Oil drop generator for foliar chemigation: Theory and laboratory evaluation

Precise control of oil drop size optimizes oil retention on plants and oil discharge uniformity along the pipeline for foliar chemigation. However, control of oil drop size with existing chemigation injection systems is difficult. A new system was developed that injects oil drops of known size distribution into a center pivot irrigation pipeline. The system removes water from the irrigation pipeline, increases water pressure with a pump, injects oil into the water stream, increases dispersion velocity in small diameter tubes in order to break up oil drops, and finally injects the water-oil dispersion back into the irrigation pipeline. In order to calculate the maximum drop size (d(max)) of viscous oil drops in the drop generator, a correction term with effective viscosity, effective density, and dispersed phase volume fraction was added to the Hinze (1955) equation for d(max) in turbulent two-phase pipe flow. The new equation calculates d(max) as a function of water flow rate, oil and water viscosity, oil volume fraction, and other measurable parameters. The average relative error and root mean square deviation between d(max) and literature data was 3 and 17%, respectively. The tubing in the drop generator is coiled in order to reduce the length of the system; thus, the coiled tubing friction factor must be used in the d(max) equation. Two equations (the Ito and Srinivasen equations)for friction factor in helical coiled tubing were evaluated in laboratory experiments with the drop generator. The Ito equation performed best; average root mean square deviation between calculated friction factor and experimental data was 2%. Three equations for the effective viscosity of oil-water dispersions (the Einstein, Taylor, and Richardson equations) were evaluated with literature and experimental data. The Richardson equation performed best; average root mean square deviation between calculated viscosity and experimental and literature data was 7%.