Sheathless Elasto‐Inertial Focusing of Sub‐25 Nm Particles in Straight Microchannels

Abstract

Nanoscale biological particles, such as lipoproteins (10–80 nm) or extracellular vesicles (30–200 nm), play pivotal roles in health and disease, including conditions like cardiovascular disorders and cancer. Their effective analysis is crucial for applications in diagnostics, quality control, and nanomedicine development. While elasto‐inertial focusing offers a powerful method to manipulate particles without external fields, achieving consistent focusing of nanoparticles (<500 nm) has remained a challenge. In this study, elasto‐inertial focusing of nanoparticles as small as 25 nm is experimentally demonstrated using straight high‐aspect‐ratio microchannels in a sheathless flow. Systematic investigations reveal the influence of channel width, particle size, viscoelastic concentration, and flow rate on focusing behavior. Additionally, through numerical simulations and experimental validation, insights are provided into particle migration dynamics and viscoelastic forces governing nanoparticle focusing. Finally, biological particles, including liposomes (90–140 nm), extracellular vesicles (100 nm), and lipoproteins (10–25 nm) is successfully focused, under optimized conditions, showcasing potential applications in medical diagnostics and targeted drug delivery. These findings mark a significant advancement toward size‐based high‐resolution particle separation, with implications for biomedicine and environmental sciences.

High‐aspect‐ratio microchannels with elasto‐inertial microfluidics effectively focus sub‐micron particles without a sheath flow. This enables precise manipulation of biological nanoparticles like liposomes and extracellular vesicles, advancing diagnostic and therapeutic applications. Additionally, these microchannels offer strong potential for size‐based particle separation through differential migration, enhancing their versatility in biomedical and analytical research.

1. Introduction

The ability to manipulate nanoparticles is crucial for many fields ranging from disease diagnostics to drug delivery.^{[ 1 ]} Nanoscale bioparticles in the body play an indispensable role in health and their dysregulation causes many diseases. For example, lipoproteins, such as high‐density lipoprotein (HDL) and low‐density lipoprotein (LDL), transfer lipids through the body. Their imbalance, as well as their deviation from canonical physical properties such as size, is a marker of dyslipidemia and metabolic diseases.^{[ 2 ]} Moreover, certain types of lipoproteins are associated with neurodegenerative diseases such as Alzheimer's.^{[ 3} , ^{4 ]} Extracellular vesicles (EVs) enable intercellular communication in the body, and certain types of EVs are associated with diseases like cancer.^{[ 5 ]} Current methods to sort biological nanoparticles, such as size exclusion chromatography (SEC),^{[ 6 ]} asymmetrical flow field‐fractionation (AF4)^{[ 7 ]} or centrifugal techniques^{[ 8 ]} are cumbersome, expensive, and rarely result in pure fractions. Therefore, developing advanced methods to sort and study particles based on their physical properties, such as size, is crucial.

In addition to biomedical applications involving biological nanoparticles, environmental nanoparticles are also relevant for human health. For example, microplastics in water pose a significant threat to human health. The toxicity and environmental impact of these contaminants are highly affected by particle size and properties.^{[ 9 ]} Therefore, size‐based enrichment of nanoparticles is critical for downstream analysis in environmental studies toward determining the toxicities of these particles in solution.^{[ 10 ]}

Microfluidics has emerged as a promising technology over the last few decades, revolutionizing fields ranging from biomedicine to chemistry and environmental science.^{[ 11} , ¹² , ^{13 ]} The ability to manipulate fluids at the microscale provides unparalleled control over particle sorting, focusing, and separation, making microfluidics a powerful tool for research and industrial applications.^{[ 14 ]} Microfluidic manipulation methods are broadly categorized into active and passive methods, depending on whether external forces are used to manipulate particles. Active methods rely on external forces, such as electric,^{[ 15} , ^{16 ]} magnetic,^{[ 17 ]} or acoustic^{[ 18} , ^{19 ]} waves to direct particle movement. These methods offer high precision micrometer sized particles but often require complex setups and significant operational costs. In contrast, passive methods utilize inherent fluid properties and microchannel geometry to achieve particle manipulation without external actuation, making the methods simpler and more cost‐effective. Among passive methods, inertial microfluidics^{[ 20 ]} and elasto‐inertial microfluidics^{[ 21 ]} have garnered significant attention due to their ability to perform label‐free focusing and separation at high‐throughput.

Inertial microfluidics leverages the interplay of shear‐induced lift forces and wall‐induced lift forces to focus particles at equilibrium positions within Newtonian fluids.^{[ 22} , ^{23 ]} A single, stable focusing position^{[ 24} , ^{25 ]} and high resolution separation^{[ 26 ]} can be achieved by the addition of curvature, but the systems demand very high pressures (tens to hundreds of bar) to focus sub‐micron particles, leaving nanoparticles out of reach. Elasto‐inertial microfluidics extends the principles of inertial microfluidics by introducing viscoelastic (VE) fluids, which generate an additional elastic force arising from the fluid's normal stress differences.^{[ 27 ]} The combination of elastic, shear‐induced, and wall‐induced lift forces enables the focusing of particles at a single, stable equilibrium position,^{[ 28 ]} even for submicron particles. This enhanced control makes elasto‐inertial microfluidics particularly suitable for nanoparticle applications. One important advantage of elasto‐inertial focusing is its enhanced control over submicron particles, eliminating the effect of Brownian motion, which becomes more significant as particle size decreases.^{[ 29 ]}

Despite the promise of elasto‐inertial microfluidics, its application to nanoparticle manipulation remains underexplored. Previous studies have achieved focusing of particles down to 100 nm in curved, spiral microchannels^{[ 30 ]} and 200 nm in straight microchannels.^{[ 31 ]} However, focusing particles smaller than 100 nm in straight microchannels has remained a challenge due to the high pressures required for effective manipulation.

