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This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the...
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... occupying a particular channel. As soon as the bubble leaves the channel, that channel returns to its original fluidic resistance. We thus infer that, as the number density of bubbles increases, the diversity of paths taken by new bubbles increases such that new bubbles populate more and more of the channels connecting the inlet and outlet. Fig. 5 summarizes an experiment in which we varied the number density of bubbles in the channels, and observed the selection of paths by these bubbles. By observing the path- selections of bubbles when the network has different distribu- tions of bubbles (see Table S1 for further details), we estimate empirically that the resistance of each ...
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... microchannel of 0.4$0.6 mm in length. Therefore, the additional resistance due to even a small number of bubbles can significantly affect the global distribution of resistances of the channels (the total length of all channels ¼ 7.1 mm). Consequently the mutual interaction among multiple bubbles leads to a complex, time-dependent pattern of flow (Fig. 5a). By counting the number of bubbles that pass through channels A, C, and D, we ranked paths according to the flux of bubbles that each path can support: path A supports the highest flux of bubbles (34) and two other paths, B / C / E (17) and B / D / E (17), support exactly the same flux of bubbles despite the obvious difference in the ...
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... and B / D / E (17), support exactly the same flux of bubbles despite the obvious difference in the fluidic resistances of View Online channels C and D. Clearly, the collective preference of multiple, mutually interacting bubbles can be very different from that of a single bubble. At a higher densities of bubbles ($ 12 bubbles in the network; see Fig. 5b), the fluidic resistance added by bubbles is comparable to the resistance of any path connecting the inlet and outlet -path A, B / C / E, and B / D / E. As before, each bubble takes a path through the network based only on the relation between flow rates along the microchannels at each junction it reaches, but those flow rates are ...
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... information about the network through changing flow rates and differences in pressure. At higher values of number density, the behavior of the system does not noticeably change; instead, the ratios between fluxes converge to values (1: 0.87: 0.63) that approach those of the flow rates of the carrier fluid (1: 0.60: 0.53) when there are no bubbles (Fig. 5c). When the number of bubbles in the network increases beyond 20 (Fig. 5d), a new bubble reaches the first junction before its predecessor enters the channel to follow; this behavior leads to direct collisions, with attendant complexities that are beyond the scope of this paper. We refer the readers interested in this 'collision regime' ...
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... in pressure. At higher values of number density, the behavior of the system does not noticeably change; instead, the ratios between fluxes converge to values (1: 0.87: 0.63) that approach those of the flow rates of the carrier fluid (1: 0.60: 0.53) when there are no bubbles (Fig. 5c). When the number of bubbles in the network increases beyond 20 (Fig. 5d), a new bubble reaches the first junction before its predecessor enters the channel to follow; this behavior leads to direct collisions, with attendant complexities that are beyond the scope of this paper. We refer the readers interested in this 'collision regime' to the work by Belloul et al. 32 Fig. 5e shows the collective behavior of ...
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Citations
... The available numerical, experimental, and analytical studies in the literature mainly focus on the droplet motion in linear sequences, known as single lane flows, in relatively simple channels, such as, simple loops, cascaded loops or sizeable regular grid of short channels, resembling porous materials. [17][18][19][20][21][22] In contrast, very few studies have been found to deal with the navigation of bubbles through a complex microfluidic network. Choi et al. 17 described the behavior of bubble/s suspended in the carrier fluid and flowing through microfluidic networks.They reported that a bubble moves by interacting with the carrier fluid around it, increases the channel resistance it occupies, and always chooses a path with the least hydrodynamic resistance. ...
... [17][18][19][20][21][22] In contrast, very few studies have been found to deal with the navigation of bubbles through a complex microfluidic network. Choi et al. 17 described the behavior of bubble/s suspended in the carrier fluid and flowing through microfluidic networks.They reported that a bubble moves by interacting with the carrier fluid around it, increases the channel resistance it occupies, and always chooses a path with the least hydrodynamic resistance. Schindler and Ajdari 18 reported a numerical model to characterize the traffic of droplets in microfluidic "dual networks." ...
