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Microfluidic networks: Design and simulation of pure hydrodynamic switching and medium access control
Nano Communication Networks 4 (2013) 164–171
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Nano Communication Networks journal homepage: www.elsevier.com/locate/nanocomnet
Microfluidic networks: Design and simulation of pure hydrodynamic switching and medium access control✩ Lidia Donvito, Laura Galluccio, Alfio Lombardo, Giacomo Morabito ∗ DIEEI, Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, Italy
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Article history: Received 6 June 2013 Accepted 4 August 2013 Available online 30 August 2013 Keywords: Microfluidics Switching MAC
abstract In this paper, we consider the Hydrodynamic Controlled microfluidic Network (HCN) paradigm which is based on purely hydrodynamic microfluidic switching and medium access control. The HCN paradigm can be applied to build programmable microfluidic devices, i.e., Lab-on-a-Chips (LoCs), that by exploiting hydrodynamic effects only, route chemical or biological samples in a microfluidic network, in a controlled way. These microfluidic devices will be highly flexible and inexpensive, and thus are expected to become extremely competitive as compared to the alternative solutions for chemical and biological analysis and synthesis or cheap sensing. This paper provides the design guidelines for the microfluidic circuits implementing the switching function and the medium access control and illustrates through simulations the feasibility of the proposed idea. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction In the last decade, considerable research effort has been devoted to design microfluidic devices where small volumes of fluids are manipulated typically for the purpose of chemical and biological analysis and synthesis (e.g., drug delivery, biomolecule synthesis, diagnostic testing, DNA sequencing, cheap sensing, synthesis of micro-structured materials) [1–5]. To accomplish these goals, microfluidic devices consist of a series of microchannels, usually in silicon, glass or Polydimethylsiloxane (PDMS), where the reagents flow and interact. The advantages of using microfluidic systems come from the specific behavior of fluids at the micro scale, where factors such as surface tension, energy dissipation, and viscosity dominate, so that liquids flow in laminar streams without mixing together. In the recent past a large number of attempts have been
✩ A previous version of this work was presented at IEEE MoNaCom 2013 [24]. ∗ Correspondence to: Viale Andrea Doria 6, 95125 Catania, Italy. Tel.: +39 095 7382355; fax: +39 095 7382397. E-mail addresses: [email protected] (L. Donvito), [email protected] (L. Galluccio), [email protected] (A. Lombardo), [email protected], [email protected] (G. Morabito).
1878-7789/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.nancom.2013.08.002
made to define a framework, including hardware and software features, for realizing programmable microfluidic systems able to execute a large number of different elementary analyses within a single device [6–9,4]. A number of problems have prevented this very ambitious goal to be reached; however recently the introduction of an emerging approach denoted as droplet-based microfluidics [3,10], first, and the introduction of the innovative concept of bubble logic [2] later, have shown that the design of microfluidic networks aimed at supporting flexible, low-cost and scalable programmable microfluidic systems is feasible. In particular bubble logic paves the way to the introduction of both communication and networking functionalities in microfluidic devices. A first step in this direction has been proposed in [11] where the possibility of encoding information in the distance between consecutive droplets and/or bubbles has been introduced; later on [12–14] this encoding methodology has been used to represent the address information in a microfluidic networked system where the flow of bubbles is driven into a microchannel network by means of other properly timed bubbles.1
1 In the rest of this paper we will refer to the droplet case; however the same concepts and discussions apply to the bubble case.