In this study, we experimentally investigate elasto‐inertial focusing of nanoparticles as small as 25 nm using high‐aspect‐ratio microchannels in sheathless flow conditions. Numerical simulations complement these experiments by providing detailed insights into the forces and dynamics governing particle migration toward the equilibrium position. We systematically evaluate the effects of particle size, channel geometry, viscoelastic fluid properties, and flow rates on focusing behavior. Our experiments include the use of polystyrene beads (25, 50, 100, 200, 500 nm, and 1 µm), two different channel widths (5 and 10 µm) and four viscoelastic fluid concentrations (500, 1000, 2000, and 4000 ppm of PEO). Additionally, we demonstrate the successful focusing of biological nanoparticles, including liposomes (90–140 nm), extracellular vesicles (100 nm), high and low–density lipoproteins (10–25 nm), at the optimal experimental conditions. These findings lay the foundation for advanced nanoparticle manipulation strategies and their applications in biomedicine and environmental sciences.

2. Theoretical Background

Elasto‐inertial microfluidics relies on a detailed understanding of the flow regime and the forces acting on particles within a microchannel. To better understand how these forces affect particle behavior under different flow conditions, the use of dimensionless numbers such as the Reynolds number (Re), Weissenberg number (Wi) and Elasticity number (El) are useful. Re describes the ratio of inertial to viscous forces in a fluid and determines the flow regime and is formulated as^{[ 22 ]} Re = 𝜌U_mL/µ, where 𝜌 is fluid density, U_m is the average fluid velocity, L is the characteristic channel length, and µ is the fluid viscosity. The Weissenberg number quantifies the ratio of elastic to viscous effects in a viscoelastic fluid, providing insight into the role of fluid elasticity on particle behavior. Wi is expressed as^{[ 32 ]} Wi = 2𝝀Q/hw², where 𝝀 is the relaxation time of the viscoelastic fluid, Q is the volumetric flow rate, h is the height of the channel and w is the channel width. The importance of the Weissenberg number arises as it involves the characteristic relaxation time of the polymers, which is an intrinsic property of non‐Newtonian fluids and varies with the polymer concentration of the fluid. This parameter is crucial for understanding elastic contribution to particle migration. Finally, the Elasticity number combines Re and Wi to describe the relative importance of elastic and inertial effects. It is defined as (El = Wi/Re)^{[ 32 ]} and is instrumental in interpreting experimental data, as it reflects the balance between inertial and elastic forces.

The blockage ratio is another dimensionless number that plays a role in particle focusing. It is defined as the ratio of particle size over characteristic dimension of the channel (ß = a/L).^{[ 33 ]} In this study, we define the blockage ratio as ß = a/w, since the microchannel width represents the characteristic length of the high aspect ratio microchannels (AR = h/w) considered in this study.

Elasto‐inertial focusing occurs when the lift force and the elastic force balance each other in a microchannel. The lift force (F_L) is considered as the combination of shear‐induced lift force and wall‐induced lift force and formulated as^{[ 34 ]} F_L = c_L𝜌U_m ²a⁴/D_h ², where c_L is the lift coefficient, a is the particle size, and D_h is the hydraulic diameter of the channel. The presence of non‐Newtonian fluid in a microchannel causes unequal normal stress differences (N₁ and N₂), which results in the formation of an elastic force.^{[ 35 ]} The elastic force is expressed as^{[ 36 ]} F_E = a³∇N₁. The final equilibrium position of the particles depends on the complex relation between the lift force and the elastic force, and the geometry of the cross‐section of the microchannel. In previous studies, it has been shown that particles can be found at the channel corners or at the center in single or multiple positions depending on the flow conditions and channel geometry.^{[ 21 ]}

3. Results and Discussion

In this section, we present experimental and numerical results on nanoparticle focusing and migration in elasto‐inertial microfluidics. First, we compare inertial and elasto‐inertial focusing for 200 nm, 500 nm, and 1 µm particles. Then, we systematically investigate the effects of particle size, channel width, viscoelastic fluid concentration, and flow rate on focusing behavior. Additionally, we explore particle migration dynamics using numerical simulations to understand the interplay between elastic and inertial forces during size‐based migration toward equilibrium positions. Finally, we demonstrate the potential of this method for biological nanoparticle focusing under optimized conditions, paving the way for applications in diagnostics, particle enrichment, and high‐resolution size‐based separation.

3.1. Inertial Focusing Versus Elasto‐Inertial Focusing

The ability to focus nanoparticles is a critical challenge in microfluidics, primarily because the forces governing particle migration scale with particle size. As it will be described below, this is the case particularly when comparing inertial and elasto‐inertial approaches. As shown schematically in Figure 1a, inertial microfluidics typically focuses particles along the channel's center‐face, resulting in two equilibrium positions in high‐aspect‐ratio straight channels. However, when viscoelastic fluids, such as PEO solutions, are used in elasto‐inertial microfluidics, the addition of elastic forces drives particles to focus at a single central position, fundamentally altering their behavior. Experimental results for 200 nm, 500 nm, and 1 µm particles under identical flow rates (3 µL min⁻¹) and channel geometry (h = 60 µm, w = 5 µm) are shown in Figure 1b. In Newtonian fluids, 1 µm particles exhibit partial focusing near the two long sides of the microchannel, as expected in inertial focusing within high‐aspect‐ratio channels.^{[ 22} , ^{37 ]} However, this focusing is incomplete, and smaller particles (200  and 500 nm) show no focusing behavior due to insufficient inertial forces,^{[ 38 ]} emphasizing the size dependency of inertial focusing. Achieving nanoparticle focusing with inertial microfluidics would require impractically high flow rates, making this approach unsuitable for such applications.

Figure 1.

Overview of particle focusing principle in high‐aspect‐ratio microchannels. a) Schematic of the microfluidic device layout. Each channel consists of a central 3 mm‐long high‐aspect‐ratio segment (width = 5 or 10 µm, height = 60 µm), flanked by 1.5 mm‐long upstream and downstream wider segments (width = 20 µm, height = 60 µm). This geometry was chosen to minimize pressure drop, simplify the fabrication of narrow segments, and suppress secondary flow. Segment transitions are tapered at 175° to ensure smooth entry into the narrow region. The inset shows the high‐aspect‐ratio section and dominant forces governing elasto‐inertial particle migration. b) Inertial focusing (left) and elasto‐inertial focusing (right) in a high‐aspect‐ratio microchannel (h = 60 µm, w = 5 µm). The upper panel shows the fluorescence images of 1 µm (orange), 500 nm (green), and 200 nm (blue) particles, while the lower panel presents the corresponding cross‐sectional intensity profiles. The flow rate is 3 µL min⁻¹. Scale bar: 50 µm.