... Choi et al., 17 in a similar experimental work, mentioned that the length of the bubbles used for investigating navigation through the network lies in the range of 100-150µm. ...
Bubble propagation in both Newtonian
and power-law obeying
uids through simple and complex micro
uidic networks is
investigated via the finite volume-based numerical method. An effort is made to understand how passive components
choose their path in various power-law
uids. The role of rheological properties of the
continuous phase on the path selection of a single bubble and mutually interacting
multiple bubbles propagating the network is presented. The understandings from this
work will be helpful and relevant in the design and fabrication of lab-on-chip devices
operating on bubbles.
... Therefore, a further dispersed phase can flow in the 2nd dispersed channels, because the fluids tend to more readily flow along the less resistive channels. [6,[80][81][82][83] Overall, the cascaded reductions in both the static pressures of the post-crossflow and the resistances of the dispersed oil phase can occur from the 1st to 8th junctions in the 1st node. Moreover, when the post-crossflow entered the next node (9th junction), the frequencies of the droplet generation abruptly fell and then recovered again from the 10th to 16th junctions. ...
The parallelization of multiple microfluidic droplet junctions has been successfully achieved so that the production throughput of the uniform microemulsions/particles has witnessed considerable progress. However, these advancements have been observed only in the case of a low viscous fluid (viscosity of 10⁻²–10⁻³ Pa s). This study designs and fabricates a microfluidic device, enabling a uniform micro‐emulsification of an ultraviscous fluid (viscosity of 3.5 Pa s) with a throughput of ≈330 000 droplets per hour. Multiple T‐junctions of a dispersed oil phase, split from a single inlet, are connected into the single post‐crossflow channel of a continuous water phase. In the proposed device, the continuous water phase undergoes a series circuit, wherein the resistances are continuously accumulated. The independent corrugations of the dispersed oil phase channel, under the theoretical guidance, compromise such increased resistances; the ratio of water to oil flow rates at each junction becomes consistent across T‐junctions. Owing to the design being based on a fully 2D interconnection, single‐step soft lithography is sufficient for developing the full device. This easy‐to‐craft architecture contrasts with the previous approach, wherein complicated 3D interconnections of the multiple junctions are involved, thereby facilitating the rapid uptake of high throughput droplet microfluidics for experts and newcomers alike.
... The available numerical, experimental, and analytical studies in the literature mainly focus on the droplet motion in linear sequences, known as single lane flows, in relatively simple channels, such as simple loops, cascaded loops, or sizeable regular grid of short channels, resembling porous materials. [17][18][19][20][21][22] In contrast, very few studies have been found to deal with the navigation of bubbles through a complex microfluidic network. Choi et al. 17 described the behavior of bubble/s suspended in the carrier fluid and flowing through microfluidic networks. ...
... [17][18][19][20][21][22] In contrast, very few studies have been found to deal with the navigation of bubbles through a complex microfluidic network. Choi et al. 17 described the behavior of bubble/s suspended in the carrier fluid and flowing through microfluidic networks. They reported that a bubble moves by interacting with the carrier fluid around it, increases the channel resistance it occupies, and always chooses a path with the least resistance. ...
... 1(a) and 1(b). 17 The first geometry [ Fig. 1(a)] is a simple microfluidic network where the inlet passage bifurcates into two downstream channels of different lengths and merges at the outlet. The second geometry in Fig. 1(b) is a complex system consisting of interconnected microchannels of different lengths. ...
This paper investigates the path selection of bubbles suspended in different power-law carrier liquids in microfluidic channel networks. A finite volume-based numerical method is used to analyze the two-dimensional incompressible fluid flow in microchannels, while the volume of fluid method is used to capture the gas–liquid interface. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.3 to 1.5. We have validated our numerical model with the available literature data in good agreement. We have investigated the nonlinearity in the hydrodynamic resistance which arises due to single-phase non-Newtonian fluid flow. The path selection of a bubble in power-law fluids is examined from the perspective of velocity distribution and bubble deformation. We have found that the bubble indeed goes to the channel with a higher flow rate for all power-law fluids, but interestingly it did not always take the shorter route channel at a junction for n = 0.3. Our results suggest that long channels need not be more resistant for every fluid and that the longest arm becomes the least resistant resulting in the bubble leading into the long arm at a junction for shear-thinning fluid. We have proposed a deterministic model that enables predicting the second bubble path in a single bubble system for any location of the first bubble. We believe that the present study results will help design future generation microfluidic systems for efficient drug delivery and biomedical and biochemical applications.
