Passive removal of immiscible spacers from segmented flows in a microfluidic probe Open Access

Techniques to localize (bio)chemicals on surfaces at the micrometer length scale enable numerous applications, such as local staining of tissue samples,¹ targeted stimulation of cells,^2,3 and patterning of biochemicals on surfaces.⁴ To this end, we developed the microfluidic probe (MFP), a non-contact scanning probe technology that leverages hydrodynamic flow confinement (HFC).⁵ HFC is achieved by injecting a processing liquid and aspirating it together with an immersion liquid to hydrodynamically confine picoliter volumes of the processing liquid at the apex of the probe (Figs. 1(a) and 1(b)).^6,7 Although the classical HFC has been demonstrated for single-step chemical processes, its potential can be further exploited by using it to perform multi-step assays. Implementation of such assays requires different chemical species to be sequentially delivered to a surface in defined volumes and concentrations.

To enable sequential chemistry, it is necessary to design a MFP head that can implement a broad range of multi-step processes while being flexible with respect to the number and properties of the sequenced liquids. Therefore, the sequence of liquids required must be generated outside the MFP head, where fast and reliable selector valves can be used. However, when using such valves, convective and diffusive dispersion⁸ occur during the transport of liquids from the valve to the MFP head, leading to cross-contamination between sequential liquids. Kreutzer et al.⁹ showed that flow segmentation by insertion of immiscible-phase (IP) spacers between slugs of a continuous-phase (CP) liquid can reduce dispersion of the slugs. Typically, the IP is an oil¹⁰ or gas,¹¹ whereas the CP is aqueous. In this letter, we use oil as the immiscible phase.

The use of oil-in-water emulsions is not compatible with surface processing by HFC. The interfacial tension of the immiscible spacers in the continuous phase will cause the spacers to accumulate and coalesce at the apex of the head when they exit the injection channel. Furthermore, the accumulated IP can contaminate the surface and alter the flow of the processing liquid, preventing it from being hydrodynamically confined.

We designed, modeled, and tested a module for the removal of immiscible spacers from segmented flows in the MFP. This module relies on pinning and passive merging of an immiscible phase, a concept previously used by Niu et al.¹² for droplet dilution and by Günther et al.¹¹ for extraction of a continuous carrier phase. In this letter, we propose an analytical model describing the spacer-removal module, outline design considerations that determine its characteristics, and study the influence of the module on HFC.

To enable the use of segmented flows in combination with HFC, we developed a MFP head comprising a module that selectively removes the immiscible spacers from the flow by leveraging the difference in channel surface wetting of the CP and the IP. This approach was chosen for two reasons. First, it is compatible with common microfabrication techniques of microfluidic devices such as MFPs,⁵ as the removal module can simply be drawn in CAD software without requiring any complex surface treatment^13–15 during fabrication. Second, the geometrical approach allows greater flexibility of microfluidic devices with respect to the used liquids.

To test the spacer-removal module (Fig. 1(c)), spacers were inserted at an on-chip T-junction and visualized in a serpentine channel (Fig. 1(b)). In the removal module (Fig. 2(a)), an aspiration channel (left) is connected to an injection channel (right) by a bypass. When an immiscible spacer arrives at the blocking pillars in the injection channel, partial pinning of its interface at the pillars causes it to be directed into the bypass, where it is then trapped due to a capillary force induced by the pinning of its front interface at the orifice.

When a subsequent incoming spacer reaches the blocking pillars, it merges with the spacer in the bypass and blocks the flow in the injection channel. The pressure increase resulting from this blockage causes a volume of IP to be ejected through the orifice into the removal channel (left in Fig. 2(a)) where it is sheared. As the module typically operates with a capillary number $Ca≈1$⁠, the size of the ejected spacers can be modified by designing a constriction in the removal channel.¹⁶ After the ejection of a fraction of the IP through the orifice, a trapped volume of IP prevents the continuous phase from flowing through the bypass. Subsequent incoming spacers will then be removed in a similar manner.

The pressure drop across the interface of the trapped spacer in the vicinity of the pillars (⁠$psi−pso$ in Fig. 2(b)) is maximal when the flow in the injection channel is briefly blocked. This blockage occurs whenever an incoming spacer is merging with a trapped spacer. For the desired operation, the pressure in the injection channel must push the front interface of the spacer through the orifice before the side interface is pushed past the blocking pillars. By comparing the maximum pressure drop across the sections of the interface pinned at these two points (I and II, respectively, below) before the interface breaks, we determine how the module will remove spacers from the flow.