In contrast, elasto‐inertial microfluidics using a 1000 ppm PEO solution demonstrates successful focusing for all three particle sizes at the channel center, with 1 µm particles displaying the highest fluorescence intensity. These results highlight the size‐dependent nature of elasto‐inertial focusing,^{[ 39 ]} where elastic forces significantly enhance the manipulation of smaller particles. Importantly, this study demonstrates that elasto‐inertial microfluidics overcomes the limitations of inertial focusing, enabling nanoparticle alignment under practical experimental conditions.

3.2. Achieving Particle Focusing Down to 25 nm

The ability to focus sub‐100 nm particles represents a significant milestone in elasto‐inertial microfluidics, addressing long‐standing challenges in manipulating nanoscale particles effectively. After successfully focusing 200  and 500 nm particles, we extended our investigation to particles ten times smaller. Figure 2 shows the focusing behavior of 25 nm particles under a fixed PEO concentration of 500 ppm in a microchannel with an aspect ratio of 6 (h = 60 µm, w = 10 µm), at four different flow rates (0.5, 1, 1.5, and 2 µL min⁻¹).

Figure 2.

The focusing of 25 nm particles. The graph shows the normalized intensity of the cross‐section of particle focusing in a high‐aspect‐ratio microchannel (h = 60 µm, w = 10 µm) at flow rates ranging from 0.5 to 2 µL min⁻¹. The inset shows the corresponding fluorescence microscopy images of 25 nm nanoparticles focusing at varying flow rates. Scale bar: 50 µm.

These experimental conditions (500 ppm of PEO and channel w = 10 µm) were chosen to identify the lower limit of polymer concentration required to maintain focusing behavior at larger channel widths. Fluorescence intensity graphs reveal that 25 nm particles predominantly focus at the channel center, albeit with slight distortions. The highest focusing quality was observed at the lowest flow rate (0.5 µL min⁻¹), with quality gradually decreasing as flow rates increased due to reduced residence time hindering particle migration fully to the center. With a blockage ratio (a/w) of 0.0025, these results are ≈20 times smaller than previously reported focusing thresholds, demonstrating the dominant role of viscoelasticity (Re < 1, Wi > 10, El ≈ 63) in overcoming Brownian motion and achieving precise nanoparticle focusing.

To achieve such high focusing efficiency without significant pressure drops, we implemented an innovative microchannel design previously introduced by our team.^{[ 40 ]} This geometry incorporates a central, narrow high‐aspect‐ratio segment that enhances focusing performance, flanked by wider upstream and downstream sections that reduce pressure drop and simplify fabrication (see Section 5 for design rationale). This layout ensures strong elastic forces while maintaining mechanical stability. Downstream, the channel gradually widens to maintain low pressure across the system while preserving the focused particle position near the channel center.

By implementing this design, we effectively balance the benefits of high‐aspect‐ratio focusing with manageable pressure drops, enhancing the practicality of elasto‐inertial microfluidic systems. We achieve precise nanoparticle focusing without the drawbacks associated with uniformly narrow channels, such as excessive pressure drops. Building on these results, we next investigate the influence of channel geometry and fluid properties on the focusing behavior, aiming to further optimize particle manipulation in elasto‐inertial microfluidics.

3.3. Effect of Channel Geometry and Viscoelastic Properties on Nanoparticle Focusing

The focusing of nanoparticles in elasto‐inertial microfluidics is strongly influenced by both channel geometry and fluid properties, such as the concentration of PEO. We systematically investigated these factors to optimize focusing behavior, using microchannel with different widths and viscoelastic fluids of varying PEO concentrations.

We used microchannels with widths of 5 µm and 10 µm, while keeping the channel height constant at 60 µm, resulting in aspect ratios of 12 and 6, respectively. As shown in Figure 3 , fluorescence intensity profiles of 50 nm particles at a PEO concentration of 1000 ppm and flow rates ranging from 0.5  to 3 µL min⁻¹ indicate that particles are primarily focused at the channel center, independent of width and flow rate. However, a higher intensity signal at the channel center was observed in the narrower channel (w = 5 µm). This behavior likely results from stronger elastic forces in the smaller channel dimensions, where enhanced stress differences^{[ 41 ]} drive particles toward the minimum stress region at the channel center. Despite the consistent central focusing, the likelihood of unfocused particles increases with wider channels due to reduced elastic force. The focusing bandwidth (FWHM/w) is smaller across all flow rates for the narrower channel (w = 5 µm), with a significant increase in bandwidth observed at the highest flow rate of 3 µL min⁻¹ in the wider channel (w = 10 µm) (see Figure S1, Supporting Information). These trends are supported by numerical simulations (Figure S2, Supporting Information), which reveal that channels with higher aspect ratios generate greater first normal stress differences (N₁), intensifying elastic forces and improving focusing efficiency. Moreover, as expected, longer relaxation times (or higher Weissenberg numbers) correlate with increased elastic stresses and higher maximum N₁ (see Figure S2a, Supporting Information). To the best of our knowledge, single‐line particle focusing at the blockage ratios as low as 0.005 and 0.01 has not been achieved previously. We believe that the increased elasticity component and the utilization of high‐aspect‐ratio microchannels are the driving factors for nanoparticle focusing at such low blockage ratios.

Figure 3.

The effect of the channel width on particle focusing. Normalized intensity graphs of the cross‐section comparing 50 nm particle focusing in microchannels with channel widths of 5 and 10 µm at a PEO concentration of 1000 ppm and flow rates ranging from 0.5 to 3 µL min⁻¹. The intensity profile highlights the effect of channel width on particle focusing quality. Scale bar: 50 µm.

