## Table of contents

In Physics, a **fluid** is a substance that continually deforms (flows and cannot resist deformation) under applied shear stress or external force. Fluids are defined as all those material bodies that, because of the mobility of the particles that compose it, can undergo large changes in shape under the action of very small forces. In particular, a fluid at rest offers no resistance to changes in shape. Fluids include gases, liquids, and plasmas.

All fluids are compressible (i.e., their density increases with increasing pressure) to some extent, but liquids are much less compressible than gases and are generally considered to be incompressible. Even gases can be treated as incompressible if the airflow speeds involved are not high. For subsonic airflow over an aircraft below about 150 m/s (492 ft./s or about 336 mph), air can be treated as incompressible, i.e., the density remains the same throughout the flow. At higher speeds, the effects of compressibility must be considered.

## Classification of fluids

Fluids are generally divided into three major classes: liquids and gases.

- Liquids are those fluids that offer great resistance to changes in volume; they do not occupy the entire volume of the respective container, whatever its shape, depositing in the lower part of the container itself and always present a “free surface” of contact (or boundary) with the overlying atmosphere.
- Gases have the opposite behavior: small forces are sufficient to vary, under normal circumstances, the volume; immediate consequence of the fact that a gas occupies the entire volume of the container in which it is contained (expanding).
- Plasma, being an ionized gas, is characterized by some physical quantities, such as temperature and density of charged particles, as fluid; others, such as Debye length and plasma frequency, are characteristic of plasma as a set of moving charges.

One of the properties that characterizes the fluids and that is very useful in technical applications is the compressibility: synthetically we say that gases are known to be more compressible than liquids that are not very compressible (or for simplicity assumed as incompressible).

## Fluids assumed as continuous systems

It is known that matter is made up of molecules located at a large distance from each other with respect to their size and that these are in a continuous state of agitation (caused by kinetic and thermal energy), even when the substance is at rest. When the substance is in motion to this permanent motion of agitation is superimposed a motion from which depends a macroscopic transport of matter.

So in such a medium for its nature discontinuous, obviously does not make sense to talk about the value of a quantity (for example density, speed, pressure, etc.) in a point, because it is variable with discontinuity from point to point and from instant to instant, depending on the presence or absence of particles in the point considered.

In fact, in fluid mechanics, molecular agitation motions are of little interest, while it is more important, for example, to know the actions that a fluid at rest or in motion exerts on the boundary surfaces of the field of motion, the height required to convey a certain flow, etc.. Consequently we can disregard the agitation motions of the molecules, indeed the very presence of the molecules, imagining to replace the real substance an ideal substance: the continuous medium, which possesses with continuity the attributes of matter actually located in the molecules (mass, weight, density, velocity, etc.).

Therefore, if in the space occupied by a fluid is drawn a closed surface that encloses a finite volume, it is assumed that the matter included in it possesses in any case a finite mass (without intermolecular spaces; as opposed to what would happen if the surface was drawn in intermolecular spaces) and it is assumed that this mass tends to zero with continuity as the volume under consideration tends to zero.

## Fluids with linear or nonlinear viscosity

Based on the viscous behavior of the fluid, determined by the linearity or nonlinearity of the stress-strain law, fluids can be classified as:

### Newtonian fluid

**Newtonian fluids** are defined as those fluids that under the action of stresses flow with a flow velocity that increases linearly with the intensity of the applied stress (the stress is proportional to the strain rate). In this case the viscosity is constant and depends only on pressure and temperature. For Newtonian fluids it is observed that:

\[\tau = \mu \dfrac{du}{dy}\]

where: τ is the applied tangential stress; μ is the dynamic viscosity; du/dt the strain rate of the fluid.

### Non-Newtonian fluid

Non-Newtonian fluids are defined as those fluids for which the dynamic viscosity μ is also dependent on the strain rate:

\[\mu =\mu (T,P,\dot{\gamma})\]

Basically, three classes are distinguished:

- fluids whose rheological characteristics are independent of time;
- fluids for which the link between stress and strain depends on the duration of the stress or strain;
- fluids that possess some characteristics of solids and that in general show a partial reversibility of deformations (elastoviscous fluids).

