Discuss the concept of kinematic viscosity. Determine the Percentage Composition of Liquid Solution Viscometrically.

 

Concept of Kinematic Viscosity

Kinematic Viscosity is a measure of the intrinsic viscosity of a fluid, which describes its resistance to flow under the influence of gravity. It is defined as the ratio of the dynamic viscosity ($\eta$) to the density ($\rho$) of the fluid:

$\nu = \frac{\eta}{\rho}$

where:

• $\nu$ is the kinematic viscosity (typically in units of $\text{m}^2/\text{s}$ or $\text{Stokes} (St)$).
• $\eta$ is the dynamic viscosity (in units of $\text{Pa} \cdot \text{s}$ or $\text{Poise} (P)$).
• $\rho$ is the density of the fluid (in units of $\text{kg}/\text{m}^3$).

Kinematic viscosity provides insight into the fluid's flow characteristics independent of the force applied. It is particularly useful in applications involving fluid flow in pipes, around objects, and in natural systems like rivers and oceans.

Determining the Percentage Composition of a Liquid Solution Viscometrically

Determining the percentage composition of a liquid solution using viscosity measurements involves the following steps:

1. Preparation of Standard Solutions:

   • Prepare a series of standard solutions with known compositions of the components (e.g., water and alcohol).
   • Measure the kinematic viscosity of each standard solution using a viscometer.

2. Calibration Curve:

   • Plot a calibration curve of kinematic viscosity versus the percentage composition of the known solutions.
   • This curve will serve as a reference to determine the composition of unknown solutions.

3. Measurement of Unknown Solution:

   • Measure the kinematic viscosity of the unknown solution using the same viscometer.

4. Determination of Composition:

   • Use the calibration curve to find the corresponding percentage composition for the measured kinematic viscosity of the unknown solution.

Example Procedure

1. Prepare Standard Solutions:

   • Example: Prepare solutions with 10%, 20%, 30%, 40%, 50% of ethanol in water.
   • Measure the kinematic viscosity of each solution.

2. Plot Calibration Curve:

   • Plot the measured kinematic viscosity ($\nu$) against the ethanol percentage.
   • The resulting curve should show how viscosity changes with composition.

3. Measure Unknown Solution:

   • Measure the kinematic viscosity of the unknown ethanol-water solution.

4. Find Composition:

   • Locate the measured viscosity on the calibration curve.
   • Determine the corresponding ethanol percentage from the curve.

Calculation Example

Suppose you have the following data for ethanol-water solutions:

Ethanol (%)	Kinematic Viscosity ($\nu$) ($\text{mm}^2/\text{s}$)
10	1.20
20	1.15
30	1.10
40	1.05
50	1.00

If the kinematic viscosity of the unknown solution is measured to be 1.10 $\text{mm}^2/\text{s}$:

• Locate 1.10 $\text{mm}^2/\text{s}$ on the y-axis of the calibration curve.
• The corresponding ethanol percentage on the x-axis is 30%.

Thus, the unknown solution is approximately 30% ethanol.

Considerations

• Temperature Control: Viscosity is temperature-dependent, so all measurements should be conducted at a constant temperature.
• Accuracy: Ensure precise measurements of viscosity and use a well-calibrated viscometer.
• Non-ideal Mixtures: For non-ideal mixtures, the relationship between viscosity and composition may not be linear, and more complex calibration curves or models might be needed.

This method provides a reliable way to determine the percentage composition of a liquid solution using viscometric data.