A Dynamic Approach to Determining the Surface Tension of a Fluid

Abstract

A new formulation has been developed that predicts flow rate of a stream draining from an orifice under the influence of gravity. This model is different from conventional formulations in that it includes the surface tension of the liquid. Results with water and ethylene glycol at various temperatures indicate that it is necessary to account for surface tension under certain conditions including small orifice diameters and operation under low head values. This model is most relevant for liquids of high surface tension including melts such as molten metals, slags and salts. These conditions are accounted for in the Bond number (ρgr_oh/σ) which is a dimensionless quantity useful in determining conditions when surface tension is expected to have considerable impact. When an operation is such that the 1/Bo approaches unity, the formulation has the greatest relevance. The formulation provides unique possibilities in measuring surface tension since this property is related to flow rate and head which are two variables that can be experimentally determined. Calibrations of the discharge coefficient, C_d, are required to determine frictional losses in the orifice. The surface tension of water at 321.5 K was calculated to be 0.067 N/m which is 1.75% from the value quoted in the literature. The measurement is highly susceptible to error. A rigorous error analysis was performed on the formulation and it was determined that as 1/Bo approaches unity, accuracy in the surface tension measurement significantly improves. It is expected that melt systems are best suited for such measurements since these liquids often exhibit large values of 1/Bo for a given orifice design.

A new formulation has been developed that predicts flow rate of a stream draining from an orifice under the influence of gravity. This model is different from conventional formulations in that it includes the surface tension of the liquid. Results with water and ethylene glycol at various temperatures indicate that it is necessary to account for surface tension under certain conditions including small orifice diameters and operation under low head values. This model is most relevant for liquids of high surface tension including melts such as molten metals, slags and salts. These conditions are accounted for in the Bond number (ρgr_oh/σ) which is a dimensionless quantity useful in determining conditions when surface tension is expected to have considerable impact. When an operation is such that the 1/Bo approaches unity, the formulation has the greatest relevance. The formulation provides unique possibilities in measuring surface tension since this property is related to flow rate and head which are two variables that can be experimentally determined. Calibrations of the discharge coefficient, C_d, are required to determine frictional losses in the orifice. The surface tension of water at 321.5 K was calculated to be 0.067 N/m which is 1.75% from the value quoted in the literature. The measurement is highly susceptible to error. A rigorous error analysis was performed on the formulation and it was determined that as 1/Bo approaches unity, accuracy in the surface tension measurement significantly improves. It is expected that melt systems are best suited for such measurements since these liquids often exhibit large values of 1/Bo for a given orifice design.

On a développé une nouvelle formule qui prédit le débit d'un écoulement qui se vide par un orifice sous l'influence de la gravité. Ce modèle est différent des formules conventionnelles en ce qu'il inclut la tension superficielle du liquide. Les résultats avec de l'eau et de l'éthylène glycol à des températures variées indiquent qu'il est nécessaire de tenir compte da la tension superficielle dans certaines conditions incluant les orifices à petit diamètre et l'opération sous de faibles valeurs de charge. Ce modèle est des plus pertinents pour les liquides tension de surface élevée incluant les bains de fusion tels que les métaux fondus, le laitier de haut fourneau, les sels, etc. Ces conditions sont prises en compte dans le nombre de Bond (ρgr_oh/σ), une quantité adimensionnelle utile dans la détermination des conditions où l'on s'attend à ce que tension de surface ait une répercussion considérable. La formule a sa plus grande pertinence quand l'opération est telle que 1/Bo s'approche de l'unité. La formule offre des possibilités uniques de mesure de tension de surface puisque cette propriété est reliée au débit et à la charge, deux variables qui peuvent être déterminées expérimentalement. Le calibrage du coefficient de débit, C_d, est requis pour déterminer les pertes par frottement à l'orifice. On a calculé que la tension superficielle de l'eau à 321.5 K était de 0.067 N/m, soit 1.75% de la valeur citée dans la littérature. La mesure est extrêmement susceptible à l'erreur. On a exécuté une analyse d'erreur rigoureuse de la formule et l'on a déterminé que l'exactitude de la mesure de tension de surface s'améliore très distinctement quand 1/Bo s'approche de l'unité. On s'attend à ce que les systèmes de bain de fusion soient les plus appropriés pour de telles mesures puisque ces liquides exhibent souvent de grandes valeurs de 1/Bo pour un concept donné d'orifice.