The concentration of PEO significantly influences the viscoelastic fluid properties, which in turn govern the elasticity and viscosity components critical for elasto‐inertial focusing. Table S1 (Supporting Information) details the rheological properties of the PEO solutions used in this study. Increasing PEO concentration enhances the relaxation time (𝝀) and fluid viscosity (µ), thereby strengthening the elastic component (F_E≈𝝀)^{[ 42 ]} while reducing the Reynold number (Re≈1/µ).^{[ 22 ]}

Figure 4 illustrates the impact of four different PEO concentrations (500 , 1000 , 2000 , and 4000 ppm) on the focusing behavior of 25  and 100 nm particles in a microchannel with an aspect ratio (AR) of 12 (h = 60 µm, w = 5 µm) at a constant flow rate of 0.5 µL min⁻¹. Notably, the particles primarily focus at the channel center even at the lowest PEO concentration of 500 ppm (Re = 0.2, Wi = 47.78, El = 235.72), but some unfocused particles are observed. Increasing the concentration to 2000 ppm narrows the focusing bandwidth, eliminating unfocused particles around the center for the 100 nm particles. At 4000 ppm, focusing further improves for 100 nm particles, but no significant enhancement is observed for the 25 nm particles, which maintain their position at the center with slight distortions. These results suggest that increasing PEO concentration improved focusing quality for larger nanoparticles, but its effectiveness diminishes at smaller particle sizes due to competing effects between the different forces involved.

Figure 4.

The effect of PEO concentration on particle focusing. Fluorescence images and normalized fluorescence intensity graphs of 25 and 100 nm particles at a constant flow rate of 0.5 µL min⁻¹. A higher PEO concentration improves focusing, especially for 100 nm particles. Scale bar: 50 µm.

The interplay between channel geometry and PEO concentration is crucial for achieving optimal nanoparticle focusing. Higher aspect ratio channels amplify elastic stresses, leading to sharper focusing, while increasing PEO concentrations enhances viscoelastic effects that further stabilize particle focusing and improve focusing efficiency. However, at higher concentrations, additional elasticity does not necessarily improve focusing for the smallest nanoparticles, indicating a need for balance between design parameters and fluid properties. These results highlight the importance of tailoring both geometric and fluidic parameters to the specific particle size and application requirements.

With these insights into the effects of geometry and fluid properties, we now turn to the roles of particle size and flow rate in further refining the focusing behavior.

3.4. Influence of Particle Size and Flow Rate on Nanoparticle Focusing

The performance of elasto‐inertial microfluidics for nanoparticle focusing is strongly influenced by particle size and flow rate, which together determine the balance between elastic and inertial forces. To systematically investigate these effects, we studied six particle sizes (25 , 50 , 100 , 200 , 500 , and 1 µm) at a fixed PEO concentration of 2000 ppm in a microchannel with an aspect ratio (AR) of 12 (h = 60 µm, w = 5 µm) across a range of flow rates from 0.5 to 3 µL min⁻¹. Figures 5 and  6 summarize the experimental results, highlighting the interplay between these parameters.

Figure 5.

The effect of particle size. Fluorescence images and corresponding normalized fluorescence intensity graphs of particles ranging from 25 nm 1 µm at a PEO concentration of 2000 ppm and a flow rate of 1 µL min⁻¹. Larger particles exhibit higher intensity due to better focusing. Scale bar: 50 µm.

Figure 6.

Effect of flow rate and PEO concentration. a) Fluorescence images of different particles (25 nm–1 µm) are overlapped with corresponding cross‐section intensity profiles to illustrate the focusing behavior at different flow rates. Scale bar: 50 µm. b) Heat map of focusing bandwidth for different particle sizes at varying flow rates and PEO concentrations. The data illustrate the interplay between fluid elasticity and flow rate.

At a fixed flow rate of 1 µL min⁻¹ (Figure 5), all tested particles exhibit focusing at the channel center, with the sharpest fluorescence intensity profile observed for 1 µm particles. As particle size decreases, the fluorescence intensity at the center weakens, reflecting an increased proportion of unfocused particles. This trend suggests that larger particles experience stronger elastic forces (F_E ≈ a³, F_L ≈ a⁴),^{[ 43} , ^{44 ]} leading to a more confined and stable focusing profile, whereas smaller particles are more prone to Brownian motion and secondary flow effects. Notably, particles as small as 25 nm still demonstrate focusing behavior, albeit with broader intensity distribution compared to larger particles. These results confirm the feasibility of using elasto‐inertial microfluidics for sub‐100 nm particle focusing, overcoming previous limitations in label‐free nanoparticle manipulation.

Beyond this fixed flow rate analysis, we explored the effect of increasing flow rate on nanoparticle focusing at the fixed PEO concentration of 2000 ppm (Figure 6). At lower flow rates (0.5 and 1 µL min⁻¹), all particle sizes predominantly focus at the channel center, with larger particles (500 nm and 1 µm) achieving the sharpest focusing profiles. Full width at half maximum (FWHM) analysis confirms that even the smallest particles (25 nm) exhibit focusing at the channel center, albeit with a broader intensity distribution. As flow rate increases to 1.5 µL min⁻¹, a transition occurs: smaller particles (50–200 nm) begin to develop additional focusing positions, while larger particles remain centered. At 2 µL min⁻¹ and higher, three stable focusing positions emerge for the 50  and 100 nm particles—one at the channel center and two symmetrically positioned near the sides. The 200 nm particles also deviate from their single central position, instead showing a weaker three‐position focusing pattern at 3 µL min⁻¹. In contrast, 500 nm and 1 µm particles maintain a single focused position at the channel center across all tested flow rates, though with decreasing fluorescence intensity at higher flow rates, suggesting a weaking of elastic forces as inertia grows dominant.

The loss of a distinct focusing at the channel center is expected in elasto‐inertial focusing as the flow rate increases and inertia becomes stronger.^{[ 45 ]} These results align with force scaling predictions: elastic and lift forces scale differently with particle size (F_E≈a³, F_L≈a⁴), leading to stronger focusing of larger particles. However, the emergence of multiple focusing positions for smaller nanoparticles at higher flow rates suggests the influence of the secondary flow effect in high‐aspect‐ratio microchannels. Previous studies have reported that secondary vortices can develop in straight channels at increased flow rates, displacing particles from the centerline due to transverse flow recirculation.^{[ 46} , ^{47 ]} Further research is required to fully characterize these effect in elasto‐inertial focusing.

These findings suggest that for optimal nanoparticle focusing, lower flow rates (≤1 µL min⁻¹) are preferable, where elastic forces dominate over inertia. At these conditions, increasing PEO concentration enhances focusing quality by reinforcing viscoelastic effects. However, at higher flow rates, increasing inertia not only disrupts focusing but also introduces new stable focusing positions for smaller nanoparticles, requiring careful optimization for size‐based separations.

In the following section, we further explore particle migration mechanisms for application in high‐resolution nanoparticle separation, integrating numerical and experimental analyses.

