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A 0.03 cm internal diameter glass capillary tube contains gas, oil, and water, thus forming two interfaces, namely, gas–oil and oil–water. The contact angles for these two interfaces are 35° and 25°, while the surface and IFTs are 15 and 30 mN/m, respectively. Calculate the gas–water capillary pressure.

User Jpwco
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Final answer:

The gas-water capillary pressure in a capillary tube is typically calculated using the Young-Laplace equation. The surface tension, contact angle at the gas-water interface, and the radius of the tube are needed. Without additional data on the combined system, a direct calculation cannot be provided.

Step-by-step explanation:

To calculate the gas-water capillary pressure in a glass capillary tube with given surface tensions (or interfacial tensions) and contact angles, we apply the Young-Laplace equation. Considering the tube has a gas-oil interface and an oil-water interface with surface tensions of 15 mN/m and 30 mN/m respectively and contact angles of 35° and 25°, we need to calculate the effective capillary pressure across the gas-water interface. The calculation involves the surface tension of the water, the contact angle at the gas-water interface, and the radius of the tube.

However, we don't have direct values for these variables at the gas-water interface but instead for the gas-oil and oil-water interfaces. The capillary pressure can be calculated by making use of the individual interfacial tensions and combining them effectively to find the pressure difference. Unfortunately, without additional data or clarification on how to treat the combined system, it's not possible to provide a direct answer. The calculation is typically done using the formula ∆P = 2T cos θ / r, where ∆P is the capillary pressure difference, T is the surface tension, θ is the contact angle, and r is the radius of the capillary.

User Abhilash Reddy
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