Measuring the film thickness surrounding a bubble inside a capillary

Abstract

The aqueous wetting film thickness surrounding a bubble (air or oil) inside a horizontal capillary tube is measured when the bubble is either stationary or moving at a constant speed ν. A wide range of flow rates are covered in the measurements: Ca ≈ 10 −7 to 10 −4 for an air bubble, and Ca ≈ 10 −6 to 10 −3 for an oil bubble. The capillary number Ca is defined as μ c υ/ γ, where μ c is the viscosity of the continuous liquid and γ the interfacial tension. Three different oils were used with oil-to-water viscosity ratio μ b/ μ c = 0.51, 1.08, and 4.35. The wetting film thickness decreases as the bubble speed decreases until it approaches a constant value. Evidence is presented which suggests that the value of the constant is due to the roughness of the tube wall. For an air bubble moving at Ca ≈ 5 × 10 −5 to 3 × 10 −4, the measured wetting film thickness h correlates with the simple formula h = 0.5rCa 1 2 , proposed by Fairbrother and Stubbs ( J. Chem. Soc. 1, 527, 1935). While for an oil bubble moving at Ca ≈ 2 × 10 −4 to 2 × 10 −3, the data agree better with h = 1.337rCa 2 3 , a relationship derived by Bretherton ( J. Fluid Mech. 10, 166, 1961). There is no appreciable difference in the film thickness for the different oils for all Ca, its value being smaller than that for an air bubble moving at the same Ca > 10 −5.