17.1: Density and Layering in Fluids

Essential to Know

• Fluids are separated by gravity into layers, each layer having a lower density than the one below it.
• Less dense fluids rise through more dense fluids.
• More dense fluids sink through less dense fluids.
• A fluid is neutrally buoyant when the fluid above has a lower density, and the fluid below has a higher density.
• A neutrally buoyant fluid will spread horizontally to form a layer.
• A fluid in which each higher layer is of lower density than the layer below it is stably stratified. There are no density-driven vertical motions within such a stably stratified fluid.
• The depth range in a fluid within which there is a marked vertical gradient of density is called a “pycnocline.” A pycnocline inhibits vertical mixing between fluid above and below the pycnocline layer.

Understanding the Concept

All substances exist in one of three physical states: solid, liquid, or gas (Chap. 5). Both liquids and gases are fluids. Seawater is a liquid, and the atmosphere is a gas, so both are fluids that flow in response to forces such as gravity. Some parts of the Earth’s interior are liquid. Other parts, including the asthenosphere and mantle (Chap. 4), although they are solid, can flow extremely slowly at the high temperatures and pressures present within the Earth. These solids behave like fluids over the million-year timescales in which geological processes occur.

When two fluids are brought into contact, gravity causes them to separate vertically according to their densities. The density of a fluid is the mass of the fluid divided by its volume. Pure liquid water has an absolute density (specific gravity) of 1000 kg·m–3 at 4°C and 1 atmosphere (atm) of pressure. Generally, density is stated as a relative density (r), which is the ratio of the fluid’s specific gravity to the specific gravity of pure water at 4°C and 1 atm pressure. Thus, pure water at 4°C and 1 atm has a relative density of 1.

The effects of gravity and other forces on fluids of different densities account for many of the processes studied in this text, including the circulation of ocean water and atmosphere, and the formation of ocean basins and continents.

Many fluids do not mix with one another. Examples include oil and water, and water and air. When two such fluids are placed in a container, the denser fluid sinks to the bottom, leaving the less dense fluid above. If the less dense fluid is a gas, such as air, it expands to fill the upper part of the container not occupied by the denser fluid. If the less-dense fluid is a liquid such as oil, it forms a separate layer on top of the denser fluid (Fig. CC1-1a). Even if we vigorously shake such mixtures, they quickly separate again into layers after we stop shaking.

Figure CC1-1. Fluids (liquids and gases) that do not mix with each other are separated into layers in such a way that the density of each layer is greater than that of the layer above. (a) Oil has a lower density than water and forms a separate layer that floats on the water. If this layer is very thin, it is called a “slick.” Air, which has a much lower density than either water or oil, forms a layer (the atmosphere) above the water. (b) Fluids are separated according to density because a more dense fluid has a greater mass and is subject to a greater gravitational force than the same volume of a less dense fluid. (c) Air, oil, water, and mercury separate into four layers, with density increasing toward the Earth’s center (that is, with depth).

Gravity is the principal force that separates fluids of different densities. Consider a container full of water with an oil layer on top, into which we introduce a small drop of water (Fig. CC1-1b). Because water is denser than oil, the drop of water has a greater mass than the same volume of oil. The gravitational force between any object on the Earth’s surface and the Earth increases in proportion to the object’s mass. Therefore, the gravitational attraction force between the Earth and the water drop is greater than that between the Earth and the oil, and the water droplet is pulled down by the Earth’s gravity more than the oil is. Because the oil can flow, the water droplet sinks, and the oil flows around it. When the water droplet reaches the top of the water layer, it is surrounded by a fluid of the same density, and the gravitational attraction on the water in the drop is now equal to the gravitational attraction on all the other water at its level. Therefore, the droplet sinks no farther. However, it does mix with the surrounding water by diffusion.

Gravitational sorting of fluids into layers according to density is called stratification. This process works equally well with more than two fluids. For example, if we mix mercury, water, oil, and air, the mixture will separate with water on top of the mercury, oil on top of the water, and air above the oil (Fig. CC1-1c). This process does not work quite the same way with solids because they cannot flow.

Density stratification can occur not only between fluids that do not mix, but also between fluids that do mix. For example, if we carefully add cream to a cup of cold coffee, it remains as a floating layer on top of the coffee until we stir the coffee and thoroughly mix the two layers. After two liquids are thoroughly mixed, the mixture has uniform density, and the two layers do not re-form.

Density stratification can also occur in a single fluid, such as pure water or air. Just as cream forms a layer on coffee, a less dense layer of any fluid will remain on top of a denser layer of the same fluid until they are mixed (Fig. CC1-2). In the natural environment, we often find fluids with multiple layers, each of slightly higher density from the shallowest to the deepest layer (Fig. CC1-2). When the density of the fluid increases progressively with depth, no layer has a tendency to sink or rise, and the fluid is said to exhibit stable stratification. Ocean waters are arranged in layers of different density in this way (Chap. 8) because the density of water varies with temperature and salinity (CC6). The atmosphere is also vertically stratified (Chap. 7), and the components of the Earth’s interior are arranged similarly (Chap. 4).

