.e. the correlations between an atom and a few shells of nearest, second nearest, ... neighbors.

A more intuitive description of these correlations is given by the radial distribution function g(r), which is basically the Fourier transform of S(q). It represents a spatial average of a temporal snapshot of pair correlations in the liquid.

Radial distribution function of the Lennard-Jones model fluid.

The above expression for the sound velocity ${\displaystyle c={\sqrt {K/\rho }}}$ contains the bulk modulus K. If K is frequency independent then the liquid behaves as a linear medium, so that sound propagates without dissipation and without mode coupling. In reality, any liquid shows some dispersion: with increasing frequency, K crosses over from the low-frequency, liquid-like limit ${\displaystyle K_{0}}$ to the high-frequency, solid-like limit ${\displaystyle K_{\infty }}$. In normal liquids, most of this cross over takes place at frequencies between GHz and THz, sometimes called hypersound.

At sub-GHz frequencies, a normal liquid cannot sustain shear waves: the zero-frequency limit of the shear modulus is ${\displaystyle G_{0}=0}$. This is sometimes seen as the defining property of a liquid.[36][37] However, just as the bulk modulus K, the shear modulus G is frequency-dependent, and at hypersound frequencies it shows a similar cross over from the liquid-like limit ${\displaystyle G_{0}}$ to a solid-like, non-zero limit ${\displaystyle G_{\infty }}$.

According to the Kramers-Kronig relation, the dispersion in the sound velocity (given by the real part of K or G) goes along with a maximum in the sound attenuation (dissipation, given by the imaginary part of K or G). According to linear response theory, the Fourier transform of K or G describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz to THz region is also called relaxation. According to the fluctuation-dissipation theorem, relaxation towards equilibrium is intimately connected to fluctuations in equilibrium. The density fluctuations associated with sound waves can be experimentally observed by Brillouin scattering.

On supercooling a liquid towards the glass transition, the crossover from liquid-like to solid-like response moves from GHz to MHz, kHz, Hz, ...; equivalently, the characteristic time of structural relaxation increases from ns to µs, ms, s, ... This is the microscopic explanation for the above-mentioned viscoelastic behaviour of glass-forming liquids.

The mechanisms of atomic/molecular diffusion (or particle displacement) in solids are closely related to the mechanisms of viscous flow and solidification in liquid materials. Descriptions of viscosity in terms of molecular "free space" within the liquid[38] were modified as needed in order to account for liquids whose molecules are known to be "associated" in the liquid state at ordinary temperatures. When various molecules combine together to form an associated molecule, they enclose within a semi-rigid system a certain amount of space which before was available as free space for mobile molecules. Thus, increase in viscosity upon cooling due to the tendency of most substances to become associated on cooling.[39]

Similar arguments could be used to describe the effects of pressure on viscosity, where it may be assumed that the viscosity is chiefly a function of the volume for liquids with a finite compressibility. An increasing viscosity with rise of pressure is therefore expected. In addition, if the volume is expanded by heat but reduced again by pressure, the viscosity remains the same.

The local tendency to orientation of molecules in small groups lends the liquid (as referred to previously) a certain degree of association. This association results in a considerable "internal pressure" within a liquid, which is due almost entirely to those molecules which, on account of their temporary low velocities (following the Maxwell distribution) have coalesced with other molecules. The internal pressure between several such molecules might correspond to that between a group of molecules in the solid form.