3.5. Particle Migration for Size‐Based Separation

The ability to manipulate nanoparticles for size‐based separation relies on a detailed understanding of their migration behavior in viscoelastic fluids. Our previous work demonstrated that prefocusing particles at the channel center is a crucial first step before achieving effective size‐based separation.^{[ 40 ]} In this study, we extend this approach to nanoparticles and investigate both numerically and experimentally how elastic forces guide particle migration.

To understand the physical mechanisms underlying particle migration in viscoelastic fluids, we consider the competition between elastic and inertial forces in a viscoelastic fluid. The shear gradient lift force pushes particles away from the centerline,^{[ 48 ]} while elastic forces counteract this by pulling the immersed particle toward the centerline for fluids which are not shear–thinning.^{[ 47} , ⁴⁹ , ⁵⁰ , ^{51 ]} To investigate this mechanism further, we performed fully resolved 3D direct numerical simulations for a particle suspended in a viscoelastic fluid flowing through a straight microchannel with cross‐sectional dimensions 𝑙_x and 𝑙_y, where z/𝑙_𝑧 = 0.5 denotes the centerline along the channel width (see Figure 7a for the coordinate system). In the following analysis, length is non–dimensionalized by the hydraulic diameter of the duct (Dh), time by D_h/U_m, and elastic stress by 𝜌U_m ², where U_m is the constant bulk velocity of the flow. Our numerical simulation is based on the direct forcing immersed boundary method (IBM), in which rigid spherical particles are represented as Lagrangian meshes interacting with the surrounding fluid, discretized on a Eulerian grid.^{[ 52} , ^{53 ]} The fluid is modeled using the incompressible Navier‐Stokes equations coupled with the Oldroyd‐B constitutive model^{[ 54 ]} to capture viscoelastic behavior, and both sets of equations are solved using finite‐difference schemes (see Section 5 for full numerical formulation and validation cases).^{[ 52} , ^{55 ]} Importantly, the simulations account for the full two‐way coupling between fluid and properties. This approach causes accurately both the elastic force and inertial effects emerge from the coupled equations as shown in our previous publications.^{[ 40} , ⁵² , ^{55 ]} In addition, particle trajectories are explicitly computed throughout the simulation domain, allowing us to directly track migration paths and steady‐state focusing positions.

Figure 7.

Numerical analysis of particle focusing and migration. a) The first normal stress difference (𝑁₁) across the channel cross–section. The particle reaches its equilibrium position at the center of the channel where 𝑁₁=0. b) Particle spanwise position for AR=12 and the particles with diameters of 1.6, 1 µm, and 750 nm over time. 𝑁₁, particle position, and time are non‐dimensional.

As shown in Figure 7a, numerical simulations of the first normal stress difference (N₁ = τ_𝑥𝑥−τ_𝑦𝑦) reveal that stress is the highest near the channel walls and significantly lowers at the center. As a result, the gradient of N₁ drives particles toward the channel center, where they encounter minimal elastic stress.^{[ 50 ]} This effect is particularly important in high‐aspect‐ratio channels, where it promotes single‐line focusing.^{[ 40 ]}

To quantify size‐dependent migration, we performed numerical simulations for 1.6 , 1 µm, and 750 nm particles. As can be seen in Figure 7b, all particles migrate toward the channel center (𝑧/𝑙_𝑧 = 0.5), but larger particles reach a steady‐state position significantly faster than smaller ones. The 1.6 µm particle achieves steady‐state in under 80 non‐dimensional time units, while the 1 µm particle requires over 100 non‐dimensional time units. The 750 nm particle continues to migrate toward the center at this point, though due to computational constraints, its full trajectory could not be resolved. The variation in migration velocity stems from size‐dependent elastic forces, which result from the non‐uniform distribution of the normal stress difference (N₁) across the particle volume. This force scales with particle size as F_E ∝ a³∇(N₁), where a is the particle radius.^{[ 39} , ^{49 ]} As a result, larger particles experience stronger elastic forces, promoting faster migration toward the centerline. Accordingly, 1  and 1.6 µm particles reach the channel center more quickly, while 750 nm particles migrate more slowly and require longer times to reach the equilibrium. The numerical data confirms that migration velocity increases with particle size. Moreover, migration velocity decreases as particles approach the centerline due to the progressively lower elastic stress gradients because of the lower local values of N₁.

It is important to highlight that particle migration is consistently more pronounced along the short axis of the channel (Z‐direction), while lateral migration along the Y‐direction remains limited. This can be explained by the distribution of the first normal stress difference (N₁), which forms a vertically extended low‐stress region along the channel center (see Figure 7a). Under strong elastic effects, particles are driven along the Z‐axis toward this central low‐N₁ zone. Conversely, the low stress gradient along the Y‐axis near the centerline results in slower migration, allowing for multiple potential equilibrium positions across the midplane.

To validate these numerical predictions, we conducted experimental studies tracking the migration of 500 nm and 1 µm particles in a two‐stage microfluidic device (Figure 8 ). In the first section, particles were prefocused at the channel center, after which the channel split into two branches, enabling observation of migration back toward the centerline. The results confirm that 1 µm particles migrate significantly faster than 500 nm particles, in agreement with numerical predictions. Figure 8b shows the intensity profile for the 1 µm particles and 500 nm particles where the 1 µm particles migrate and reach the centerline faster while the 500 nm particles are lagging behind and exhibit broader spatial distribution, increasing overlap with 1 µm particles, which could pose challenges for high‐purity separation.

Figure 8.

Particle pre‐focusing and migration for separation. a) Schematic of a microfluidic chip with the pre‐focusing and migration sections, where fluorescence images are taken to observe the migration of 500 nm and 1 µm particles. Scale bar: 50 µm b) The fluorescence intensity profiles of both 500 nm and 1 µm particles. The pink line indicates the center of the channel c) Trajectories of both particles based on average intensity points. The larger (1 µm) particles migrate faster to the center.

However, further optimizations are needed to achieve complete size‐based separation since 500 nm particles are spread wider while migrating toward the channel center, overlapping with 1 µm particles. Under similar conditions, we successfully separate 2  and 3 µm particles, indicating that separation resolution is size‐dependent (see Figure S3, Supporting Information), with smaller nanoparticles requiring additional optimizations.