(I) Maximum pressure drop—across the front interface: The front interface of a trapped spacer is pinned at the orifice (Fig. 2(a)). The maximum pressure drop that this interface can withstand before breaking is given by the Laplace equation¹⁷ 

where $γ$ is the interfacial tension of the oil-in-water emulsion, and $Rf$ is the minimum curvature radius of this interface in the $x,y$ plane, given by¹² $Rf,i=−do/(2 cos(θ−ψi))$ (⁠$i=1,2$⁠). Through similar geometrical reasoning, for the curvature radius in $z$-direction, we use¹² $Rz=−2 cos(θ)/h$⁠, where $h$ is the channel height and $θ$ is the contact angle. In the broadly applicable case where $ψ1≠ψ2$⁠, both $Rf,1$ and $Rf,2$ must be evaluated as the larger of these two yields a lower maximum pressure drop $ΔPf,max$ and therefore determines the pressure drop at which the front interface breaks.

(II) Maximum pressure drop—at the blocking pillars: The side interface of a trapped spacer is in contact with the blocking pillars at all times. The development of a section of the side interface between pillars A and B consists of three stages.

• No pinning occurs when the pressure drop across the side interface is small compared with the maximum pressure drop that it can withstand before breaking (Fig. 2(b)).

• As the pressure drop across the interface increases, the interface expands until the contact line at pillar B pins at point S (Figs. 2(c) and 2(d)). As $θ≤π$⁠, the interface is not affected by the straight left edge of pillar B below point S, and the interface will assume a symmetrical profile between S and T (Fig. 2(d)). We obtain an expression for the minimum curvature radius in the $x,y$ plane by forcing the crossover angle (which provides a minimum curvature radius) $φ1=α1=π/2+β$ in the expression for pinning on cylindrical pillars¹⁸ 

  $R1,min(φ1)=d/2−dp sin(α1) sin(θ−α1).$

  (2)

  In Eq. (2), $d$ is the pillar pitch in a rotated reference frame, given by $d=(dg+dp)/ cos(β)$⁠. The maximum pressure drop that the interface can sustain before breaking is then $ΔP1,max=γ(1/R1,min+1/Rz)$⁠.

• When the pressure drop across the side interface exceeds $ΔP1,max$⁠, the contact line on pillar A will proceed from T to U and the contact line on pillar B will slide downwards from S to V (Figs. 2(e) and 2(f)). A new pinning situation is established at U. The radius of the interface in the $x,y$ plane in this position is derived geometrically

  $R2,min(φ2)=1−cos(β+φ2−π2)+dg cos(β2+φ22−π4)sin(θ−β2−φ22−π4),$

  (3)

  where $β$ is the oblique angle of the pillars, $dg$ is the spacing between pillars, and the crossover angle $φ2$ was found numerically (Fig. 2(f)). We note that if the crossover angle does not satisfy $φ2≥α2=π/2−β$⁠, the point U will be situated on the transition from the circular to the straight edge of the pillar, and we must force $φ2=α2$ to find the minimum curvature radius. Laplace's law gives the maximum pressure drop that the interface can withstand in this position before breaking as $ΔP2,max=γ(1/R2,min+1/Rz)$⁠.

The three stages described above can be translated into design requirements to obtain a functional module. At the side of the interface pinned at the pillars, the smaller of $R1,min$ and $R2,min$ will indicate whether the strongest pinning occurs in stage (ii) or (iii). We define a pressure ratio $κ$⁠, which provides a comparison between the maximum pressure drop across the interface at the orifice and the blocking pillars. Equations (1)–(3) can be combined with Laplace's law to form the inequality

For the front interface of the spacer to break at the orifice before the side interface breaks at the blocking pillars, $κ$ must be smaller than one. Figure 3 shows the pressure ratio $κ$ against the oblique angle of the pillars for various ratios of orifice width to pillar spacing (⁠$do/dg$⁠).

According to Fig. 3, the design with $do/dg=2$ and $dg=15 μm$ satisfies $κ<1$ for all oblique angles. Therefore, any angle can be chosen if the gap parameters $do$ and $dg$ are kept constant. In doing so, we took into account the two additional consequences of changing the oblique angle $β$⁠: (i) as $β$ increases, the radius $Rr$ of the rear interface decreases. A smaller radius of the rear interface of the trapped spacer leads to a higher pressure drop across that interface. This leads to more rapid merging with the front interface of an incoming spacer. (ii) The oblique pillars direct the incoming volume into the bypass more strongly as $β$ increases, as pinning of the interface only occurs at the left edge of the pillars, while the section of the interface at the right edge is able to deform towards the bypass in the $–x$ direction. These two influences of $β$ are related to the dynamics of spacer removal (interface propagation and merging) and are less easily quantified than the static (pinning) situation described by Laplace's law.

