Modification of channel geometry is used without external stimuli in passive mixing methods. The passive designs rely on changes in flow direction, including zigzag, serpentine, spiral, and T-shaped micromixers. These geometries guide the fluid to follow the paths. This way, the flow periodically reorients and enhances mixing through stretching and folding. While these methods are simple and easy to fabricate, the strength and uniformity of the induced secondary flows are generally limited. In addition, the performance depends on the flow rate and the aspect ratio of the channel. In a study, researchers used a 15 µm deep staggered herringbone mixer (Figure 1a) to create chaotic flow (Stroock et al., 2002) and showed a significant reduction in band broadening in 70 × 200 μm channels. This concept relies on an asymmetric groove patterned on the channel wall to create chaotic advection. The alternating ridge orientation generates transverse flow that folds and stretches fluid elements, resulting in an increase in interfacial contact and enhancing mixing. However, the performance of herringbone structures is highly sensitive to the groove dimensions and channel size. In wider channels, the vortices often fail to span the whole cross-section. The grooves must be made very small to remain effective. As a result, practical implementation can become difficult, particularly when long columns or fabrication constraints are involved.

Another hydrodynamically driven passive mechanism is called Dean mixing, which occurs in curved channels due to centrifugal forces acting on fluid elements. An example of this is the study of Tijssen and co-workers in which Dean vortices are investigated in curved capillaries (Tijssen, 1978). They proposed that the resulting secondary flow could mitigate Taylor–Aris dispersion by up to 5-fold (Johnson and Kamm, 1986; Jayaraman, 1998). Dean vortices only become significant at sufficiently high axial velocities because they arise from inertial effects. At low Reynolds number regimes, a characteristic of microfluidics, the induced secondary flow remains weak. In the initial stages of research, efforts were made to benefit from turbulent mixing in larger channels (Giddings et al., 1966; Bauer, 1989). These efforts showed stronger transverse transport. However, these mechanisms were not suitable for microscale systems. These systems need due to the necessity of higher flow rates to induce turbulence, resulting in higher axial dispersion. In summary, passive micromixers have proven instrumental in demonstrating that geometry can induce lateral flow. However, the resulting mixing is either weak, geometry-dependent, or contributes to axial velocity. These limitations have encouraged the development of generating controlled lateral flow.

Active methods use external stimuli to generate lateral flows, unlike passive micromixers. This allows secondary flows to be generated independently from axial flow at low Re values. Active strategies also offer greater control over the location of mixing, strength, and frequency of induced vortices. This makes them more versatile than passive approaches. Several principles have been used to introduce active methods, including magnetic, acoustic, and electroosmotic mixing.

Magnetic mixing depends on the interaction between magnetic fields and magnetic particles. When the oscillating or rotating magnetic field is applied, the particles induce local disturbances while generating transverse microvortices (Shanko et al., 2022). These can enhance mixing efficiency, especially in larger channels where inertial effects are minimal. A well-known example of this is shown in Figure 1b where the rotating magnetic fields are used to generate nanoscale vortices in a 1 mm diameter capillary (Hajiani and Larachi, 2012). Magnetic actuation enhanced the transverse mixing and lowered Taylor dispersion by a factor of five compared with the (uniquely applied) pressure-driven flow situation. The approach also allows the flow to be controlled remotely and reversed without direct contact with the channel walls. However, applying this method in LC systems brings several practical difficulties. Magnetic particles introduced into the stream can disturb separation, so they should be removed after the operation. More importantly, the column did not have any (stationary phase) particles and relevant (micron-scale) chromatographic dimensions, and it seems difficult to apply the method in such (chromatography compatible) conditions.

Acoustic streaming is another active mechanism in which lateral flows are induced through the interaction of acoustic waves and the fluid. Bulk acoustic waves have been used to generate streaming vortices. When the acoustic waves travel along the channel surface or through the fluid, they create localized oscillations that produce time-averaged flow patterns as vortices. This acoustic streaming can be achieved by connecting a piezo-ceramic element (PZT) to the silicon chip to generate a standing wave (Figure 1c). These vortices can be extended across the entire cross-section of the channel under frequency matched conditions. The efficiency of vortex formation depends on the relationship between the acoustic wavelength and channel dimensions to ensure stable streaming patterns. An initial study on the effect of acoustic streaming resulted in more than a two-fold reduction (Figure 2a) and demonstrated that acoustically induced lateral convection is a viable strategy for dispersion reduction (Gelin et al., 2021). A recent study introduced depth matched acoustic resonance as a new approach, compared with the traditional width matching, generating lateral vortices across a 10 μm × 75 µm silicon channel (Naghdi et al., 2025). These acoustic-induced lateral vortices resulted in a 10-fold reduction in Taylor-Aris dispersion and demonstrate the scalability and compatibility of the method in micron-scale dimensions (Figure 2b).

Electroosmotic flow (EOF) occurs when an electric field is applied along a channel whose walls carry a surface charge, generating fluid movement near the electrical double layer. Unlike pressure-driven flow, which produces a parabolic velocity profile with a shear near the walls, EOF exhibits a nearly plug-like profile across the channel. While in traditionally EOF is being used to generate axial flow, it can also be employed to produce lateral (vortex) flows.

