Sample preparation is crucial for chemical analysis, and particle manipulation techniques are gaining importance in applications like sample filtration, flow cytometry, and separation. Submicron-resolution separation is challenging due to the size dependence of lateral particle movement forces. Passive manipulation techniques, such as inertial flow focusing, pinched flow, Dean flow fractionation, and deterministic lateral displacement (DLD), offer advantages like simple device configuration and high throughput, but require precise tuning of parameters. Active techniques, including opto-phoresis, dielectrophoresis, magnetophoresis, and acoustophoresis, provide high precision but are complex and costly. Elasto-inertial microfluidics, using viscoelastic fluids, offers enhanced performance. The elastic lift force generated in viscoelastic flows enables lateral migration of particles, leading to improved separation. Previous studies using co-flows of Newtonian and viscoelastic fluids have utilized Reynolds number (Re), Weissenberg number (Wi), and elastic number (El) for analysis, but these have limitations, especially in co-flow configurations. This study addresses these limitations by introducing modified Wi and El numbers to better understand particle behavior.

The paper reviews existing microfluidic manipulation techniques, highlighting the challenges in achieving submicron resolution separation. Passive techniques, while offering high throughput and simple device design, are sensitive to various parameters, potentially compromising separation accuracy and efficiency. Active techniques, though precise, are complex and expensive. The authors then focus on elasto-inertial microfluidics, which leverages the elastic lift force in viscoelastic fluids to improve particle manipulation. Existing studies utilizing co-flows of Newtonian and viscoelastic fluids are discussed, noting the limitations of previously employed dimensionless numbers (Re, Wi, El) in accurately predicting particle behavior in such systems.

The study proposes a novel dimensionless analysis to predict microsphere migration across the interface of Newtonian and viscoelastic fluids. Modified Weissenberg (Wi_m) and elastic (El_m) numbers are introduced, addressing the limitations of existing dimensionless numbers by considering only the viscoelastic fluid properties. A new dimensionless number is defined as the ratio of Newtonian fluid stream width to microsphere diameter to categorize microsphere migration into three regimes: inertial focusing, elasto-inertial transition, and elastic focusing. Experiments are conducted using polystyrene (PS) microspheres (2.1 and 3.2 µm) in a co-flow of deionized (DI) water (Newtonian) and polyethylene oxide (PEO) solution (viscoelastic) in a microfluidic device with two inlets and three outlets. The microfluidic device is designed to create a three-layered co-flow where the Newtonian sample fluid containing PS microspheres is sandwiched between two streams of viscoelastic sheath fluid. The location of the Newtonian/viscoelastic fluid interface is investigated under varying flow rate conditions. Fluorescent microscopy is used to visualize the interface and microsphere migration. The experimental results are compared with theoretical predictions based on the proposed dimensionless analysis. The methodology also includes validation testing using a mixture of platelets and *E. coli* to demonstrate the applicability of the developed method for biological samples.

The study's key findings include the introduction of modified dimensionless numbers (Wi_m and El_m) that more accurately describe particle behavior in the co-flow system compared to previously used numbers. A new dimensionless number based on the ratio of Newtonian fluid stream width to microsphere diameter is shown to effectively categorize microsphere migration into three distinct regimes. Experimental results validate the theoretical predictions, demonstrating that the proposed analysis accurately predicts microsphere migration across the Newtonian/viscoelastic fluid interface. Submicron-resolution separation of polystyrene microspheres (2.1 and 2.5 µm) is achieved with high throughput, purity (>95%), and recovery rate (>97%). The method is successfully applied to separate platelets from similarly sized *E. coli*, highlighting its practical applicability for bioparticle separation. The analysis of the Newtonian/viscoelastic interface reveals deviations from theoretical predictions at low flow rates, attributed to insufficient inertial effects to stabilize the co-flow. At higher flow rates, the experimental data aligns more closely with theoretical predictions.

The successful prediction of microsphere migration using the proposed dimensionless analysis demonstrates the effectiveness of the modified Wi_m and El_m numbers and the new dimensionless number based on the Newtonian fluid stream width. The high throughput, purity, and recovery rate achieved in the microsphere separation highlight the potential of this method for high-efficiency particle separation. The successful separation of platelets and *E. coli* further validates the applicability of the method to real-world biological samples. The observed deviations from theoretical predictions at low flow rates highlight the importance of considering inertial effects in the co-flow configuration. The findings contribute to a deeper understanding of particle behavior in elasto-inertial microfluidics and provide a valuable tool for designing and optimizing microfluidic separation devices.

This study presents a novel dimensionless analysis for elasto-inertial microfluidic separation, introducing modified dimensionless numbers and a new criterion for predicting microsphere migration. Experimental validation demonstrates high-throughput submicron separation with high purity and recovery rate. Application to bioparticle separation proves its practical relevance. Future research could focus on optimizing device design, exploring different viscoelastic fluids, and expanding the technique to separate a wider range of particle sizes and types.

The study primarily focuses on polystyrene microspheres and a specific viscoelastic fluid (PEO solution). Extending the analysis to other types of particles and viscoelastic fluids would strengthen its generality. The observed deviations from theoretical predictions at low flow rates suggest the need for more refined models that fully account for the complex fluid dynamics in the co-flow configuration. Further investigation is needed to explore the impact of other parameters, such as channel geometry and surface properties, on separation efficiency.