... The bubble/droplet logic is based on bubble-to-bubble hydrodynamic interactions. Since the droplets have resistance, their presence in the microchannel affects the overall flow [24][25][26][27] . For example, the trajectory of the droplets entering a junction depends on the history of decisions taken by the previous droplets that are still in the outlet branches [28][29][30][31][32][33] . ...
Droplet-based microfluidic logic gates have many applications in diagnostic assays and biosciences due to their automation and the ability to be cascaded. In spite of many bio-fluids, such as blood exhibit non-Newtonian characteristics, all the previous studies have been concerned with the Newtonian fluids. Moreover, none of the previous studies has investigated the operating regions of the logic gates. In this research, we consider a typical AND/OR logic gate with a power-law fluid. We study the effects of important parameters such as the power-law index, the droplet length, the capillary number, and the geometrical parameters of the microfluidic system on the operating regions of the system. The results indicate that AND/OR states mechanism function in opposite directions. By increasing the droplet length, the capillary number and the power-law index, the operating region of AND state increases while the operating region of OR state reduces. Increasing the channel width will decrease the operating region of AND state while it increases the operating region of OR state. For proper operation of the logic gate, it should work in both AND/OR states appropriately. By combining the operating regions of these two states, the overall operating region of the logic gate is achieved.
... Compared with the single T-junction, the bifurcations are connected and coupled with each other, which requires a comprehensive study that takes into consideration the interaction between all levels of bifurcations. The flow rate in the branches is proven to be determined by the global structure of the network and the flow resistance caused by bubbles contributes to the complexity of the flow [25]. The density of the bubbles is also critical in determining the path of the bubble as well. ...
Hydrodynamic behaviors of bubble stream flow in fractal tree-shaped microchannels is investigated numerically based on a two-dimensional volume of fluid (VOF) method. Bubble breakup is examined in each level of bifurcation and the transition of breakup regimes is discussed in particular. The pressure variations at the center of different levels of bifurcations are analyzed in an effort to gain further insight into the underlying mechanism of bubble breakup affected by multi-levels of bifurcations in tree-shaped microchannel. The results indicate that due to the structure of the fractal tree-shaped microchannel, both lengths of bubbles and local capillary numbers decrease along the microchannel under a constant inlet capillary number. Hence the transition from the obstructed breakup and obstructed-tunnel combined breakup to coalescence breakup is observed when the bubbles are flowing into a higher level of bifurcations. Compared with the breakup of the bubbles in the higher level of bifurcations, the behaviors of bubbles show stronger periodicity in the lower level of bifurcations. Perturbations grow and magnify along the flow direction and the flow field becomes more chaotic at higher level of bifurcations. Besides, the feedback from the unequal downstream pressure to the upstream lower level of bifurcations affects the bubble breakup and enhances the upstream asymmetrical behaviors.
... Interestingly, even in such basic systems, the droplets were found to exhibit quite complex behaviours such as cyclic repetition of memorized sequences and transitions to chaotic dynamics for specific ranges of parameters [21][22][23][24][25][26]29,30 . Studies of more intricate networks have been limited to cases with low occupation of channels and included series of simple loops 34 , cascaded loops 21,35 or large regular grids of short channels, mimicking porous materials 36 . There have been no systematic studies of less trivial networks with channels long enough (as compared to their cross-section) to contain a large number (hundreds and more) of droplets. ...