Taking the design considerations above into account, we chose $β=30°$ as a trade-off between a low pressure ratio $κ$⁠, a small rear interface radius $Rr$ and a unobstructed path along $–x$ for rapid merging of spacers.

Typically, the apex of the MFP head is about $20 μm$ from the surface, and the volume of confined liquid is on the order of $100 pl$⁠. A change in the volume of injected processing liquid from $100 pl$ to $120 pl$ then corresponds to a 10% increase of the radius of the footprint. The extent of the footprint variation, caused by hydrodynamic coupling between the removal module and the HFC, is important as it determines the accuracy and reproducibility of local surface processing. To study this coupling, we designed and compared two probe heads with different spacer-removal modules (Figs. 4(a) and 4(b)).

In a dual-aspiration module (Fig. 4(a)), $Qi,HFC=Qi−Qr,oil=0$ as the incoming spacer blocks the flow at the blocking pillar. This brief period without injection of processing liquid lasts for $Δtdual=Vi/Qi$⁠. However, during this time, some processing liquid remains between the apex and the surface. If the time required to aspirate the remaining volume of processing liquid exceeds $Δtdual$⁠, the hydrodynamic confinement persists. Therefore, by simply setting a higher arrival rate of spacers at the module, fluctuations in the footprint can be reduced.

In the two-channel module (Fig. 4(b)), a single aspiration inlet is used to form a HFC and to remove spacers coming from the removal module. In this case, an additional time $Δt2=Vo/Qa$ is considered during which the flow of the immiscible phase from the bypass into the aspiration channel blocks the aspiration of continuous-phase processing and immersion liquid. Typically, the volume of incoming spacers is equal to the volume of ejected spacers.¹² Therefore, the time during which the area of the footprint is not constant is increased by $Δt1+Δt2−Δtdual=1+Qi/Qa$ in the single-aspiration module as compared with the dual-aspiration module. Under standard operating conditions, where $Qa≈3Qi$⁠, this corresponds to a total fluctuation time that is approximately $30%$ longer for the single-aspiration module.

We tested a spacer-removal module integrated into a MFP head using an emulsion of Fluorinert FC-40 in water containing $50 μM$ Rhodamine B for visualization. The fabrication of the silicon/glass MFP head is described elsewhere.⁵ The MFP head had an on-chip T-junction for the insertion of FC-40 spacers upstream of the removal module. We observed a continuous HFC during removal (Fig. 5). It can be seen that the front interface at the orifice breaks before pinning occurs at pillar A, and that pinning of the interface at pillar B occurs with a crossover angle $φ1≈120°$⁠. This indicates that the simple model based on the dimensionless parameter $κ$ is sufficient to predict that pinning will first occur at the orifice, followed by pinning at pillars B and A.

We note that the model quantitatively describes only the static pinning behavior of the oil interface. Therefore, the model can be expected to accurately scale to different geometries (⁠$β$⁠, $do$⁠, $dg$⁠). However, as discussed above, the model does not quantitatively describe the two dynamic influences on the removal characteristics of the spacer-removal module. The dynamic influences are independent of $do$ and $dg$ but contribute to the removal characteristics more strongly as the oblique angle increases. This contribution is convenient when designing a functional device, as dynamic influences will lower the apparent pressure ratio $κ$⁠. Correspondingly, our quantitative model of the static influences is expected to more accurately describe module geometries with low oblique angles than geometries with high angles (⁠$β>45°$⁠).

During typical experiments lasting tens of minutes, no injection of spacers into the immersion liquid was observed. After the flow was initiated, the module showed a consistent, predictable behavior, removing all spacers, and adapting to changes in the flow rates up to an arrival rate of ∼15 spacers per second.

We demonstrated that two-phase segmented flows can be used in a microfluidic probe while maintaining a stable confinement of processing liquid. Such segmented flows open the route for localized sequential chemistry by reducing dispersion. With this, one can envision highly efficient patterning of proteins on surfaces and multiplexed immunohistochemistry on tissue sections.

This work was supported by the European Research Council (ERC) Starting Grant, under the 7th Framework Program (Project No. 311122, BioProbe). We thank Julien Cors, Ute Drechsler, and Yuksel Temiz for their help in fabrication and Andrew deMello and Robert Wootton (ETH Zürich) for valuable discussions. Carlotta Guiducci (EPFL), Robert Lovchik, Emmanuel Delamarche, Bruno Michel, and Walter Riess are acknowledged for their continuous support.