The electrode configuration affects vortex formation in EOF-driven microfluidic systems. The most straightforward co-planar configuration typically generates symmetric flow patterns that primarily enhance mixing near the channel walls, therewith limiting the mixing efficiency. On the other hand, vertically integrated electrode arrangements can induce multiple vortices with much more pronounced mixing throughout the entire channel cross-section (Figure 1d). Researchers compared regular and chaotic electrode configurations were compared and found that chaotic patterns provided promising dispersion reduction, especially at higher flow rates and lower adsorption constants (Venditti et al., 2022). Also, the computational simulations showed that secondary flows driven by electroosmosis can reduce dispersion more effectively than geometrical modifications alone (Zhao and Bau, 2007). Recent experimental studies have demonstrated dispersion reduction up to 5-fold in vertically patterned electrode configurations (Westerbeek et al., 2020) in micron-scale dimensions. In these studies, the electrode design is critical.

In the presence of a non-uniform electric field, EOF can be used to enable controlled vortex formation within the entire channel cross-section. This ability to actively shape the flow field makes EOF attractive for dispersion control in LC. Early studies on electroosmotic mixing focused on direct current (DC) EOF where a constant electric field drives the flow. Theoretical studies showed that combining DC-EOF with hydrodynamic flow in open-channel hydrodynamic chromatography would generate lateral vortices strong enough to reduce the separation time by nearly 50-fold (Figure 2c) (Biagioni and Cerbelli, 2022). This shows the potential of electrokinetic forces to perform significant performance gains. However, in a practical application, DC-EOF limitations include electrolysis at the electrodes, bubble formation, and changes in ionic strength due to Faradaic reactions. These effects can impact the performance over time and complicate the practical implementation.

In AC-EOF, the electric field oscillates in time, which prevents permanent accumulation of ions at the electrodes (and a concomitant reduction of the effective electrical field) and reduces the occurrence of Faradaic processes. This allows for higher field strengths while still avoiding electrochemical degradation. AC-EOF enables control over the frequency of the electric field while affecting the structure of the induced lateral vortices.

At low frequencies, the flow behaves similarly to DC-EOF. However the electric field cannot fully penetrate the electrical double layer, leading to complex flow patterns at high frequencies. Higher frequencies produce stronger and stable vortices. The voltage amplitude also plays a role, as higher voltages increase the slip velocity in the electrical double layer and enhance the secondary flow. Ionic strength is another critical parameter salt concentrations compress the electrical double layer, reducing the EOF. On the other hand, a very low ionic strength may destabilize the flow. Therefore, AC-EOF offers a rich parameter space with frequency, voltage, and ionic strength as key parameters that can be optimized to generate appropriate lateral flows under chromatographic conditions.

As a first reference system, chip-based open-tubular chromatography have been successfully evaluated. AC-EOF was used to generate transverse vortices in 40 × 20 µm (w x h) microchannels and reported a three-to five-fold reduction in the κaris parameter (Figure 2d) (Westerbeek et al., 2020). In a subsequent study, vortex-induced flow was used to reduce the C-term in 5 × 20 μm (w x h) channels by up to five-fold in 3 µm channels, demonstrating strong scalability to dimensions relevant for high-resolution separations (Figure 2e.) (Westerbeek et al., 2023). This analysis was then extended numerically to include unretained (Figure 2f) and retained (k > 0) conditions and found that even when analytes interact with the stationary phase, lateral vortices significantly reduce dispersion, more than 5-fold (Bihi et al., 2024). Vortex-induced EOF performance is depended on channel aspect ratio (Bihi et al., 2026) and the largest gains have been, obtained with square channels (AR = 1). These results show the versatility of EOF-based methods and their ability to target both axial velocity gradients and mass transfer resistance. Numerical simulations demonstrated that electroosmotically induced secondary flows could reduce dispersion beyond the limits of geometric optimization (Zhao and Bau, 2007). Experiments showed that AC EOF-induced lateral vortices lowered κ_{a ri s} up to 80% and reduce the C-term up to five-fold in open-tubular columns (Westerbeek et al., 2020; Westerbeek et al., 2023). The electrode patterning has also been explored to alternate between regular and chaotic vortex structures, allowing mixing strategies to be adjusted to different separation conditions (Venditti et al., 2022). These studies shows that vortex-based lateral mixing is not only effective but also highly controllable. GDT also provides a quantitative link between mixing strength and column efficiency while enabling a predictive design of these lateral mixing strategies. When combined with retention models, GDT can be used to determine the optimal vortex amplitude and frequency for different solute-surface interactions. These experimental and theoretical support distinguishes vortex-based methods from earlier approaches and highlights their potential as a foundation for next-generation LC systems.

Passive and active mixing strategies represent two distinct approaches for generating secondary flows. In passive approaches, secondary flows arise from the axial flow. As a result, vortex generation scales with axial velocity, and effective mixing typically requires higher flow rates, resulting in (inherent) increased axial dispersion. By contrast, active approaches generate secondary flows independently of the axial flow. This allows lateral transport to be adjusted at the same axial flow. This, however, requires additional system integration. In both cases, dispersion reduction is associated with enhanced transverse transport, achieved through different physical mechanisms.

Vortex-based active methods minimize dispersion by decoupling the lateral flow from the primary axial flow. Instead of relying on extreme miniaturization or geometric complexity, they use flow-field engineering to enhance mass transfer. This concept forms the basis of Vortex LC, where lateral vortices are deliberately integrated into the separation process. The ability to generate strong andtunable secondary flows makes vortex-based methods one of the promising directions for achieving high performance in liquid chromatography.