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The availability of such solutions may foster a paradigm shift in the microfluidic domain similar to the introduction of the network-on-a-chip concept in the systemon-a-chip domain [15]. Today’s programmable droplets microfluidic chips, in fact, rely on the active droplets manipulation methods, such as the electrowetting-ondielectric method, requiring a complex multilayer microfabrication process for the chip, external instrumentation for the operation and sometimes are not suitable for some biological settings due to the problems of biocompatibility of electrical signals on cells or biomolecules [1,16,17]. On the contrary the approach proposed in our work is to use purely hydrodynamic technologies to support networking capabilities in a network of microfluidic devices. Accordingly we consider the Hydrodynamic Controlled microfluidic Network paradigm (HCN). To this purpose, we address a system architecture consisting of a physical ring topology implementing a logical star topology as shown in Fig. 1. All packets are generated by or delivered to the central hub connected to the same ring; the hub performs a managing role which incorporates both the system logic necessary to perform job scheduling, and the sorting functionalities among the individual elements. For this reason we will name this hub microfluidic router µR. It is evident that the µR is connected to other boundary elements, such as pumps, by using standard electrical/electronic interfaces in order to control the injection of reagents into the system. Similar to what is done in the network-on-chip domain, we assume that a networking element that we call Microfluidic Network Interface (MNI) is attached to each element to perform the operations required for efficient, flexible and reliable exchange of samples with the other elements. More specifically, basic objectives of the i-th MNI are:
165
Fig. 1. HCN system architecture.
• to detect droplets that must be delivered to the i-th element and switch them accordingly,
• to appropriately insert droplets generated by the i-th element in the shared microfluidic channel only when this is ‘‘possible’’. In other words, the MNI is responsible for switching and medium access control. In this paper we will describe how these functionalities can be implemented and provide a validation for both. The rest of this paper is organized as follows. In Section 2 we describe the design of the switching functionalities and assess these through simulations. In Section 3 we focus on the medium access control performed by the MNI. Finally, in Section 4 conclusions are drawn. 2. Switching droplets in HCN Let us suppose that the samples which should be chemically treated or analyzed by the HCN are included in a payload droplet. In order to route the payload droplet appropriately, our HCN switching scheme exploits another droplet, which is called header droplet, used for network signaling only and, in particular, for encoding the destination address. The destination address is encoded in DHP , that is the distance between the header droplet and the payload
Fig. 2. HCN switching block of the i-th MNI.
droplet. The HCN switching block of the i-th MNI consists of the T-junction circuit shown in Fig. 2. This circuit has one inlet coming from the previous MNI in the ring, i.e. the (i − 1)-th MNI. The inlet is connected to a pipe which bifurcates in B in two opposite pipes denoted as pipe 1 and pipe 2. The points at the end of pipe 1 and pipe 2, denoted as A and C , respectively, are connected by a channel characterized by a very low hydrodynamic resistance, which we denote as bypass channel. Then, pipes 1 and 2 continue into pipes 3 and 4, respectively. At the end of pipes 3 and 4 there are two outlets: the outlet out ′i at the end of pipe 3 is connected to the i-th el(Σ )
ement, Ei , while the outlet out ′′i at the end of pipe 4 is connected to the inlet of the (i + 1)-th MNI. The bypass channel connecting A and C is used as a pressure shunt to equalize the pressure at these two points [18]. Accordingly, the pressure difference between (BA) points B and A, which we denote as 1Pi , is equal to the pressure difference between points B and C , which we de(BC ) note as 1Pi . This occurrence makes the droplet behavior
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(a) Microfluidic equivalent circuit of the MNI.
(b) Electrical equivalent circuit of the MNI.
Fig. 3. Equivalent microfluidic and electrical circuits for the MNI represented in Fig. 2.
