Microfluidic technologies have the potential to transform industries where high-value chemicals are processed in small quantities, such as health care, medical diagnostics, fine chemicals, etc. Some diagnostic devices, such as glucose meters and immunoassays are in use. Successful devices typically involve capillary action for fluid transport, and they do not incorporate fluid pumping or mixing within the device.
There are technological challenges to down-scaling processes that involve mixing, heating/cooling, pumping, reacting and metering of fluids, due to which there are no commercially available products that carry out these complex operations.
At small scales, fluid flow is in the laminar regime, and mixing takes place by molecular diffusion. This is in contrast to large scale industrial processes, where the flow is usually in the turbulent regime; turbulent mixing is faster, by orders of magnitude, in comparison to molecular diffusion. To provide a perspective, the diffusion coefficient of small molecules in liquids such as water is of the order of 10−9 m2/s, and that of larger molecules such as proteins could be as low as 10−13 m2/s. Based on simple dimensional analysis, the time required for diffusion across a channel of width 1 mm could be as long as 1000 s for small molecules, and as large as 107 s for larger molecules.
Due to the slow mixing, it is necessary for fluids to remain in contact for long periods of time. A blood cell counter requires a path length of many tens of centimeters so that the flow contact time is sufficient for the blood and cell lysing agent to mix completely.
In a micro fluidic device as the path length increases, the pressure drop for driving the flow also increases (proportional to the length). The pressure drop across a micro-channel of length 1 m, width 1 mm and height 100 μm can be as large as 4-5 atm even for a very small flow rate of 1 ml/min when the flow is laminar. Such large pressure drops require pumps and compressors to drive the flow, and increase the complexity and cost of equipment involved. Such large pressure drops require a high mechanical strength of the device itself, since high pressures in systems of small dimensions could lead to mechanical failure. The large path length also increases the volume of fluids and expensive reagents that are required.
There is also the difficulty of setting up fluid interconnects between the device and the surrounding fluid inputs or outputs which are strong enough to withstand the high pressures without leakage.
In view of the foregoing reasons microfluidic devices for pumping, mixing, heating/cooling, reacting, metering and other handling of fluids typically involve large path lengths (of the order of tens of centimeters), due to the slow mixing. In microfluidic applications, where the Reynolds number is low because the channel/pipe diameter is small, the flow is usually in the laminar regime. Here, the Reynolds number is (ρV L/η), where ρ and η are the fluid density and viscosity, L is the characteristic length (tube diameter or channel height) and V is the characteristic velocity. In a laminar flow with smooth streamlines, mixing occurs only by molecular diffusion, which is much slower than turbulent diffusion. Therefore, one encounters the engineering limitation that the rates of mass and heat transfer are much lower than that in a turbulent flow. This results in the requirement for long fluid paths in order to provide adequate residence time for mixing, and the consequent increase in the pressure requirements for pumping the fluid at low velocities. The devices are typically connected to external inlets and outlets and driven by external pumps and compressors. Moreover, the large pressure differences often result in mechanical failure of the equipment due to the inability of the tubes and channels to withstand the large forces.
Complex microfluidic circuits with large numbers of tubes, valves and actuators, which resemble electronic integrated circuits, have been fabricated. The fluid flow in these typically is driven by positive displacement syringe pumps or by pressure sources and the valves are also opened and closed by pressure sources. The requirement of external connections makes the device more complex and inflexible in its operation. Even though the microfluidic device itself is very small in size (one square centimeter or less), there are a large number of large external devices connected to it, such as syringe pumps, piston pumps, compressors, electrical and magnetic actuators, etc.
The important technological bottleneck to developing smaller and less complex networks is the slow mixing in these devices. Several proposals for enhancing mixing in micro-channels and micro-tubes have been proposed. However, these strategies have the undermentioned limitations.
Passive mixing due to tortuous channels or due to roughness at the boundaries. These include channels with repeated bends to curve the streamlines, wall grooves to introduce secondary flows, hydrodynamic focusing where substantially different flow rates come into contact, split-and-recombine strategies (splitting the inlet into a large number of small streams using channel bifurcations and then recombining them by an inverse bifurcation) either in parallel or in series. These require expensive fabrication techniques, where micron and sub-micron features have to be etched in silicon. This increases the path-length of the flow and consequently the pressure drop and the power required. This also increases cost due to complexity of fabricating tortuous channels or sub-micron structures.