Figure CC1-2. Water may form distinct layers, each of which has a different density because it has a different temperature or salinity. (a) A water column is stably stratified if each successive layer has a higher density than the one above it and, thus, no water sinks or rises. (b) If water is introduced to a stratified water column, it will sink or rise until it reaches an equilibrium level at which the density of the water above it is lower and the density of the water below it is higher. It will then spread out to form a new layer at this depth. Some mixing of the introduced water with other water layers will occur as it sinks through layers of lower-density water or rises through layers of higher-density water. However, when the vertically moving volumes of water are very large (as they are in the oceans), such mixing is limited.

If we add a fluid to a column of other fluids, each with a different density and none of which mix, the added fluid will sink or rise until it reaches a depth where the fluid immediately above it is of a lower density and the fluid immediately below it is of a higher density. At this equilibrium level, the introduced fluid is neutrally buoyant, so it will neither sink nor rise, but will spread out to form its own layer (Fig. CC1-2). For example, if we introduce oil underwater to an air-water layered system, the oil will rise to the surface of the water and spread out. This is exactly what happens when sunken ships release their oil.

When a fluid of slightly different density is added to a density-stratified column of the same fluid or of a fluid with which it mixes, some mixing will occur as the added fluid sinks or rises to its equilibrium level. We can see this effect if we pour cream from a height into a cup of coffee. Both the cream and the coffee are primarily water, but different chemicals are dissolved or suspended in each, so they have different densities. If we pour the cream in carefully, it will be partially mixed as its momentum carries it down into the coffee and as it subsequently rises because of its lower density. The cream, mixed with some coffee, will rise to form a layer on top of the coffee and will then mix only very slowly (by molecular diffusion) unless we stir the mixture (and create turbulent diffusion). When the volumes of fluid in each layer are very large and vertical motions are slow, as they are in the oceans, mixing is very limited. The oceans are vertically stratified (Chap. 8), and density-driven vertical motions of water masses move large volumes of water vertically to find their equilibrium level with little mixing between the ascending or descending water masses and the layers of water through which they rise or sink.

Our cream and coffee experiment can illustrate another important concept. After we carefully place a layer of cream on the coffee, there is a distinct cream layer of lower density and a distinct lower coffee layer of higher density. Between these layers is a thin region where coffee and cream are mixed in varying amounts. The vertical distribution of density in this experiment is shown in Figure CC1-3. Density is uniform in the surface layer of cream, becomes progressively higher (this is referred to as a density gradient) in the transition layer of mixed cream, and is uniform in the lower layer of coffee. The transition region in which there is a vertical density gradient is called a pycnocline. More energy would be needed to move a molecule of water vertically through this pycnocline than would be needed to move a molecule the same vertical distance in either the cream or the coffee. Thus, pycnoclines act as barriers to vertical mixing.

Figure CC1-3. If cream (which has a lower density than coffee) is introduced at the surface of a cup of cold coffee, the cream forms a surface layer overlying the coffee. Between the cream and coffee layers, there is a zone within which the cream and coffee are mixed in proportions that change progressively with depth from pure cream to pure coffee. In this zone between the coffee and cream layers, there is a rapid change in their respective proportions, which results in a sharp increase in density with depth. This zone, in which density changes rapidly with depth, is called a pycnocline zone. Vertical mixing between the two layers takes place only slowly across a pycnocline because the lower-density upper layer (cream) has no tendency to sink, and the higher-density layer (coffee) has no tendency to rise.

The strength of the density gradient in a pycnocline determines how strong a barrier to vertical mixing it is. Try the experiment again, but use milk instead of cream. Milk has a slightly higher density than cream (because it contains less fat). It is almost impossible to pour the milk into the coffee without the two mixing, even though milk does have a lower density than water. In this case, the density gradient, and therefore the pycnocline between milk and coffee, is very weak.

Pycnoclines form in many parts of the oceans, particularly where warm surface water overlies colder deep water, and they are important because they inhibit vertical mixing. The density of a fluid is altered as heat is gained from the sun at its surface and as heating or cooling occurs by conduction and radiation at its interfaces with its container or other fluids surrounding it. Density is also altered by changes in pressure and by changes in fluid composition, such as the addition of salts to water (Chap. 5) and of water vapor to air (Chap. 7). The factors that affect the density of air are discussed in CC5 and Chapter 7, and the factors that affect the density of water are examined in CC6 and Chapter 5. CC3 explains more about the vertical motions created by such density changes.