in the MNI microfluidic circuit represented in Fig. 2 dependent only on the geometric characteristics of pipes 1 and 2 only. In the following we derive the HCN design parameters which allow the MNI to correctly decode the destination address and therefore to switch the payload droplet accordingly. More specifically, in Section 2.1 we will first identify the conditions in which the header droplet works appropriately, that is, it enters pipe 2 at the bifurcation B. Then, we will identify the conditions in which the payload droplet appropriately implements the switching functionalities: it enters pipe 1 if its distance from the header droplet is such that the latter is still in pipe 2 when the payload droplet arrives in B, while enters pipe 2 when the header droplet has already left pipe 2:
• in the first case, the payload droplet will be processed (Σ )
by the i-th element, Ei ; • in the second case, the payload droplet follows the header droplet in the ring, and is forwarded to the next MNI. In Section 2.2 we will assess the switching functionalities through simulations. 2.1. Controlling the droplets We will study the microfluidic circuit shown in Fig. 2 by exploiting the Hagen–Poiseuille’s law 1P = Rhyd Q , where 1P is the difference in pressure at the end points of a pipe, Rhyd represents the hydrodynamic resistance of the pipe, and Q is the flux in the pipe. Accordingly, to completely describe the circuit we need to solve the microfluidic circuit represented in Fig. 3(a). An analogy with the Ohm’s law (1V = RI) can be easily drawn [19] where the pressure difference 1P is equivalent to the voltage difference 1V , and the flow rate Q is equivalent to the electric current I. In both Fig. 3(a) and (b), note that R1 and R2 represent the equivalent resistance of pipe 1 and 2, respectively, R3 represents the equivalent resistance (Σ ) at the end point of pipe 1, A, towards the element Ei , and R4 represents the equivalent resistance at the end point of pipe 2, C , towards the next MNI in the ring. A droplet arriving at a bifurcation always enters the pipe with higher flow rate [11,20]. Therefore, to appropriately address the (Σ ) element Ei , initially we should guarantee that Q2 > Q1 (or analogously I2 > I1 ) when the header droplet arrives at the bifurcation point. By applying the Kirchhoff laws and considering that we can assume Pout,2 ≈ Pout,1 , Rby ≪ min{R3 , R4 } and R3 and
R4 very large as compared to the other hydrodynamic resistances involved in the circuits, we can further approximate as follows
(Q1 − Q2 ) ≈ k(R2 − R1 )
(1)
where k is an appropriate constant. In Eq. (1) the sign of Q1 − Q2 depends on the sign of R2 − R1 . Accordingly, if R2 < R1 and thus Q2 > Q1 , then the header droplet enters pipe 2 when arrives at the bifurcation point B, as desired. By using the results in [19] to impose that R2 < R1 , and recalling that the hydrodynamic resistance R of a rectangular microchannel with length L, height h, and width w , traversed by a monophase flow can be written as R=α
L
with h < w (2) w where µ denotes the fluid viscosity and α is defined as α = 12 µ/[h3 (1 − 0.63 h/w)], it follows that to have R2 < R1 , the length of pipe 2 must be smaller than the length of pipe 1. When the header droplet is in pipe 2, it is needed that (Σ ) the payload droplet enters element Ei if it is addressed to it. Otherwise, it should go on along the ring. To this purpose, the presence of the header droplet in pipe 2 should invert the sign of the difference between the hydrodynamic resistances of pipes 2 and 1, respectively. This is reasonable by remembering that the presence of a droplet in pipe 2 increases the hydrodynamic resistance of such pipe [21–23]. We denote the increased resistance as R′2 . By recalling the results in [21–23], the condition R′2 > R1 can be equivalently rewritten as
L2 < L1 ζ [µc L2 + LD (µd − µc )] > ζ µc L1
(3)
where ζ = µα , µc is the viscosity of the continuous phase, c µd is the viscosity of the dispersed phase and LD is the length of the droplet. Accordingly the MNI design must satisfy the following condition: 0 < L1 − L2 < LD
µ
d
µc
−1 .
(4)
2.2. Switching functionalities validation In this section, we report the simulation results obtained to assess both the support of the MNI receiving functionalities and its design as described in the previous paragraph of this section.