These findings demonstrate that elasto‐inertial migration can effectively enrich nanoparticles, but further refinements are needed to achieve complete separation at the sub‐micron scale. At this size range, Brownian motion and reduced elastic force gradients introduce challenges that must be addressed by optimizing channel geometry, flow conditions, and viscoelastic properties. Despite these complexities, the observed migration behavior paves the way for high‐resolution nanoparticle sorting using elasto‐inertial microfluidics. Future efforts will focus on multi‐stage separation strategies and further tuning of viscoelastic stress distributions to enhance separation fidelity.

3.6. Focusing of Biological Nanoparticles

To demonstrate the potential of elasto‐inertial microfluidics in high‐aspect‐ratio microchannels for biomedical applications, we investigated the focusing behavior of biologically relevant nanoparticles. We conducted experiments using high‐density lipoproteins (HDL, 10 nm), low‐density lipoproteins (LDL, 25 nm), liposomes (90 nm), and extracellular vesicles (EVs, 100 nm) in a viscoelastic fluid at 1000 ppm PEO as this concentration showed the most consistent focusing quality results (detailed size distribution of biological particles are provided in Figure S4, Supporting Information).

Our results, presented in Figure 9 , reveal that biological particles exhibit central focusing within the microchannel, consistent with the behavior observed for polystyrene nanoparticles. The smallest particles (HDL, 10 nm) exhibited the highest background signal, likely due to their small size and increased diffusion. However, LDL (25 nm), liposomes (90 nm), and EVs (100 nm) were fully focused at the channel center, demonstrating the ability of elasto‐inertial forces to counteract Brownian motion and drive nanoscale bioparticles to a single equilibrium position.

Figure 9.

Focusing on biological nanoparticles (HDL, LDL, liposomes, EVs) in high‐aspect‐ratio microchannels at a PEO concentration of 1000 ppm and a flow rate of 1 µL min⁻¹. a) HDL (10 nm), b) LDL (25 nm), c) Liposome (90 nm), d) EVs (100 nm). Scale bar: 50 µm. Results demonstrate the applicability of elasto‐inertial focusing for biological samples.

These findings establish the feasibility of elasto‐inertial focusing for the manipulation of biological nanoparticles, which is crucial for applications requiring particle enrichment, high‐purity isolation, and potential size‐based separation. Unlike conventional methods such as size‐exclusion chromatography, ultracentrifugation, and asymmetrical flow field‐flow fractionation, which often require multiple processing steps and specialized equipment, elasto‐inertial microfluidics provides a label‐free, single‐step approach with minimal sample preparation. Additionally, compared to microfluidics based active methods such as acoustofluidics and dielectrophoresis, which rely on external fields and complex device architectures,^{[ 56} , ⁵⁷ , ⁵⁸ , ⁵⁹ , ^{60 ]} the method presented here enables high‐throughput nanoparticle manipulation with a simple, single‐inlet design.

Previous studies have explored viscoelastic microfluidics for extracellular vesicle and lipoprotein enrichment, but these methods have been limited in their ability to precisely focus particles below 50 nm in sheathless conditions. The present work extends the lower focusing limit to 10 nm, demonstrating that high‐aspect‐ratio channels combined with optimized viscoelastic conditions provide a scalable platform for sub‐100 nm particle manipulation. Beyond focusing, our findings lay the groundwork for future developments in size‐based separation of nanoparticles (<500 nm) using elasto‐inertial forces.

We also conducted supplementary experiments in a low‐aspect‐ratio channel geometry (width = 60 µm, height = 20 µm; AR = 0.33) using 1  and 3 µm particles to assess confinement in the orthogonal direction. In such channels, the first normal stress difference is minimized along the lateral axis (x‐direction),^{[ 61 ]} in contrast to high‐aspect‐ratio channels where confinement primarily occurs in the vertical (z) direction. As shown in Figure S5 (Supporting Information), particles in the low‐aspect‐ratio channel did not achieve tight lateral single‐line focusing after 8 mm of channel length. However, at 16 mm, both 1  and 3 µm particles migrated to the centerline laterally, indicating that elasto‐inertial forces still promote centerline confinement when sufficient elastic force is present. It is important to note that the images shown in Supplementary Figure S5 (Supporting Information) reflect lateral (x‐y) behavior only. While they suggest progressive centerline migration, no side‐view imaging was performed to confirm 3D confinement. Minor sidewall signal observed for 1 µm particles may be due to out‐of‐plane particles or imaging artifacts, thus this figure should be interpreted as demonstrating lateral migration trends rather than definitive single‐stream confinement. All‐in‐all, although these particles are larger than the nanoscale targets of this study, the results provide qualitative support that focusing behavior in viscoelastic flows can be symmetric with respect to channel orientation. Nevertheless, for downstream applications such as size‐based migration and flow cytometry, lateral confinement is functionally critical. Therefore, we chose high‐aspect‐ratio designs to ensure that single‐line lateral focusing is achieved efficiently in shorter channels, enabling predictable particle entry into separation modules.

4. Conclusion

This study establishes elasto‐inertial focusing of nanoparticles as small as 25 nm in a sheathless flow, high‐aspect‐ratio channels. While elasto‐inertial microfluidics has previously demonstrated advantages for microscale particle manipulation, its application to nanoscale particles has been significantly limited. While previous research demonstrated focusing down to 200 nm in straight microchannels, we extend this limit to 10 nm, marking a significant leap in elasto‐inertial microfluidics by achieving nanoparticle focusing in high‐aspect‐ratio microchannels.

Numerical and experimental analyses together provide a deeper understanding of particle migration dynamics in elasticity‐dominated flows (0.03<Re<1.22, 11<Wi<1110, 63<El<6000), reinforcing the robustness of this approach and its potential for broad applications. Our systematic study confirms the feasibility of elasto‐inertial focusing for biologically relevant nanoparticles, including HDL (10 nm), LDL (25 nm), lipoproteins (90 – 140 nm) and EVs (100 nm), under optimized flow conditions. The ability to focus biologically relevant nanoparticles, including those used in drug delivery (e.g., liposomes for mRNA vaccines), opens new avenues for high‐resolution fractionation of biomolecular carries, with implications for both diagnostics and therapeutic applications. We envision that this approach will pave the way for next‐generation microfluidic systems capable of high‐throughput particle separation, bioparticle enrichment, and precision medicine applications. Future work will explore integration with downstream analytical techniques and the development of parallelized systems for enhanced throughput.

