User:Erbilabaci/Drop Spinning Method

Definition
Spinning drop method (rotating drop method) is one of the common methods that is used to measure interfacial tension. Basicly, measurements are carried out by the placement of a fluid in a liquid drop of higher density contained in a rotating horizontal tube. The fluid drop is elongated by the centrifugal force and elongation of the fluid stops when the centrifugal forces are balanced by the surface tension forces. A device called “spinning drop tensiometer” is generally utilized for this purpose.

Spinning drop method is widely used for the measurement of very low interfacial tensions (less than 10-2 mN/m) in the systems such as crude oil associated with micellar flow, polymer blends, bitumen, organic solvents , ultra thin amino methacrylate membranes , non spherical organosiloxane capsules.

Detailed Description
In spinning drop method, a small bubble of an immiscible liquid or gas “A” suspended in a liquid “B” is put under rotation about a horizontal axis, because of the centrifugal forces, “A” to find an equilibrium position will migrate to the centre forming a drop astride the spinning axis. As the centrifugal force increases to a sufficiently high value, the drop changes to a cylindrical shape.

In 1942, Bernard Vonnegut suggested that this principle based on the balance of centrifugal and interfacial tension forces at mechanical equilibrium can be used to measure the surface tension of fluids and he developed an approximate theory where the fluid drop is considered as a circular cylinder.



Assuming that, length of the drop is large compared to the radius (L>>R) and angular velocity (ω) is sufficiently high so that the drop can be considered as a cylinder with hemispherical ends, the interfacial tension can be obtained by Vonnegut’s expression for the equilibrium shape and minimum energy:

EQUATION 1

where σ is the interfacial tension, ρ the density difference between phases, ω the angular velocity and R is the cylinder radius. This equation can be obtained by considering the change of total kinetic energy  EQUATION  of fluid drop and liquid due to the case in which the cell contains only liquid. The total change in the energy is obtained by summation of kinetic energy change and surface energy of the cylinder:

EQUATION 2

where L is the length of the cylinder. Solution of this equation for minimum energy change with respect to R at constant volume of fluid drop gives Vonnegut’s expression.

Comparison With Other Methods
Spinning drop method makes it easier to measure interfacial tension compared to the other widely used methods, since in this method the liquid drop is not in contact with a solid surface, therefore no contact angle has to be measured. Moreover, this method does not require the estimation of curvature which usually makes the problem much more diffucult, involving the estimations of the first and second derivatives of shape of the drop.

This theory suggested by Vonnegut, is restricted with the speeds of rotation. Since a liquid of high interfacial tension requires much higher angular velocities to maintain a shape which is close to a cylinder, spinning drop method is typically used for the fluids with a surface tension lower than 10-2 mN/m.

Additionally this method was improved by Silberberg in 1966, by calculating correction factor for low speeds of rotation. Furthermore, Princen extended the theory by using exact equations for the bubble shape and have developed an experimental method based on measuring the bubble length without the need for optical correction.