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where δMargin is a confidence margin utilized to absorb fluctuations in the actual value of the distance between the header and the payload droplets at the receiving MNI which could cause errors in the delivery of the payload droplet. The value of δMargin must be set by considering that the distance between droplets changes as they move forward in the microfluidic channels. In our simulations we (i) have chosen δMargin = 100 µm and DHP = 600 µm which satisfy the relationship in Eq. (5). We show two snapshots of the simulation output representing:
• the situation immediately before the header droplet arrives at the bifurcation point B of the i-th MNI (Fig. 5(a)); • the situation immediately after the payload droplet left the bifurcation point B of the i-th MNI (Fig. 5(b)). (i)
Fig. 4. MNI configuration considered for simulations. Table 1 Parameters characterizing the geometry illustrated in Fig. 4. (i)
(i)
Parameter
w
wby
L1
L2
h
Value (µm)
100
300
1200
600
33
For the worth of clarity and brevity we have chosen to report only the simulation results obtained upon considering one MNI as shown in Fig. 4.2 As we already explained, the bypass channel is a crucial element in the circuit. Note that it must be large enough to guarantee very low hydrodynamic resistance while it must be designed in such a way that droplets do not enter it. In Table 1 we give the values of the parameters characterizing the geometry used in Fig. 4, where wby is the width of the bypass channel. For the sake of conciseness, in these simulations we only illustrate the case in which there are oil droplets dispersed in water continuous phase. Accordingly, the viscosities of the dispersed and continuous phases are µc = 1 mPa s and µd = 10 mPa s, respectively. The parameters characterizing the geometry given in Fig. 4 must satisfy Eq. (4), where LD = 150 µm. We have considered two cases. In the first case, the (Σ ) payload droplet must be delivered to Ei , whereas in the second case the payload droplet must be forwarded to the (i + 1)-th MNI. Accordingly, in the first case the distance between the droplets entering the i-th MNI must be such that when the payload droplet arrives at the bifurcation point the header droplet is still in pipe 2. To this end, it has been shown (i) in [24] that by applying the current divider analogy DHP (i.e. the distance between two droplets entering the i-th MNI) must satisfy the following relationship: (i)
DHP <
(i)
(i)
L1 + L2 (i)
L1
· L(2i) − δMargin = 800 µm
(5)
2 We omitted here the results in the case of more than one MNI only because more complex microfluidic dynamics are met which cannot be intuitively understood as in the case of only one MNI.
In Fig. 5(a) we observe that the distance DHP satisfies the condition in Eq. (5), whereas in Fig. 5(b) we observe that (Σ ) the payload droplet enters the pipe leading to Ei . In this case the header droplet will be eliminated by the sink at the end of the HCN. In the second case in order for the payload droplet to go towards the (i + 1)-th MNI, we must guarantee that the distance between the header droplet and the payload droplet before they arrive at the bifurcation point B of the i-th MNI should not satisfy Eq. (5), namely: (i)
DHP >
(i)
(i)
L1 + L2 (i)
L1
(i)
L2 + δMargin .
(6)
In Fig. 6 we represent the corresponding simulation re(i) sults by setting DHP = 1.1 mm, which satisfies the condition in Eq. (6). More specifically we show two snapshots of the simulation output representing:
• the situation immediately before the header droplet arrives at the bifurcation point B of the i-th MNI (Fig. 6(a)); • the situation immediately after the payload droplet leaves the bifurcation point B of the i-th MNI (Fig. 6(b)); 3. Droplet sense multiple access In this section we present the design of another important network element that provides a channel access control mechanism to avoid the coalescence, due to undesired collisions, between droplets that come from different microfluidic elements and flow into the same shared channel. More specifically, in Section 3.1 we describe the rationale of the proposed scheme and an overview of the device which implements it. In Section 3.2 we derive a model of the proposed device which can be used to set the design parameters. Finally, in Section 3.3 we verify that the proposed device works as expected through simulations. 3.1. Rationale and overview of the device The approach that we propose here, is inspired by the medium access control (MAC) protocol used in communication networks when a number of transmitting stations
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(a) Condition before the header droplet arrives at B.
(b) Condition after the payload droplet leaves B. (Σ )
Fig. 5. Simulation results for the case in which the payload droplet is addressed to the i-th element Ei
(a) Condition before the payload droplet arrives at the point B of the i-th MNI.
.
(b) Condition after the payload droplet leaves the point B of the i-th MNI.
