Definition of liquid :

A liquid as a proper volume but has no proper form. In this way, a liquid is the intermediate state of matter between solid matter which has got a proper volume and a proper form, and a gas which has no proper volume and no proper form.

Capillarity :

Whole phenomena which interact at liquid surfaces and when the liquid surface is in contact with other materials solids or liquids, or gases.

Viscosity :

Resistence of a fluid (liquid or gas) to uniform flowing without turbulences.

Miscibility of liquids :

Two liquids or more are miscible if their blend has got only one phase. It means that the blend has the shape of an homogeneous liquid.


2.1) Microscopic view :
The molecules of a liquid are moving and their displacements are slower and shorter then in a gas. These displacements may occur because of the existence of free volumes between the molecules. These free volumes can recombinate while the liquid molecules move. These free volumes are responsible of liquid compressibility and their number and their size vary with the temperature. But the variations of the total volume of the liquid are very low compared to gases and one assume that the volume a given mass of liquid is almost constant. Liquid compressibilities are much higher then gases ones and are generally lower then solids ones.

2.2) Viscosity properties :

Because of the limited free volume and the occurrence of bumps between the molecules, there is some obstruction to their displacements. this microscopic phenomenon results, in a macroscopic point of view, in a liquid resistence to flowing, which is called the viscosity. The free volume in the liquid increases with the temperature and then the movements become less obstructed. The vicosity is then lowered.

2.3) Liquid cohesion :

Cohesion of the liquid is due to the existence of attractive interactions at short distances between its molecules. These interactions may be Van der Waals interactions in non polar liquids such as hydrocabonic solvents, or polar interactions in polar liquids such as water. The kinetic energy of the molecules is lower to the cohesion energy induiced by this attractive forces. The apparent resulting surfacic forces are called the superficial stress.

The unity of the superficial stress coefficient Gamma is the N/m.

2.4) Energy of interfacial forces :

The variation of the surface energy dG is expressed as follows :

    dG = Gamma ds
where ds is the variation of the liquid surface.

Some appproximative thermodynamic modelization allows to calculate the boiling energy of a liquid :

    DeltaG = Gamma Sm - R T
Where :
    Sm is the total surface of the spread molecules
    R = 8.314 J/K
    T is the boiling temperature.

2.5) Interfacial behaviours :

At the surface of the liquid which may be in contact with a gaseous phase such as its vapor or air, or in contact with a solid phase or another liquid, on observ a more ore less important discontinuity in the repartition of molecular interactions at the bounding interface. For exemple in the case of contact with air, one have relatively strongs interactions in the liquid and very low interactions in air. Liquid molecules are then attracted inside the liquid. If the liquid is not submitted to the gravity, its bounding surface will be spheric because of minimization of surfacic cohesion energy.

If the liquid is submitted to the gravity and poured in a large container, its surface is flat because the gravity is so high that the superficial stress forces cannot minimize the cohesion energy. on the container walls, one may observe a curvation turned to the top or the bottom. It depends on the nature of interaction forces between the liquid and the solid :
a) if this curvation is turned to the top, the liquid wets the container material.
b) if this curvation is turned to the bottom, the liquid does not wet the container material.

The whole of the liquid surface and its curvations is called the meniscus.

2.6) Liquid blends miscibility :

Hydrophilic liquid : An hydrophilic liquid is miscible to water. It contains usually polar groups and may usually involve hydrogen bounds or polar interactions. Some hydrophilic liquids are light alcohols, liquid mineral acids, light organic acids, aceton. When an hydrophilic liquid is blended with water, the interactions are existing between all the different molecules and they are strong. The blend is stable.

Hydrophobic liquid : An hydrophobic liquid is not miscible to water. Its Molecules are not polar and do usually not involve hydrogen bounds too. Some hydrophobic liquids are hydrocarbonic solvents, oils, benzen, anilin. When hydrophobic liquids are blended with water, the blend is not stable and the two liquids will separate. If the liquids are submetted to the gravity and poured in a container, the more dense liquid will go in the bottom of the container and the lighter will float above.

Remark : All the hydrophobic liquids are not miscible : for instance aniline and some fuels are not miscible at ambiancy temperature.


