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MEASUREMENTS - TRACKER

 

MEASUREMENT OF THE INTERFACIAL TENSION

The interfacial tension between the two fluids is determined by a digital processing of the shape of a drop of the first fluid formed at the tip of a capillary diving in a cuvette containing the second fluid.

The drop is in equilibrium between the interfacial tension and the gravity. These forces are opposed. The interfacial tension gives the drop a spherical shape whereas the gravity elongates it. Then the drop seems to be pear-shaped. The influence of the interfacial tension on the shape of the drop can be observed during the adsorption of any surfactant. The drop becomes more and more elongated and the area of the interface increases when the interfacial tension decreases with time.

t=0mn ---- t=1mn ---- t=2mn ---- t=3mn

Variation of the shape of a drop during the adsorption of a surfactant.

 

The calculation of the interfacial tension is achieved using the two following equations:

  • the Laplace-Young equation

  • the equilibrium equation of the drop between the interfacial tension and the gravity:


where:

DP    is the pressure difference through the interface, resulting from the curvature of the interface,
g is the interfacial tension,
R and R' are the main curvature radii of the interface,
x and z are the coordinates of M on the contour of the image of the drop,
q is the angle of the tangent at M to the  contour of the image of the drop,
V is the volume of the fluid unde the plane of altitude z,
rh and rl are the volumic masses of the two fluids,
g is the gravitational acceleration.

The detailed processing of these two equations is given in XXX.

The TRACKER makes it possible with Pentium type computers (>750 Mhz) to carry out up to 12 calculations of the interfacial tension per second. When higher speed kinetics have to be tracked, the instrument makes it possible to record a film of the images of the drop and to calculate the interfacial tension from the recorded images.

DETERMINATION OF THE RHEOLOGICAL CHARACTERISTICS  OF THE INTERFACES IN DILATATION AND COMPRESSION 

 

The area variations of the interface are created  by controlled variations of the volume of the drop. They are 
programmed by the user and automatically implemented by the computer.

Several type of deformations versus time are available. The most simple are step deformations as in the following example, or periodic deformations (periodic deformations make it possible to track the variations of the rheological characteristics of the interface, as explained in the following section).

Exemple:

When a step dilatation DELTA A of the area of the interface is created, the TRACKER records a step increase DELTA G of the interfacial tension.

figure

This step is due to the sudden decrease of the interfacial concentration due to the sudden increase of the area of the interface. The gradual decrease of the interfacial tension which is following is sometimes called "relaxation of the interfacial tension" and is due to the adsorption of surfactants. The interfacial elasticity is equal to the ratio:

It is called the "GIBBS elasticity".
DETERMINATION OF THE RHEOLOGICAL CHARACTERISTICS  OF THE INTERFACES VERSUS TIME

 

When one wants to determine the evolution of the interfacial elasticity with time, it is obvious that the application of successive area increases will quickly make the drop detach from the tip of the capillary. The protocol consists in creating periodic variations of the area of the interface. The most simple ones which also allows the easiest interpretation of the results is the sinusoidal variation. The response of the interfacial tension is periodic, as shown in the following example:

Response of the interfacial tension variation at the bitumen/distilled water interface (pH XXX, 140°C) to a sinusoidal oscillation of the area of the interface (hertz, ampitude)

 

The TRACKER makes it possible to create sinusoidal variations of the area of the interface at different amplitudes and frequencies, over any period of time (the duration of the experiments may be limited only by the characteristics of the computer).

The rheological characteristics of the interface are calculated by FOURIER analysis. The deformation of the area of the interface  is considered as the input and the response of the interfacial  tension  as the output. The transfert function is the complex viscoelastic modulus of the interface.

The TRACKER makes it possible to calculate automatically at any moment of the recorded experiment the complex viscoelastic modulus of the interface, giving the real and imaginay parts or modulus and phase angle.

with:
   

It also makes it possible to calculate automatically the variations of the viscoelastic modulus with time.

Note :

ITCONCEPT is organised for carrying out ANALYTICAL SERVICES, with its instruments.