Fig. 6. Simulation results for the case in which the payload droplet is forwarded to the (i + 1)-th MNI.
share the communication medium (i.e. bus, ring, etc.) to coordinate their transmissions so that they do not interfere with each other. Networks with this kind of topologies, typically apply a Carrier Sense Multiple Access (CSMA) mechanism to share the communication medium. In CSMA before transmitting, a node senses the medium to detect if this is already occupied by another transmitting node. If a carrier signal from another connected device is detected, the device attempting to transmit identifies the medium as busy; accordingly it will wait and try again sensing the channel after a random time interval. If no carrier signal is detected, the device can transmit its data. This mechanism avoids data collisions on the medium. In microfluidic networks the carrier signal is a droplet and the shared channel is the ring that connects the mi(Σ ) crofluidic elements Ei to each-other and to the microflu(Σ )
idic router. When a microfluidic element, Ei , completes the needed set of operations on a droplet, the latter will flow through the output channel of this element again on the ring. Then, if needed, the droplet could be addressed towards another element. So, when an element has to transmit a droplet over the ring, a mechanism is necessary to manage the medium access because a collision can occur if another droplet is in the proximity of the junction
(Σ )
and the between the output channel of the element Ei shared channel. In analogy with the CSMA mechanism, the (Σ ) that has a droplet to send on the channel element Ei must listen the channel before transmitting it. If the device detects a droplet on the ring that comes from a previous (Σ ) element, Ej , where j = 1, . . . , i − 1, near its output junction, it must wait and slow down or stop its output droplet as long as the area close to the junction is not busy. When there is no other droplet detected on the ring, the device releases its one. In Fig. 7 we show the device we propose for executing the medium access control functionalities and in the small plot we sketch its scheme in detail. To ensure that no collisions occur between the droplet that has to be inserted into the shared channel and the other droplets that flow through it, we exploit two ‘‘sensing channels’’ upstream and downstream of a junction, respectively. We denote as ‘‘sensing zone’’ the part of the shared channel between the two sensing channels; we also denote as ‘‘trapping zone’’ the part of the output channel of the microfluidic element between the two sensing channels. If a droplet that travels along the shared channel is in the sensing zone and another droplet simultaneously comes in the trapping zone, the latter will be slowed
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is calculated according to Eq. (2). Using this model, we set the channel sizes that would result in the desired behavior. To simplify the circuit we make some assumptions. We assume that the flow rates at the inlet 1 and 2 are equal. This can be achieved by configuring the flow paths to provide uniform resistances to fluid flow.3 We consider the droplet moving in the sensing zone as an additive resistance and take it into account by representing R2 and R5 as two variable resistors. We analyze four situations which can be met in the sensing zone: Case 1: no droplets are available in the sensing zone. Case 2: there is a droplet in branch 2: the resistance of branch 2 is set to R′2 = R2 + RD . Fig. 7. Device implementing medium access control for droplets.
Case 3: there is a droplet in the branch 5; the resistance of branch 5 is set to R′5 = R5 + RD . Case 4: there is a droplet in branch 2 and another in branch 5, so we set R′2 = R2 + RD and R′5 = R5 + RD . The system must be designed in such a way that a droplet in the trapping zone enters the shared channel only in Case 1. The droplet, once in the trapping zone, can take two pathways: along the branch 4 or along the branch 6. The latter is designed with pillars at one end to prevent droplet from entering it. We solved the circuit using the Symbolic Math Toolbox to evaluate the voltage drops across RD1 and RD2 that represent the differential pressures across the droplet when this is in the trapping zone. By studying the sign of the difference between these two voltage drops ϵ = 1VRD − 1VRD we find the 2 1 conditions for trapping. In fact, if ϵ > 0 the droplet is trapped because it is forced to take the branch 6 but it is blocked because this branch is designed in such a way that droplets cannot enter it; if ϵ < 0, the droplet goes along branch 4 and enters the shared channel. We found that the desired behavior is obtained for the values of resistances listed in Table 2, for which we have:
Fig. 8. Electrical equivalent circuit of a device for MAC.
