Published on 24 April 2025
The present study performed in Kutateladze Institute of Thermophysics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk, Russia) describes how researchers controlled the liquid-liquid flow in their T-junction microchannel by using the OB1 Pressure Controller to apply external high-fidelity pulsations to the flow rate of a dispersed phase.
The research summary is based on the peer-reviewed article “Influence of dispersed phase flow-rate pulsations on the liquid-liquid parallel flow in a T-junction microchannel” co-written by Alexander V. Kovalev, Konstantin S. Pervunin, Artur V. Bilsky, Anna A. Yagodnitsyna and published in Chemical Engineering Journal 2024, 488, 150734 and “Control of Plug Flow Dynamics in Microfluidic T-junction Using Pulsations of Dispersed Phase Flow Rate” co-written by Alexander V. Kovalev, Anna A. Yagodnitsyna, German V. Bartkus and Artur V. Bilsky in Journal of Thermofluids 2024, V. 23, 100720. The research was funded by the Russian Science Foundation (grant No. 21-79-10307).
In this study, Anna A. Yagodnitsyna et al. investigated liquid-liquid parallel and plug flow under the dispersed phase flow-rate pulsations in a T-junction microchannel. To that matter, sinusoidal flow rate disturbances with variations in amplitude and period were applied to dispersed phases of different viscosities.
Two distinct flow regimes, parallel flow and plug flow, are investigated, both showing wave propagation disturbances influenced by the viscosity of the dispersed phase. In the parallel flow regime, the interaction between transverse and longitudinal waves varies based on viscosity of the dispersed phase, leading to different mechanisms of disturbance evolution and flow instability, governed by the Ohnesorge number. In the plug flow regime, flow rate pulsations at frequencies proportional to the natural plug formation frequency result in diverse plug length distributions, including multi-mode and drop-on-demand patterns. The impact of pulsations is particularly significant at low dimensionless frequencies (f < 1), especially for high-viscosity ratio fluids. While pulsations stretch streamlines within plugs, the plug length remains unchanged.
Overall, the study highlights how viscosity, frequency, and flow amplitude shape the dynamics of wave propagation and flow stability in both regimes.
In two-phase microsystems, manipulating the flow to broaden or narrow the range of desired conditions is an important practical issue that urges conducting research on how various control measures, especially active ones involving external periodic disturbances, affect two-phase flow.
Segmented or plug flow in microchannels is known to be limited by the maximum flow rate of the dispersed phase or the minimum flow rate ratio of both phases. Moreover, the more viscous the dispersed phase is, the shorter the range of flow velocities, at which the segmented flow pattern exists, appears to be. This means that it is impossible to achieve a plug (segmented) flow pattern for any arbitrarily high flow rates, which limits the efficiency of microreactors operated in segmented flow regimes. Additionally, plug flow or droplet generation via passive methods fails to produce the desired plug lengths or droplet sizes across a wide range of values
In addition, the external excitation can expand the range of existence of segmented flow and increase microreactor efficiency along with accurate control over droplet breakup dynamics. Among the existing methods of active flow control, piezoelectric actuation is perhaps the most widespread and well-developed tool that, however, has a number of drawbacks. In particular, disturbances introduced by piezo elements are local in nature and depend on a specific microdevice, which does not allow the generalization of experimental data.
In contrast, herein a periodic variation of the flow rate of the dispersed phase was employed to influence the flow conditions globally. This method seems to be simpler and cheaper for implementation compared to piezoelectric actuation and, thus, represents a promising alternative for controlling the entire set of regimes.
Figure 1a illustrates the microfluidic apparatus, the T-junction experiment was set up using a flow controller and a syringe pump to introduce the two liquids from opposite sides into the discharge duct, ensuring controlled flow conditions. It includes:
Flow Rate Regulation
Visual Observation of Phase Interface
Micro-PIV Velocity Measurements
First, the undisturbed two-phase flow was visualized, revealing three distinct flow patterns (Fig. 2).:
Based on these visual observations, flow pattern maps were constructed for various liquids used as the dispersed phase. These maps were then generalized using a universal dimensionless complex, defined as We0.4∙Oh0.6, which proved applicable across different liquid–liquid systems with varying physical properties.