Some experimental systems build to study capillarity and viscosity properties have lead to some modelization at it is exposed now :

3.1) Study of capillarity properties with Jurin's tube :

A thin tube of a defined solid material, for example glass, is plunged in a container filled with a liquid. The liquid is submetted either to the gravity and either to the interfacial stress among the walls of the tube.
If the liquid wets the material, it drops to the top inside the tube and its level inside the tube is stabilized above the liquid level in the container.
If the liquid does not wet the material, it drops down inside the tube and its level inside the tube is stabilized under the liquid level in the container.

In the cas of a tube, one have the following equilibrium relation :

    Hoo = - 4 Gamma cos(Teta) / (Ro g d)

where :

    Hoo is the equilibrium high of the liquid in the tube in m : positive or negative.
    Gamma is the value of the superficial stress coefficient in N/m.
    d is the diameter of the tube in m.
    Ro is the volumic mass of the liquid in kg/m3
    g is the gravity : g = 9.8 m/s2
    Teta is the interfacial angle between the tube and the liquid level :
      If Teta is superior than 90, the liquid wets the tube material and Hoo is positive.
      If Teta is inferior to 90, the liquid does not wet the tube material and Hoo is negative.

If the tube is replaced by two parallel strips separated by a interstice d, this relation becomes :
    Hoo = - 2 Gamma * cos(Teta) /(Ro g d)
      (equivalent to a monodimensional relation).

The equilibrium level in the tube is reached step by step and at the beginning of the liquid droping, one can neglegt the gravity and the kinetic of droping H(t) may be described by the following equation :

    H(t) = A (d Gamma cos(Teta) t / )^1/2

The kinetic curve drawed with a square root of time scale has got an initial slope beta :

    beta = A (d gamma cos(teta) / )^1/2

where :

    is the viscosity of the liquid in Pa.s
    A is a dimensionless constant which depends on the geometry of the experimental system (tube or parallel strips).

Remark : The shape of this kinetic curve remains rather well a Fickian sorption kinetics. Thus, when a sorption process of a liquid is studied in a material containing hollow fibers, for example water sorption in wood, one should be carefull about the interpretation of the phenomena involved and should evocate a possibility of capillarity phenomena too.

3.2) Study of viscosity properties with a vertical viscosimetric tube (or strips) :

If a colomn of liquid with a defined lengh is submitted to the gravity and has an uniform flowing in a tube (or between strips), a stationnary regime with a constant mean speed of flowing may be reached and then this mean speed of flowing v is following the next law :

    v = B Ro g d^2 / .

where :

    is the viscosity of the liquid in Pa.s
    Ro is the volumic mass of the liquid in kg/m3
    d is the diameter of the tube or the interstice between the strips in m.
    g is the gravity : g = 9.8 m/s2
    B is a dimensionless constant which depends on the geometry of the experimental system (tube or parallel strips).

One consider here that the interfacial forces can be neglegted. It may be the case if the lengh of the liquid column is sufficiently high.

3.3) wetting, drop test :

A drop of liquid is put on a flat horizontal support. The drop becomes more or less spread on the support and the interfacial front angle between the liquid and the support around the drop is more or less opened. It is then possible to calculate the interfacial energy.


These simulation have been written in order to simulate some properties of liquids and just illustrate some particular cases. The different involved thermodynamic and kinetic constants are without dimension and are represented by random values compared to parametrized numerical thresholds. A two dimensional visualization allows to give a topological view of the liquid phase. In these visualizations, only global informations are given on the localization of the fluid molecules represented as pixels on the screen. No chemical structure is represented. Liquid molecules and atoms of the substrate are associated to specific energetic contributions wich may be different. The cohesion of the liquid is induiced by the fact that a molecule of the liquid cannot be displaced if there is less then a total threshold of energy in a limited square environment around it.

Gravity forces are represented by imposing to the molecules randomly and temporary displacements to the bottom. Bumps between molecules may contribute to disperse these imposed displacements.

Liquid viscosity is controlled by changing the jump frequency of the molecules and by the free volume too.

Overview of the simulations :

4.1) Some properties of liquids : This simulation allows to reproduce three experiments with a liquid in an excluded volume dynamics :
a) Capillarity properties through the system of Jurin's tube.
b) Viscosity properties through flowing in a vertical tube.
c) Wetting experiment through the drop test.

4.2) Separation of liquids : Two liquids are mixed at the beginning of the simulation run and then may more or less separate depending the values of the interfacial stress. The simulation is written in a excluded volume dynamics.

Applet developed by Dr Jean-Yves Dolveck
Feb. 2008