5. Experimental Section

Device Fabrication

Microfluidic devices were designed with the AutoCAD software (Autodesk). The master mold to fabricate the PDMS (polydimethylsiloxane) chips was prepared with SUEX (dry SU‐8 film) on a silicon wafer through photolithography process.^{[ 62 ]} In addition to the standard photolithography process, an i‐line filter was used in the mask aligner to fabricate high‐aspect‐ratio microchannels with well‐defined edges. After UV exposure, the wafer was initially left at room temperature, then gradually heated on a hot plate, followed by slow cooling. This controlled temperature ramping helped minimize internal stress and prevent cracking of SU‐8 structures. The PDMS base (SYLGARD 184) was mixed with the curing agent at the mixing ratio of 10:1. The mixture was poured onto the master mold. Degassed in a desiccator and baked at 65 °C for 6 h for curing. The cured PDMS was peeled off, and inlet and outlet holes were punched. The prepared PDMS chip and microscope glass slide were bonded using oxygen plasma activation. The final device was post‐baked at 120 °C for 15 min for better sealing.

Design of Microfluidic Channels

Two different high‐aspect‐ratio microfluidic channels were designed to study nanoparticle focusing. Both microfluidic channels included a central 3 mm‐long high‐aspect‐ratio straight channel (width = 5 or 10 µm, height = 60 µm), flanked upstream and downstream by 1.5 mm‐long wider segments (width = 20 µm, height = 60 µm). This design strategy was selected to 1) minimize pressure drop along the channel, 2) facilitate fabrication by avoiding long, narrow geometries prone to collapse or distortion in PDMS molds, and 3) maintain flow stability and mechanical integrity throughout the device. The segment transitions were tapered at a 175° angle to suppress secondary flow effects and ensure smooth particle entry into the high‐aspect‐ratio section. Two designs (AR = 6 and 12) were used to investigate the effect of width on focusing performance while keeping the height constant at 60 µm. Each device included a wide expansion region (width = 150 µm) prior to the outlet to allow high‐resolution imaging of focused particles. Channel cross‐sections are shown in Figure S6 (Supporting Information), and the overall design is illustrated in Figure 1.

Sample Preparation

In this study, PEO (Polyethylene Oxide, M_w = 2 × 10⁶ g mol⁻¹), elasticity enhancer, was used for the preparation of viscoelastic fluids. The PEO powder was dissolved in deionized water at four different concentrations (500 , 1000 , 2000  and 4000 ppm) (See Table S1, Supporting Information for the rheological properties of the fluids and see Table S2, Supporting Information for the dimensionless numbers). The fluorescent polystyrene (PS) particles (Fluoro‐Max, ThermoFisher Scientific) with diameters of 25 , 50 , 100 , 200 , 500 nm, and 1 µm were suspended in the prepared viscoelastic fluids prior to the flow experiments (3 µL of particles at the concentration of 1% solids were suspended at 3 mL of PEO).

Numerical Analysis

Fully resolved 3D direct numerical simulations were performed to investigate the cross‐streamline migration of particles suspended in viscoelastic (VE) fluids within a relatively high aspect ratio straight microchannel. These simulations aim to further confirm and explain the experimental observations. The in‐house code utilizing a direct forcing immersed boundary method (IBM) was employed to simulate the particles as moving Lagrangian grids, while the carrier fluid is discretized within a stationary Eulerian frame, in which the Navier‐Stokes and the viscoelastic constitutive equations are discretized using finite differences.^{[ 52 ]} The suspending fluid motion is governed by the incompressibility constraint and conservation of momentum as follows:

$$\nabla ·u=0$$ (1)

$$\left(\frac{\partial u}{\partial t}+\left(u·\nabla \right)u\right)=-\nabla p+\frac{1}{Re}\nabla ·\tau +f$$ (2)

Here, u is the fluid velocity, p is the pressure field, τ is the total deviatoric stress tensor, and Re is Reynolds number. The extra term f on the right‐hand side of Equation (2) is the immersed boundary force field representing the particle‐fluid interaction; details of the immersed boundary method can be found in the work of Breugem.^{[ 53 ]} The total deviatoric stress tensor, τ, is composed of contributions from the solvent (Newtonian fluid) and polymer parts as τ = τ𝑠 + τ𝑝. The solvent stress tensor is defined as τ𝑠 = 𝛽𝑠 (∇u + ∇u𝑇), where 𝛽𝑠 = 𝜇𝑠/𝜇 is the ratio of the solvent viscosity to the total viscosity. In addition to the equations mentioned earlier, a constitutive equation should be employed to model the evolution of the non‐Newtonian contribution (τ𝑝) of the VE material. The Oldroyd‐B model^{[ 54 ]} is implemented to consider the viscoelasticity of the material. The linear and angular velocity of particles are calculated by solving Newton‐Euler equations as follows:

$${\rho }_p{V}_p\frac{d{u}_p}{dt}={\oint }_{\partial V}\sigma ·nd+F_c$$ (3)

$$I_p\frac{d{\omega }_p}{dt}={\oint }_{\partial V}r\times \left(\sigma ·n\right)dA+T_c$$ (4)

Here, u_p and ω _p denote the linear velocity of mass centrum and angular velocity of the particle. The Cauchy stress tensor for the viscoelastic fluid is given by 𝜎 = −𝑝I + τ_𝑝 + 𝛽_𝑠 (∇U +∇U^T ), where τ_𝑝 is the viscoelastic stress and 𝛽_𝑠 is the solvent viscosity ratio. The vector r denotes the position of Lagrangian grids relative to the particle center, and 𝜕𝑉 represents the particle boundary. 𝜌_𝑝, 𝑉_𝑝, and 𝐼_𝑝 denote the density, volume, and moment of inertia of the particle. Last, F_c and T_c correspond to the force and torque resulting from particle‐wall collisions. This numerical approach has been extensively validated and applied in prior publications.^{[ 52} , ⁵³ , ^{55 ]} Here, one of the validation cases is included involving the rotation of a particle in a viscoelastic Couette flow, where a neutrally buoyant spherical particle of radius R in the center of a viscoelastic Couette flow is modeled using a domain of size 4R × 8R × 8R with 24 grid points per particle diameter.^{[ 40 ]} Shear is generated by moving the top and bottom walls at velocities ±V, yielding a shear rate of 2 V/8R, with periodic boundaries applied in the other directions. The Reynolds number is fixed at Re = 0.025, and the flow is governed by the Oldroyd‐B model, with Wi ranging from 0 to 2 (see Figure 10a). The particle angular velocity about the x‐axis is computed and compared these results with the experimental data provided by Snijkers et al.^{[ 63 ]} and the numerical results of Goyal and Derksen.^{[ 64 ]} As shown in Figure 10b, the results exhibit excellent agreement, confirming the accuracy of the solver.