Droplets forming sequences in simple microfluidic networks are known to exhibit complex behaviours, but their dynamics are yet to be probed in channels long enough to accommodate many droplets simultaneously. Here we show that uniform sequences of liquid droplets flowing through microfluidic networks can spontaneously form ‘trains’ that periodically exchange between different branches of the network. Such system-wide oscillations do not rely on direct droplet–droplet interactions, are common to networks of various topologies, can be controlled or eliminated by adjusting network dimensions and can synchronize into larger flow patterns. The oscillations can also be suppressed via droplet collisions at diverging junctions. This mechanism may explain why red blood cells in microcapillaries exhibit only low-amplitude oscillations, preventing dangerous local hypertension or hypoxia that might otherwise ensue. Our findings are substantiated by a theoretical model that treats droplets as sets of moving points in one-dimensional ducts and captures the dynamics of large droplet ensembles without invoking the microscopic details of flows in or around the droplets. For blood flow, this simplified description offers more realistic estimates than continuous haemodynamic models, indicating the relevance of the discrete nature of blood to the excitation of oscillations.
... These studies involve the use of either internal forces such as interfacial tension, viscous drag, inertial, lift and centripetal forces (Xu et al. 2008;Garstecki et al. 2006;Teh et al. 2008;Tan et al. 2008) to control liquid droplet movement or the application of external fields (magnetic, electrical, optical etc.) to engineer microdroplet mobility (Zakinyan et al. 2012;Mugele et al. 2010;Lee 2013). Literature suggests that the path chosen by a droplet in a symmetric binary junction microchannel depends on the global architecture of the microfluidic network (Tan et al. 2004;Choi et al. 2011;Schindler and Ajdari 2008;Sessoms et al. 2009;Jousse et al. 2006;Belloul et al. 2011;Bruus 2007) (assuming complete droplet slip at the walls) analogous to the Kirchhoff's law for current flow in an electrical circuit. This means that the volumetric flow rate of the continuous phase carrying the droplet is the highest in the path having the least resistance. ...
We present an experimental and in silico investigation of path selection by a single droplet inside a tertiary-junction microchannel using oil-in-water as a model system. The droplet was generated at a T-junction inside a microfluidic chip, and its flow behavior as a function of droplet size, streamline position, viscosity, and Reynolds number (Re) of the continuous phase was studied downstream at a tertiary junction having perpendicular channels of uniform square cross section and internal fluidic resistance proportional to their lengths. Numerical studies were performed using the multicomponent lattice Boltzmann method. Both the experimental and numerical results showed good agreement and suggested that at higher Re equal to 3, the flow was dominated by inertial forces resulting in the droplets choosing a path based on their center position in the flow streamline. At lower Re of 0.3, the streamline-assisted path selection became viscous force-assisted above a critical droplet size. As the Re was further reduced to 0.03, or when the viscosity of the dispersed phase was increased, the critical droplet size for transition also decreased. This multivariate approach can in future be used to engineer sorting of cells, e.g., circulating tumor cells (CTCs) allowing early-stage detection of life-threatening diseases.
... Since the rate of flow through a branch of a network is a function of resistance, the inflow of a droplet into a particular microchannel influences the trajectories of subsequent drops. The dynamics of flow of drops in networks has been studied in detail in a spectrum of microfluidic systems, ranging from the simplest, two-channel loops [2,3,10], long series of identical loops [5], successively bifurcating cascade of loops [15,21] to a large square grid of short channels [22]. Even the simplest non-trivial network, i.e. the simple loop exhibits highly complicated dynamics and complex dependencies on parameters [2-4, 10-15, 23] such as flow rates, intervals between droplets (or, equivalently, frequency of feeding droplets into the system), the additional hydraulic resistance incorporated by droplets, and length of arms of the loop. ...
The simplest microfluidic network (a loop) comprises two parallel channels
with a common inlet and a common outlet. Recent studies, that assumed constant
cross-section of the channels along their length, have shown that the sequence
of droplets entering left (L) or right (R) arm of the loop can present either a
uniform distribution of choices (e.g. RLRLRL...) or long sequences of repeated
choices (RRR...LLL), with all the intermediate permutations being dynamically
equivalent and virtually equally probable to be observed. We use experiments
and computer simulations to show that even small variation of the cross-section
along channels completely shifts the dynamics either into the strong preference
for highly grouped patterns (RRR...LLL) that generate system-size oscillations
in flow, or just the opposite - to patterns that distribute the droplets
homogeneously between the arms of the loop. We also show the importance of
noise in the process of self-organization of the spatio-temporal patterns of
droplets. Our results provide guidelines for rational design of systems that
reproducibly produce either grouped or homogeneous sequences of droplets
flowing in microfluidic networks.