## Types of fluids

### Pseudoplastic Fluid

Pseudoplastic fluids are defined as a type of non-Newtonian fluid (with time-independent behavior) that has a strong resistance to motion for small speeds, but the resistance decreases as the speed increases; in other words, the viscosity coefficient (μ) decreases as the shear stress increases.

Unlike Newtonian fluids, the rheogram has a curvilinear trend and therefore it is not possible to express with a single value the viscosity coefficient of the fluid. The decrease in viscosity that characterizes pseudoplastic fluids is due to the orientation (in the direction of motion) of the suspended particles or molecules in solution, which corresponds to a lowering of the resistance to motion (shear thinning). Generally they are:

- concentrated polymer solutions;
- Suspensions of concentrated particles;
- concentrated emulsions.

### Dilatant fluid

Dilatant fluids are defined as those fluids (with time-independent behavior) in which the flow begins even by the action of modest forces; that is, they have the opposite behavior to that of pseudoplastic fluids. The apparent viscosity increases with the deformation rate: shear thickening.

The dilatant flow is characteristic of very concentrated suspensions (over 50% by weight) of sufficiently small, non-flocculated solid particles. Particles at rest are packed to such an extent that inter-particle spaces are minimized and the amount of liquid retained in these spaces is just sufficient to provide lubrication that allows, at low shear rates, some flow.

When the system is agitated rapidly, it becomes more viscous because the motion of the particles causes an increase in the volume of the system, so that the limited amount of liquid vehicle being insufficient to fill the gaps can no longer provide the lubrication necessary to reduce inter-particle friction (responsible for the increase in viscosity).

### Bingham-style plastic fluid

Fluids that exhibit Bingham plastic behavior have zero strain rate until the tangential stress (shear force) exceeds a certain threshold value (τ_{0}), which is called the “creep limit”. Once this value is exceeded, the fluid behaves as a Newtonian. The equation that represents this behavior is the Bingham equation:

\[\tau = \dfrac{\partial \gamma}{\partial t}\eta +\tau_0\]

These are fluids with time-independent behavior.

### Thixotropic fluid (or thixotropic)

Thixotropic fluids (also called thixotropic) are defined as fluids with time-dependent behavior whose tangential stress gradually decreases over time, eventually tending to a limit value, at which the fluid behaves as Newtonian. Thixotropic systems typically contain asymmetric particles which, through numerous points of contact, form a certain unstable lattice structure within the medium.

This structure, at rest, gives the system a gel-like stiffness; then, when a shear force is applied, and flow begins, the structure begins to break down as the contact points are reduced and the particles align in the direction of flow, causing the system to change from a gel to a sol with a decrease in viscosity. Once the action of shear forces ceases, the cross-linked structure slowly begins to reconstitute itself as a result of Brownian motions of asymmetric structures.

They differ from non-Newtonian time-independent fluids in that they do not have a perfectly reversible behavior in time, i.e. they do not regain their initial characteristics through an inverse sequence. Thixotropic fluids present a rheological curve that is distinguished in ascending branch and descending branch, enclosing a characteristic area of hysteresis that represents the energy spent for the dissociation of bonds per unit of time and volume. The behavior of a thixotropic fluid is analogous to that of a pseudoplastic fluid, in fact its flow is facilitated by prior agitation and viscosity decreases as the time of force application increases: if the latter is kept constant, however, the fluid will decrease its viscosity.

Left at rest, the fluid can also regain its primitive properties, but moving from fluid to viscous state does not follow the same path. Apparent viscosity does not depend solely on the velocity gradient, but also on the duration of the applied stress and thus on the particular rheological history of the sample under test. Thus, thixotropy is a physical phenomenon due to the lack of simultaneity in the processes of destruction and reconstruction of structures subjected first to stress and then at rest.

### Rheopectic (or reopessic) fluid

Reopectic fluids (also called reopessic or reopectic) are those fluids with time-dependent behavior, which unlike thixotropic fluids, as time increases, the tangential stresses continue to increase until they become, in some cases, so great that the fluid takes on the appearance and behavior of a solid (viscosity increases as a function of the time of force application).

## Related keywords

- Superfluid [superfluidity]
- Magnetic fluid
- Ferrofluid