Mixing by using electric or magnetic fields in to exert forces on ions within fluids containing ionic entities, due to the electrodynamic or magnetic forces exerted on the ions or suspended magnetic particles. This approach is applicable only for fluids which have suspended ions or magnetic particles, and it involves separations in case the particles are added specifically for driving the flow. The pumping or mixing efficiency in these systems is sensitive to the concentrations of the ions or magnetic particles. The system also becomes more complicated and expensive due to the requirement of external electrical and magnetic circuits.
Active mixing, using displacement of elements within the tube or channel by external means in order to generate a more complicated flow profile and thereby enhance mixing. Active strategies include pressure pulsing, electro-kinetic disturbances induced due to fluctuating electric fields, actuation by acoustic waves, and micron sized stirring devices. This involves moving parts of microscopic scale in order to generate displacements and produce mixing. This increases the complexity and cost of fabrication significantly, and the pressure drop required to drive flow is also significantly higher.
Droplet microfluidics, where the fluid is processed within a droplet, which is in turn suspended within an external immiscible fluid. The mixing in droplet microfluidics is usually generated by flow within the droplet due to the fluid motion around the droplet. This concept could be useful for pure fluids which do not contain suspended particles such as blood cells, but it is difficult to use for fluids with suspended particles, since the droplet size could be similar to the size of the suspended particles. There are other disadvantages as well. Complex channel shapes are usually required to enhance mixing and these increase the pressure drop, power requirement, and cost. The inlet manifolds and the controls are also more complicated since two fluids have to be injected in specified sequence at pre-determined rates. Droplets can be combined and separated and moved in pre-specified paths, but these require intricate controls which increase complexity and cost of the device. Further, separation of the droplets after processing is necessary to recover the products.
The technology barrier due to slow mixing has been well recognized for some time now. In fluid mechanics, rapid mixing is often achieved by disrupting the laminar flow and making the flow turbulent. Turbulent flows have mixing rates that are orders of magnitude higher than those of laminar flows. The transition to turbulence takes place when the Reynolds number exceeds a threshold value, which is about 1000 for the flow in a channel and about 2100 for the flow in a tube. Flows are usually turbulent in large scale applications, where the flow exhibits violent and unsteady motion, and mixing is rapid due to turbulent ‘eddies’ (parcels of fluid in correlated motion). In microfluidic applications, flows are usually laminar, because the dimensions are small and the Reynolds number is lower than the threshold value.
The laminar-turbulent transition in tube flows continues to be an active area of research over a hundred years after it was discovered. It is fair to say that the exact transition mechanism is still not clear, and this transition cannot be captured by standard methods of stability analysis.
In the flow through flexible tubes, there theoretical studies have shown that there could be instability due to the interaction between the fluid and wall material. This instability could occur at a Reynolds number lower than 2100, provided the wall material is sufficiently soft. The instability mechanism, which involves wall oscillations due to the coupling between the fluid and wall dynamics, is qualitatively different from the transition mechanism in rigid tubes. The transition Reynolds number is a function of the dimensionless Σ=(ρGR2/η2), the ratio of the elastic forces in the wall material and the viscous forces in the fluid. Here, G is the shear modulus of the wall material, R is the tube radius, and ρ and η are the fluid density and viscosity.
It is also known that there could be instability even at Reynolds number less than 1, provided the fluid has very high viscosity (about 1000 times the viscosity of water) and the wall of the channel/tube is made sufficiently soft. A modest enhancement in the mixing rates of about 25% is also known, due to the instability at low Reynolds number. However, it is infeasible to use such low Reynolds number flows of very viscous fluids for microfluidic applications. Large pressure gradients required to drive very viscous fluids through conduits of small dimension would break apart conduit and rupture connections.
It was previously considered to be infeasible to use this mechanism for microfluidic applications where the Reynolds number with fluids having low viscosity from 1 to 10 times the viscosity of water at standard conditions, because the instability can be triggered at a Reynolds number less than the transition Reynolds number of 1000 in a channel only if the wall elasticity is less than 1 kPa, which is difficult to realize in practice. Our experiments show that the transition Reynolds number can be reduced below 1200 even with soft materials of shear modulus 100 kPa, which are achievable in practice. Thus, it is possible to induce instability of the laminar flow and enhance mixing just by making the tube walls soft in microfluidic applications. This opens up the opportunity for tailoring sections in microfluidic applications to have soft walls, which spontaneously oscillate in the presence of fluid flow in order to induce mixing.