... Microfluidics technologies are now capable of manipulating nanoliters of fluid, molecules, bubbles, particles, and cells [3], and these have been used for micro-fabrication in engineering settings as well as diagnosis in clinical settings [4]. Recently, techniques for producing microbubbles using microfluidic devices have been developed, and the two-phase flow in microchannels has been measured [5][6][7][8][9][10][11][12]. Some groups have succeeded in fabricating monodispersed microbubbles for drug delivery, and in clinical diagnosis they have been used as contrast agents. ...
Microfluidics is used increasingly for engineering and biomedical applications due to recent advances in microfabrication technologies. Visualization of bubbles, tracer particles, and cells in a microfluidic device is important for designing a device and analyzing results. However, with conventional methods, it is difficult to observe the channel geometry and such particles simultaneously. To overcome this limitation, we developed a Darkfield Internal Reflection Illumination (DIRI) system that improved the drawbacks of a conventional darkfield illuminator. This study was performed to investigate its utility in the field of microfluidics. The results showed that the developed system could clearly visualize both microbubbles and the channel wall by utilizing brightfield and DIRI illumination simultaneously. The methodology is useful not only for static phenomena, such as clogging, but also for dynamic phenomena, such as the detection of bubbles flowing in a channel. The system was also applied to simultaneous fluorescence and DIRI imaging. Fluorescent tracer beads and channel walls were observed clearly, which may be an advantage for future microparticle image velocimetry (μPIV) analysis, especially near a wall. Two types of cell stained with different colors, and the channel wall, can be recognized using the combined confocal and DIRI system. Whole-slide imaging was also conducted successfully using this system. The tiling function significantly expands the observing area of microfluidics. The developed system will be useful for a wide variety of engineering and biomedical applications for the growing field of microfluidics.
... 1.2 High flow rate hypothesis Choi et al. (2011) investigated the path selection of a bubble in a microfluidic network. They focused on networks based on T-shaped junctions where the bubble had only two choices (one of two downstream channels). ...
... The numerical model was validated qualitatively by comparison with the empirical results. Three different microfluidic systems, two of which were used by Choi et al. (2011), were simulated as shown in Fig. 3a, c, e. In Fig. 3a, c, the numerical results show that the vesicle chose the same path as in the experimental cases (Choi et al. 2011). ...
... Three different microfluidic systems, two of which were used by Choi et al. (2011), were simulated as shown in Fig. 3a, c, e. In Fig. 3a, c, the numerical results show that the vesicle chose the same path as in the experimental cases (Choi et al. 2011). Figure 3e, f shows the path selection at a tertiary junction; the simulated routing of the vesicle again matched our empirical observation. ...
We investigate the path selection (navigation) of a single moving vesicle in a microfluidic channel network using a lattice Boltzmann-immersed boundary method (IBM). The lattice Boltzmann method is used to determine incompressible fluid flow with a regular Eulerian grid. The IBM is used to study a vesicle with a Lagrangian grid. Previous studies of microchannels suggest that the path selection of a bubble at a T-shaped junction depends on the flow rates in downstream channels. We perform simulations to observe the path selection of a vesicle with three different capillary numbers at a tertiary junction. The hypothesis that higher flow rate determines path selection is not validated by our data on low capillary number (Ca ≤ 0.025) of a vesicle in tertiary downstream channels. We use the resultant velocity hypothesis to explain the path selection of a vesicle in microfluidic systems. Our results suggest that, for a low capillary number, instead of being affected by the viscous force from a high flow rate, a vesicle in a tertiary junction tends to follow the resultant velocity hypothesis. We analyze the change in hydrodynamic resistance caused by the movement of a vesicle to support the resultant velocity hypothesis. We also study the residence time of a vesicle at a junction for different cases and analyze the relationship between the residence time and the resultant velocity. The resultant velocity (rather than the flow rate in individual channels) can be used to predict the path selection of a vesicle in low capillary number. In addition, the residence time of vesicle is decided by average velocity of each channel.
