Gas Bubble Radius Calculation in Excel

Gas bubble radius is a measure of how big a gas bubble is when it forms in a liquid. The size of the gas bubble depends on several factors, such as the pressure, temperature, surface tension, viscosity, and density of the liquid and the gas.

One way to think about gas bubble radius is to imagine blowing air through a straw into a glass of water. The air bubbles that come out of the straw have different sizes depending on how fast you blow, how big the straw is, and how much water is in the glass.

Some liquids, like water, tend to make the bubbles stick together or coalesce, which makes them bigger. Other liquids, like salt water or alcohol, tend to keep the bubbles separate or non-coalescent, which makes them smaller. You can see this difference by comparing the bubbles in a fresh water aquarium and a salt water aquarium. The bubbles are much smaller in the salt water aquarium.

The shape of the gas bubble also changes with its size. Small bubbles are almost spherical, because the surface tension of the liquid tries to minimize the surface area of the bubble. Larger bubbles are more ellipsoidal, because the drag force of the liquid tries to flatten the bubble as it rises. Very large bubbles can even break apart into smaller bubbles due to the turbulence of the liquid.

The motion and velocity of the gas bubble depend on how fast it rises in the liquid. The faster the bubble rises, the more it oscillates or wobbles. The oscillation of the bubble can affect its radius, because it changes the pressure and temperature inside the bubble. The bubble can also exchange heat and mass with the liquid, which can affect its radius as well.

Basic Theory:

The gas bubble radius (r) can be calculated using the Young-Laplace equation:

$P = \frac{2T}{r}$

Where:

$P$ is the pressure difference across the gas bubble.
$T$ is the surface tension of the gas-liquid interface.
$r$ is the radius of the gas bubble.

Rearranging the equation to solve for $r$ :

$r = \frac{2T}{P}$

Procedures:

Collect Data:
- Pressure difference ( $P$ ): Measured in Pascals (Pa).
- Surface tension ( $T$ ): Measured in Newtons per meter (N/m).
Excel Formula:In Excel, you can use the formula:
$\text{Gas Bubble Radius} (r) = \frac{2 \times \text{Surface Tension} (T)}{\text{Pressure Difference} (P)}$

Explanation:

Let’s consider a scenario where we have a pressure difference of 500 Pa and a surface tension of 0.02 N/m.

Scenario:

Pressure Difference ( $P$ ): 500 Pa
Surface Tension ( $T$ ): 0.02 N/m

Excel Calculation:

Create an Excel table with the following columns: Pressure Difference, Surface Tension, Gas Bubble Radius.
Input the scenario data into the corresponding columns.
In the Gas Bubble Radius column, use the formula mentioned earlier to calculate the gas bubble radius for each row.

Pressure Difference (Pa)	Surface Tension (N/m)	Gas Bubble Radius (m)
500	0.02	=2 * B2 / A2

MATLAB Comparison:

In MATLAB, the code for the gas bubble radius calculation would be:


            % Scenario data
            P = 500; % Pressure Difference (Pa)
            T = 0.02; % Surface Tension (N/m)

            % Gas Bubble Radius calculation
            r = 2 * T / P;
            disp(['Gas Bubble Radius (MATLAB): ' num2str(r) ' meters']);

Result:

Gas Bubble Radius (Excel):

$\frac{2 \times 0.02}{500} \approx 0.00004 \, \text{meters}$

Gas Bubble Radius (MATLAB):