down or stopped until the sensing zone is empty of other droplets. The length of the sensing zone is such that the droplet is inserted not too close to other droplets to avoid interaction and coalescence between them. The basic idea is to exploit the increase in resistance due to the presence of droplets in the sensing zone to affect the pressure field and modify the flow fields around the droplet that is in the trapping zone so as to stop it. In fact, an increase in resistance in the sensing zone results in an increase of flow rate in the sensing channels and thus in a pressure field hindering the droplet motion in the trapping zone. 3.2. Design of the device To design the device in detail, we modeled it as the equivalent Ohm circuit shown in Fig. 8. The trapped droplet is represented as two fluidic resistors (RD1 , RD2 ) for the two branches of the circuit that it directly affects. We focus on a static model in which the droplet is in the trapping zone in order to find the conditions for which this droplet is trapped or not. We assume that RD1 = RD2 = RD , where RD is the resistance introduced in a channel by a droplet and
Case 1 ϵ < 0 ∀RD . Case 2 ϵ > 0 for RD > 3.9α . Case 3 ϵ > 0 for RD > 1.19α . Case 4 ϵ > 0 for RD > 0.97α . Therefore, when choosing RD > 3.9α , all the four cases can be satisfied. In fact, although it is difficult to predict exactly the droplet resistance, a suitable rule of thumb is that each droplet will increase the resistance of the segment of the channel it occupies by about 2–5 times [25]. 3.3. MAC functionalities validation To test the theoretical results we perform a set of numerical simulations by setting the viscosities of the dispersed and continuous phases to µd = 1 mPa s, µc = 1.3 mPa s and densities to ρd = 1000 kg/m3 , ρc = 1820 kg/m3 with the interfacial tension between the two phases given as σ = 12 mN/m. By using the values given in Table 2 we have verified that the system works properly.
3 Observe that in the case of a cascade of two MAC elements the assumption that the two flow rates at the inlets 1 and 2 are equal does not hold. However, also in this case, it can be proved that the condition on the resistance RD discussed in the following still holds.
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(a) Time 0.01 s.
(b) Time 0.11 s.
(c) Time 0.154 s.
(d) Time 0.203 s.
(e) Time 0.235 s. Fig. 9. Simulation results that assess the correct MAC functioning.
Table 2 Parameters characterizing the geometry illustrated in Fig. 7. Parameter
L1
L2
L3
L4
L5
L6
L7
L8
L9
L10
L11
Value
5
1
2
1
1
0.8
2
5
6.5
15
5
w
w
w
w
w
In Fig. 9 we plot the snapshots of the simulation output representing:
• the case in which two droplets flow in the sensing zone and the droplet in the trapping zone is stopped and released only when the last droplet leaves the sensing zone; • the case in which no droplets flow in the sensing zone so the droplet is not trapped and flows into the shared channel. The small plots in Fig. 9 show the system behavior in the case the device implementing the medium access control is not available. Observe that in
w
w
w
w
w
w
Fig. 9(b) and (d) the small plots show droplets collisions which will be incurred if no MAC functionalities are implemented. 4. Conclusions In this paper, we have discussed the Hydrodynamic Controlled microfluidic Network (HCN) paradigm which is based on a pure hydrodynamic switching and medium access control of droplets in microfluidic devices. Major objective of HCN is to support a new family of programmable LoCs
