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Droplets are studied widely in the scientific community because of their importance in many engineering
applications like liquid-liquid extraction, boiling, flotation, distillation and spray drying etc. Droplet diameter is a key parameter that needs to be studied as it influences the interfacial area in contact with the surrounding fluid. The droplet diameter at the time of evolution affects the shape and path trajectory of the droplet during their subsequent detachment and rise. Therefore, the droplet diameter becomes an important parameter for various studies related to
droplet dynamics, heat and mass transfer etc. The droplet diameter is profoundly affected by the physiochemical
property of the continuous as well as the dispersed phase. In the present study, oil has been used as the dispersed
phase and a water-glycerin mixture has been used as the continuous phase. An effort has been made to study the
effect of the various variables like flow rate (Q), capillary diameter (d), interfacial tension (σ) and viscosity (μ) on droplet diameter at the time of detachment of the droplet from a capillary tip. A total of five sample of varying viscosity were prepared by mixing glycerin in different proportion to water. Two more samples were prepared by mixing a surfactant to vary the interfacial tension. Eight different flow rates of the dispersed phase ranging from 30 ml/h to 100 ml/h in steps of 10 have been used. Three different sizes of capillary have been used. It is found that the droplet diameter strongly depends on the capillary diameter, but is a weak function of the flow rate. Buckingham's ϖ theorem has been used to find various non-dimensionless number that determine the droplet diameter. A multiple regression analysis is used to find a correlation of the form

E_{0} = e^{3.439}λ^{1.327}K^{0.972}M_{0}^{0.203}/Re^{0.182}

Where

E_{0} Eotvos number

M_{0} Morton number

K Viscosity ratio

λ Density ratio

Re Reynolds number

The correlation has been validated for a known sample and the percentage error for droplet diameter prediction is found to be within a 11 % range.

E

Where

E

M

K Viscosity ratio

λ Density ratio

Re Reynolds number

The correlation has been validated for a known sample and the percentage error for droplet diameter prediction is found to be within a 11 % range.