A microfluidic valve with bubble trap and zero dead volume

Microfluidics is used for its ability to perform physical,^1,2 chemical,^3,4 biotechnological, and medical^5,6 studies in a precise and cost-effective manner. Many kinds of functional elements, including valves, pumps, switches, sensors, and mixers, have been scaled down to minimize the use of reagents and to perform experiments faster.^2,7,8

Despite the many advantages of microfluidics,^3,8 several applications are still challenging to perform, e.g., multi-step chemical syntheses.^9–11 Accurate flow control is required to achieve the overall goal of efficiently performing multiple functions in synthesis, purification, and biological assessment.¹² Multiple reaction steps performed in the same chamber require the sequential exchange of reactants, which is achieved by using multiple valves and one or more junctions. A major drawback of valves and junctions is that large volumes of reagents are needed for rinsing between steps, which is both time-consuming and wastes sample or reagent. Valves and complicated networks of micro-channels inevitably include dead volumes causing undesirable mixing between consecutive solutions. This further increases the volumes needed to change reagents to minimize cross-contamination, and it can produce undesired concentration gradients during the exchange. In addition, long and complex microfluidic setups with multiple junctions and valves are susceptible to the formation and entrapment of gas bubbles.

We present a microfluidic design without valves or junctions connected to the channel. Our microfluidic system allows the addition of liquid drops at a single inlet for swift exchange of the liquid in a capillary, sample chamber, or detection volume with minimum reagent use while limiting the maximum shear. Our design also removes bubbles efficiently.

Figure 1 shows the microfluidic setup. It consists of a glass capillary, possibly fitted with appropriate detectors, which can, e.g., be placed on a microscope. One end with a cross section of typically a square millimeter (e.g., 0. 1 × 1 mm² Vitrocom, Inc. 5010) is left open and fixed on a solvophobic surface, such as a polystyrene Petri dish (e.g., Art. No. KHY7.1 CarlRoth); the other end is connected to a reservoir via a flexible tube (e.g., Darwin Microfluidics-1610-20 with the connection sealed with Norland Optical Adhesive 61). It is essential that the capillary is initially filled and that the lower end of the tube is immersed in the reservoir. The height difference h between the open end of the capillary and the liquid level in the reservoir (cf. Fig. 1) yields a finite hydrostatic pressure that pulls the liquid out of the capillary. However, the surface tension at the open orifice of the capillary can withstand a pressure of several mbar before the meniscus detaches.¹³ Hence, if the height h is less than a few cm, the meniscus stops the flow (see Table I).

A droplet pipetted close to the open end of the capillary coalesces with the liquid in the capillary and is sucked in by the hydrostatic pressure, if the liquids are miscible. The hydrostatic pressure and thus the flow rate are controlled by h. Any bubbles in the pipette would coalesce with the atmosphere during this process due to the surface tension (see movie 1 in the supplementary material). The solvophobicity of the surface underneath the capillary entrance guarantees that the droplet is sucked up completely. As soon as the droplet has completely entered the capillary, the surface tension at the entrance equilibrates with the hydrostatic pressure, stopping the flow instantly.

One could manually pipet drops of reagent at the capillary entrance or use a robot to do so. We devised a novel way to automate and improve the droplet delivery, including a feedback signal to confirm delivery, with a minimum of moving parts. A vertical needle guides drops to the capillary entrance. Each reagent is pipetted against this vertical needle from a separate feeder needle. In our setup, we controlled the pressure driving these flows with an array of valves using an Elveflow-MUX Flow Switch matrix, providing a manifold for selecting different liquids or samples for injection. Any drop that bridges between a feeder needle and the vertical needle is detected by the electric conductivity between the two needles to stop the flow as soon as the drop has detached from the vertical needle using an Arduino (see the supplementary material for details). The minimum drop size deposited by this design is set by the reagent properties and the distance between needles.

In Fig. 2(a), we show subsequent epifluorescence micrographs of the water close to the sidewall of a square capillary as we alternatingly add water with and without 5(6)-carboxyfluorescein (Sigma-Aldrich, 2763311) at the capillary entrance. In Fig. 2(b), we used images of Fig. 2(a) to plot the normalized dye concentration measured via the fluorescence intensity upon addition as a function of the distance from the wall and time. In accordance with the Poiseuille flow profile,¹⁴ the dye concentration goes to the final value first in the center of the capillary and subsequently closer to the wall (i.e., movie 2 in the supplementary material). In Fig. 2(c), we plot the fluorescence intensity close to the wall as a function of time during six subsequent solvent exchanges. We can completely change the fluid composition within 6 s at a flow of Q = 0.47 µl/s. The injected liquid volume for the complete exchange is only two times larger than the volume of the capillary to the observation point (see the calculation in the supplementary material). Given the capillary size, our design uses the minimum required volume for complete content replacement due to its zero dead volume.

Fluid motion in this system is driven by pressure differences and stopped by the pinning of the meniscus acting as a valve. The flow profile in the channel is Poiseuille-like, and the mixing at the capillary wall is minimized and controlled by the flow rate. Working with hydrostatic pressure rather than mechanical pumps assures a smooth vibration-free operation. Our microfluidic design can be used for any solvent, provided that suitable solvophobic surfaces and solvophilic capillaries are used, respecting the condition (supplementary material)

where ρ is the density of the solution, g is the acceleration due to gravity, D is the side length of the capillary entrance, r is the tube radius, γ is the surface tension of the solution, and ϑ is the contact angle between the solution and the material of the orifice.¹⁵ Table I lists the maximum heights, h_max, for a neutrally wetting capillary (cos ϑ = 1) for some common solvents.

The flow rate for Poiseuille flow through a channel is

where R_hyd is the hydrodynamic friction determined by the viscosity of the solution μ and the geometry of the channel. For a horizontal circular pipe of radius r and length L, R_hyd becomes

and for a square channel with the side length D, it is¹⁶ 

Therefore, one can maximize the flow rate and minimize the time it takes to replace the volume between the orifice and the detector section through maximizing h, which can be increased by a small orifice, combined with minimizing friction in the capillary and tubing by choosing a large R_hyd. The required exchanged volume increases with $Dcapillary2$⁠. In contrast, the flow rate increases with $Dcapillary4$ until the hydrodynamic friction is dominated by that of the orifice. Hence, it is possible to greatly increase the flow rate with a corresponding minor increase in the sample volume.

In summary, we introduce a microfluidic system that is programmable, fast, and reliable for any application requiring the exchange of small amounts of liquid samples in a confined environment.

See the supplementary material for the description of droplet delivery (Movie 1—bubble and Movie 2—dripper) and calculation of Eq. (1) and Fig. 2.

This research was funded by the Austrian Science Fund (FWF) (Grant No. P27544).