The instability in the flow through soft tubes of diameter 1.2 and 0.8 mm and of length between 14.5 and 20 cm, were studied experimentally by M. K. S. Verma and V. Kumaran and the work was published in the J. Fluid Mech., 705, 322-347, 2012, under the title “A dynamical instability due to fluid-wall coupling lowers the transition Reynolds number in the flow through a flexible tube”. It was observed in this document that the transition Reynolds number could be reduced below the value of 2100 for a rigid tube, and the lowest transition Reynolds number of about 500 was achieved for the softest tubes used in the experiments. Though the objective of inducing a disruption of the laminar flow was achieved, the device was not found suitable for rapid mixing of fluids for many reasons such as the minimum dimension that could be achieved in the disclosed device was 0.8 mm, whereas for microfluidic applications, a minimum cross-section dimension of less than 500 μm, preferable 200 μm, is necessary. Moreover, fabrication of microconduits of length 15-20 cm was also challenging task for use in microfluidic applications, since the dimensions of the known devices are in the order of 3-5 cm. More significantly, the disclosed device does not disclose a complex network of microconduits that can be used in micro fluidic applications.
In this disclosed device, it was observed that even though there was instability of the fluid flow after transition from the laminar flow of the fluid, the velocity fluctuations in the flow were not large enough that could result in turbulent flows, since the turbulent velocity fluctuations were typically measured at not more than 10% of the mean flow velocity, which were much smaller than those in turbulent flows, where typically the fluctuations are at least 50% or more of the mean flow velocity. Consequently, mixing efficiency of the fluids in the device was poor. The mixing of fluids was examined by injecting a dye-stream at the center of the tube, and observing the dye-stream as it progressed through the tube. In the laminar flow, the dye-stream followed a straight line path with no cross-stream disturbance. After transition, the dye-stream was disrupted, but even at the end of a tube of length 5 cm, as shown in FIG. 1, it was observed that there is an uneven distribution of dye across the tube, with most of the dye concentrated in blobs at the center. In order to measure the quality of mixing, the mixing index can be defined as a measure of the uniformity of concentration at the end of the device when two streams, one containing dye or solute and the other with no dye or solute, are introduced at the inlet. In this experiment the average concentration across the entire cross section of the device is subtracted from the local concentration to obtain the concentration fluctuations. The root mean square of the concentration fluctuations is divided by the average concentration to obtain the segregation index SI. The mixing index is defined as MI=(1−2 SI). The mixing index is 1.0 for perfectly mixed streams, and is 0.0 when there is no mixing between the two streams. In dye stream experiments on the flow through tubes in prior work, the mixing index does not exceed 0.4 even after transition, indicating very imperfect mixing.
Therefore, due to the combination of poor mixing and small cross-stream velocity fluctuations, it was considered infeasible to use the devices of this nature to generate rapid mixing in still smaller devices, since for microconduits of the length 3-5 cm and with the height of about 200 μm and 3-5 cm in length, the residence time of the fluid in the microconduit becomes smaller, by a factor of 4 to 6 in comparison to a tube of length 20 cm. Due to this, the small magnitude of the velocity fluctuations results in poor mixing of fluids in such devices.
It is also desirable to develop devices that can carry out multiple sample preparation and/or physical/chemical transformation steps such as mixing and reactions, heating/cooling, metering, and pre-determined time delays for the completion of reactions or physical transformation of fluids such as blood which could contain suspended particles. These devices are required to have pre-loaded reactants/reagents/sample conditioners of precise and tunable volumes, which can be mixed together for sample preparation in the case of diagnostics or for point-of-delivery adjustment of reactant volumes in the case of chemical synthesis. It is also desirable to carry out multiple operations in series or parallel, and the system should be fluidically insulated from the surroundings, apart from sample loading or product collection for diagnostics or therapeutics either externally or integrated with the device, in order to maintain sterility and avoid contamination.
Complex microfluidic circuits with large numbers of tubes, valves and actuators, which resemble electronic integrated circuits, have been fabricated. The flow in these typically is driven by positive displacement syringe pumps or by pressure sources and the valves are also opened and closed by pressure sources. The requirement of external connections makes the device more complex and inflexible in its operation. Even though the microfluidic device itself is very small in size (one square centimeter or less), there are a large number of large external devices connected to it, such as syringe pumps, piston pumps, compressors, electrical and magnetic actuators, etc. Even though these devices are commonly called lab-on-a-chip′ devices, they are actually ‘chip-in-a-lab’ devices which require large laboratory equipment to drive the flows. The technological bottleneck to developing smaller and less complex networks is the slow mixing in these devices.