Further analysis was conducted on the parameters of stable plug flow, including plug length, velocity, and related characteristics. The behavior of undisturbed plug flow in a T-junction microchannel was compared with existing correlations for plug length, velocity, and the thickness of the continuous phase film. Within the range of tested flow rates, plug formation was observed in two regimes:
(NB: Cac = Capillary number, a dimensionless parameter that quantifies the balance between viscous drag forces and surface tension forces at the interface between a gas and a liquid, or between two immiscible liquids.)
The relationship between plug velocity and bulk velocity (defined as Ubluk = Ud + Uc) was evaluated for all fluid sets and is presented in Fig. 3a. An empirical approximation for plug velocity was found to be valid across all tested fluids:
where C1 and C2 are the constants that depend on the viscosity of the continuous phase and the microchannel geometry.
The natural frequency of plug formation ƒplug, was determined as the average number of plugs generated over a given time interval. Estimating the value of ƒplug from initial flow conditions was considered essential prior to experimental measurements. In consequence, an equation for the effective frequency of plug formation was derived based on certain simplifications.
This effective frequency of plug formation is determined by the superficial velocities of the dispersed and continuous phases, Ud and Uc, and the microchannel width, w.
As shown in Fig. 3b, the relationship between the measured plug formation frequency (ƒplug) and the effective formation frequency (ƒeff) was examined. It was found that a power-law function accurately describes this relationship. Moreover, the actual formation frequency ƒplug consistently exceeds the effective frequency and increases following a power-law trend with respect to ƒeff. This behavior is attributed to the thickening of the continuous phase film, which aligns with the observed trend in plug velocity.
As the control parameters were varied, the two-phase microflow in the parallel regime was observed to lose stability under the influence of imposed flow-rate pulsations. Initially, the interface exhibited wave-like deformations, which eventually led to breakup and the formation of a plug flow regime. Notably, interfacial waves decayed more rapidly when the dispersed phase consisted of a less viscous liquid.
This phenomenon was interpreted through the lens of the Ohnesorge number of the dispersed phase Ohd.
Consequently, a unifying dimensionless complex was proposed to generalize the observed flow patterns (Fig. 4).
It was observed that velocity gradients associated with shear stresses were significantly higher for the less viscous liquid, with differences reaching approximately an order of magnitude. As a result, viscous stresses exerted a stronger influence in cases where the dispersed phase had lower viscosity, further impacting the stability and dynamics of the two-phase flow.
To investigate the interaction between naturally occurring plug or droplet generation at constant flow rates and externally imposed pulsations, the plug flow pattern under pulsatile flow conditions was systematically studied. As a reference point, the natural plug formation frequency in undisturbed flow, denoted as ƒplug, was used. This allowed for the definition of a dimensionless frequency, ƒ= ƒpulse/ƒplug represents the frequency of the imposed pulsation signal, chosen to be proportional to ƒplug.
The analysis focused on key parameters expected to be affected by pulsations, namely the plug length (Lplug), plug velocity (Uplug), and their standard deviations. A general trend of increasing average plug length and its standard deviation was observed for ƒ<1, although the precise form of this dependence on the dimensionless frequency remained unclear.
To clarify these observations, plug length distributions over time were analyzed. The evolution of plug length as a function of time is shown in Fig. 5, along with the corresponding histograms. It was found that the largest increase in standard deviation occurred in cases where double- or triple-mode distributions emerged. These distribution patterns were particularly evident at ƒ=1/2 and ƒ=1/4, although they did not appear uniformly across all amplitude values.
Considering the observed similarity between the resulting plug length distribution patterns and the phenomenon of modulation—characterized by the superposition of two harmonic signals—a mathematical model was derived to describe plug length behavior under pulsatile flow rate conditions.
Here, Tplug = 1/ƒplug is the natural period of plug formation, and φ0 represents the natural signal phase, Tpulse is a pulsation period, φ1 – the disturbance signal phase, and CA is the signal amplitude, which generally represents a function of pulsation amplitude A and liquid properties CA = CA(A, µc, µd,…). The coefficient CA was determined for all investigated regimes based on the experimental data. Representative examples demonstrating the application of Equation (1) are presented in Fig. 6.
A good agreement between model (1) and the experimental results was observed for both gas–liquid and liquid–liquid flow systems. Each identified plug length distribution could be explained by the superposition of signals with varying amplitudes. According to the model, plug detachment occurs at the local maxima of the combined signal.