Figure 10.

Numerical validation. a) Schematic of the particle suspended in an Oldroyd‐B Couette flow, b) Particle angular velocity about the x‐axis as a function of Weissenberg number (elasticity of the fluid). Blue circles show our DNS results, black markers correspond to the experimental data from Snijkers et al., and green stars indicate the results from Goyal and Derksen.

Preparation of Biological Nanoparticles

Lipoproteins were isolated from the blood plasma of apparently healthy donors, obtained from Blood transfusion station of Karolinska Hospital (Dnr: 2025‐01255‐01, Ethics Review Authority Stockholm). The density of 3 ml of blood plasma was adjusted to 1.021 g mL⁻¹ using KBr powder. The KBr buffers of different densities (1.006 , 1.019 , 1.063 , 1.24 g mL⁻¹) and blood plasma were layered in a gradient, transitioning from denser to less dense solutions in 14 mL tubes (14 × 95 mm, Open‐Top Thinwall Ultra‐Clear Tubes, Backman Coulter, USA). The tubes were ultracentrifuged for 48 h at 37 000 rpm at 15 °C (Optima‐XE Ultracentrifuge, SW 40 Ti Swinging‐Bucket Rotor, Backman Coulter, USA). Post‐centrifugation, LP fractions containing separate Very Low‐Density Lipoproteins (VLDL), Low Density Lipoproteins (LDL) and High‐Density Lipoproteins (HDL) were carefully removed using a medical needle and syringe avoiding the blending of different classes of LPs. Furthermore, VLDL, LDL, and HDL were concentrated using Ultra Centrifugal Filter, 30 kDa MWCO (Amicon). Protein concentration was measured using Bradford assay (Biorad) at NanoDrop Microvolume Spectrophotometer (ThermoFisher). The sizes of lipoproteins were confirmed using Dynamic Light Scattering at Zeta‐sizer (Malvern). HDL and LDL were labeled with TopFluor‐Cholesterol (Avanti Polar Lipids). Finally, 50 µL of HDL and LDL particles at the concentration of 0.5 mg mL⁻¹ were diluted to 1 mL with PEO prior the flow experiments.

For production of extracellular vesicles (EVs), immortalized fibroblasts (BJ‐5ta cell line, ATCC CRL‐4001) were cultured in a 4:1 mixture of Dulbecco's medium supplemented with 4 mM L‐glutamine, glucose (4.5 g L⁻¹) and sodium bicarbonate (1.5 g l⁻¹) and Medium 199 supplemented with Hygromycin B (0.01 mg mL⁻¹) (ThermoFisher Scientific) and 10% fetal bovine serum (Invitrogen). Cells were cultured at 37 °C and 5% CO₂ in a humidified atmosphere and regularly tested for the presence of mycoplasma. For EV harvesting, media was changed to OptiMem (Invitrogen) 48 h before harvest of conditioned media (CM) as described before.^{[ 65 ]} Collected CM was directly subjected to a low‐speed centrifugation step at 500 × g for 5 min followed by a 2000 × g spin for 10 min to remove larger particles and cell debris. Precleared CM was subsequently filtered through 0.22 µm bottle top vacuum filters (Corning, cellulose acetate, low protein binding) to remove any larger particles. EVs were then prepared by tangential flow filtration (TFF) as described before.^{[ 66 ]} In brief, precleared CM was concentrated via TFF by using the KR2i TFF system (Spectrum Labs) equipped with modified polyethersulfone hollow fiber filters with 300 kDa membrane pore size (MidiKros, 370 cm² surface area, Spectrum Labs) at a flow rate of 100 mL min⁻¹ (transmembrane pressure at 3.0 psi and shear rate at 3700 sec⁻¹) as described previously. Amicon Ultra‐0.5 10 kDa MWCO spin‐filters (Millipore) were used to concentrate the sample to a final volume of 100 µL. Final EV samples were stored at −80 °C in PBS‐HAT [PBS supplemented with HEPES, human serum albumin and D‐(+)‐Trehalose dihydrate] until usage.^{[ 67 ]} For labeling, FastDiO (5 µl, Avanti, 0.01 mm in DMSO) was added to purified EVs (50 µL) and kept at least 10 min before the experiments.

Synthetic Liposomes were prepared using the lipid 1,2‐Dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC). DOPC was dissolved in 2 mL of chloroform at 0.25 mg mL⁻¹ in the glass vial. Chloroform was then evaporated under the nitrogen flow. The lipid residue was hydrated using the buffer (150 mm of NaCl, 10 mm of HEPES) and vortexed harshly until the solution became turbid whereas the lipid residue disappeared from the wall of the glass vial. Then, the liquid was transferred to the 15 mL falcon tube and sonicated at power 3, duty cycle 40%, for 10 min using a Branson Sonifier 250. The second aliquot, instead of sonication was extruded 21 times using the mini extruder (Avanti) with a filter size of 100 nm. The size was verified using DLS (Malvern) (see Figure S3, Supporting Information).

Experimental Setup and Analysis

The microfluidic experiments were performed with a mid‐pressure pump (neMESYS CETONI GmbH) using a 3 mL steel syringe. The data acquisition was accomplished using an inverted microscope (Nikon Eclipse TI) with a sCMOS camera (Andor Zyla) and an LED lightning system (Lumenor Spectra X LED). Micro Manager software was used to control the microscope and record the images. The recorded images were processed by ImageJ software.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Tanriverdi S., Cruz J., Habibi S., et al. “Sheathless Elasto‐Inertial Focusing of Sub‐25 Nm Particles in Straight Microchannels.” Small 21, no. 33 (2025): 21, 2503369. 10.1002/smll.202503369

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.