Microfluidic droplet generation: an experimental study of size distribution using probability density function analysis

Abstract Controlling the volume and geometrical ratio of microdroplets offers numerous advantages, particularly in fields like pharmaceutics, photonics, soft electronics, and robotics. For microdroplets generated via microfluidics, precise control of their length-to-width ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mi>L</mml:mi> <mml:mi>w</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> ) ratio enhances their overall performance and contributes to a comprehensive understanding of the results. Advanced experimental tools, including droplet generation systems, visualization techniques, digital processing algorithms, and analysis, are crucial, especially for in situ control of microdroplet size during generation. This study investigates the variation in microdroplet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mi>L</mml:mi> <mml:mi>w</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> ratio and their generation frequencies using two novel approaches: the probability density function (derived both from the Gaussian assumption and directly from experimental data distribution) and the fast Fourier transform. The configuration utilizing one syringe pump (1mp) and syringes (made entirely of plastic) demonstrated the best monodispersity in microdroplet generation with volume differences ranged from 40 ± 2.2 nl to 65 ± 6.7 nl, corresponding to coefficient of variation values of 5.5 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> and 11 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> , respectively. The analysis of ∼7 million <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mi>L</mml:mi> <mml:mi>w</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> data points revealed different types of oscillation frequencies. Specifically, a frequency of around 1 mHz originated from the syringe pump, while frequencies between ∼0.5 and 3 Hz were attributed to the syringe materials and the interaction of a combination of syringe pumps. These results contribute to the phenomenological understanding and classification of droplet generation within the T-junction microfluidic system. Furthermore, they present an enhanced method for visualizing the geometrical variations of the generated microdroplets.