The coefficient CA was observed to increase with rising pulsation amplitude A, while other parameters were held constant. Additionally, the influence of the fluid viscosity ratio λ was noted, along with a clear dependency of CA on ƒ and the flow rate ratio, establishing these as key functional arguments of the model. By applying the proposed model, it becomes possible to qualitatively describe system behaviors such as the emergence of double-mode distributions or the drop-on-demand mode, where a single, consistent plug length is generated. These flow patterns offer potential for use in microfluidic logic systems and other applications where controlled flow rate pulsations can be employed to regulate flow characteristics.
To assess the impact of flow rate pulsations on the internal velocity fields of plugs, micro-PIV measurements were performed using a phase-averaging approach. Representative velocity distributions obtained from these measurements are presented in Fig. 7. In the central cross-section, viewed in a reference frame moving with the plug velocity Uplug the flow structure revealed two counter-rotating circulation zones, resembling the classic pattern observed in Taylor flow.
Importantly, this symmetry remained intact even under the highest pulsation amplitudes tested. However, significant stretching of streamlines was observed near the maxima of the pulsation signal. Given that plug length remained largely unaffected by pulsation parameters within the studied range for ƒ>1, it was concluded that such pulsations can be effectively used to enhance mixing and mass transfer in T-junction microchannels without altering plug dimensions dictated by the channel geometry.
In summary, a flow control method was proposed and implemented, based on the application of external sinusoidal perturbations to the dispersed phase flow rate. This approach enabled effective manipulation of liquid–liquid flow within a T-shaped microchannel, with both the amplitude and period of the input signal varied, while the continuous phase flow rate remained constant.
The findings lay the groundwork for the development of active control strategies for managing two-phase microflows. The proposed dimensionless parametric complex and the plug length model under pulsatile flow offer practical tools for precisely adjusting control parameters in future research and applications.
Overall, the use of this active control strategy can expand the accessible range of segmented flow patterns, even in systems involving high-viscosity dispersed phases, thereby potentially enhancing the performance of microreactors. Furthermore, it allows for the generation of plugs with targeted lengths and can significantly enhance mixing and mass transfer—capabilities that are crucial for various chemical and biological processes.
The advantage of Elveflow instruments in this T-junction setup lies in their ability to precisely monitor and control flow rates on demand, whether constant or periodically varying. To achieve this, the OB1 flow controller was used for its high accuracy in pressure control, paired with the BFS+, the most precise flow meter in our range, which provides feedback to the controller to ensure stability. The ESI software enabled full control of the system, allowing the creation of custom flow rate profiles. In this setup, the dispersed phase was regulated by the OB1 flow controller, while the continuous phase was initially injected using a syringe pump. However, thanks to the autonomy of the OB1’s independent channels, the syringe pump can be replaced by a second OB1 channel to control the continuous phase in parallel. All our systems are modular and upgradable—don’t hesitate to get in touch with us!
Full publication: Influence of dispersed phase flow-rate pulsations on the liquid-liquid parallel flow in a T-junction microchannel” co-written by Alexander V. Kovalev, Konstantin S. Pervunin, Artur V. Bilsky, Anna A. Yagodnitsyna and published in Chemical Engineering Journal 2024, 488, 150734 and “Control of Plug Flow Dynamics in Microfluidic T-junction Using Pulsations of Dispersed Phase Flow Rate” co-written by Alexander V. Kovalev, Anna A. Yagodnitsyna, German V. Bartkus and Artur V. Bilsky in Journal of Thermofluids 2024, V. 23, 100720.
Written and reviewed by Anna Yagodnitsyna and Louise Fournier, PhD in Chemistry and Biology Interface. For more content about microfluidics, you can have a look here.
OtherUpgradeSupportAdvanced RangeOEMServices / Training / Installation / RentalsMicrofabricationEssential RangeAccessories
Get in Touch
Need customer support?
Name*
Email*
Serial Number of your product*
Support Type AdviceHardware SupportSoftware Support
Subject*
Message
I hereby agree that Elveflow uses my personal data Newsletter subscription
[recaptcha]
Message I hereby agree that Elveflow uses my personal data Newsletter subscription
We will answer within 24 hours