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characterized by higher flexibility and lower cost. In this paper, we have made a few fundamental steps towards the complex design and characterization of HCNs. In fact, we have identified the design rules for both the architecture and the functionalities to be implemented. In particular switching and medium access control devices have been introduced, analyzed, and assessed through simulations. Results of our simulations have confirmed the feasibility of this paradigm. References [1] D. Mark, S. Haeberle, G. Roth, F. von Stetten, R. Zengerle, Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications, Chemical Society Reviews 39 (2010). [2] M. Prakash, N. Gershenfeld, Microfluidic bubble logic, Science 315 (2007). [3] S.Y. Teh, R. Lin, L.H. Hung, A.P. Lee, Droplet microfluidics, Lab on a Chip 8 (2008). [4] J.P. Urbanski, W. Thies, C. Rhodes, S. Amarasinghe, T. Thorsen, Digital microfluidics using soft lithography, Lab on a Chip 6 (2006). [5] G.M. Whitesides, The origins and the future of microfluidics, Nature 442 (2006). [6] A.M. Amin, M. Thottethodi, T.N. Vijaykumar, S. Wereley, S.C. Jacobson, Aquacore: a programmable architecture for microfluidics, in: Proc. of ISCA’07. [7] L.M. Fidalgo, S.J. Maerkl, A software-programmable microfluidic device for automated biology, Lab on a Chip 11 (2011). [8] T. Hasegawa, K. Nakashima, F. Omatsu, K. Ikuta, Multi-directional micro-switching valve chip with rotary mechanism, Elsevier Sensors and Actuators A: Physical 143 (2008). [9] K. Ikuta, A. Takahashi, K. Ikeda, S. Maruo, Fully integrated micro biochemical laboratory using biochemical IC chips, in: Proc. of IEEE MEMS 2003. [10] C.G. Yang, Z.R. Xu, J.H. Wang, Manipulation of droplets in microfluidic systems, TrAC Trends in Analytical Chemistry 29 (2010). [11] M.J. Fuerstman, P. Garstecki, G.M. Whitesides, Coding/decoding and reversibility of droplet trains in microfluidic networks, Science 315 (2007). [12] E. De Leo, L. Galluccio, A. Lombardo, G. Morabito, On the feasibility of using microfluidic technologies for communications in labs-on-achip, in: Proc. of IEEE ICC 2012. [13] E. De Leo, L. Galluccio, A. Lombardo, G. Morabito, Networked labs-ona-chip (NLoC): introducing networking technologies in microfluidic systems, Elsevier Nano Communication Networks 3 (2012). [14] A. Zanella, A. Biral, Introducing purely hydrodynamic networking mechanisms in microfluidic systems, in: Proc. of IEEE MoNaCom 2013. [15] W.J. Dally, B. Towels, Route packets not wires: on-chip interconnection networks, in: Proc. of ACM DAC’01. [16] R.B. Fair, Digital microfluidics: is a true lab-on-a-chip possible? Microfluidics and Nanofluidics 3 (2007). [17] L. Galluccio, S. Palazzo, G.E. Santagati, Characterization of molecular communications among implantable biomedical neuro-inspired nanodevices, Elsevier Nano Communication Networks 4 (2013). [18] G. Cristobal, J.P. Benoit, M. Joanicot, A. Ajdari, Microfluidic bypass for efficient passive regulation of droplet traffic at a junction, Applied Physics Letters 89 (2006). [19] H. Bruus, Theoretical Microfluidics, in: Oxford Master in Condensed Matter Physics, Oxford University Press, 2007. [20] O. Cybulski, P. Garstecki, Dynamic memory in a microfluidic system of droplets traveling through a simple network of microchannels, Lab on a Chip 10 (2010). [21] H. Wong, C.J. Radke, S. Morris, The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow, Journal of Fluid Mechanics 292 (1995). [22] F. Jousse, R. Farr, D.R. Link, M.J. Fuerstman, P. Garstecki, Bifurcation of droplet flows within capillaries, Physical Review E 74 (2006). [23] C.N. Baroud, F. Gallaire, R. Dangla, Dynamics of microfluidic droplets, Lab on a Chip 10 (2010).
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[24] E. De Leo, L. Donvito, L. Galluccio, A. Lombardo, G. Morabito, Microfluidic networks: design and test of a pure hydrodynamic switching function, in: Proc. of IEEE MoNaCom 2013. [25] T. Glawdel, C. Ren, Global network design for robust operation of microfluidic droplet generators with pressure-driven flow, Microfluidics and Nanofluidics 13 (2012).
Lidia Donvito received her the Laurea Degree in telecommunications engineering from the University of Catania, Italy, in 2012. Currently she is a Ph.D. student with the Dipartimento di Ingegneria Elettrica, Elettronica ed Informatica of the University of Catania. Her research interests include microfluidics, nanomachine communications and large-scale information networks analysis.
Laura Galluccio received her Laurea Degree in electrical engineering from the University of Catania, Catania, Italy, in 2001. In March 2005 she received her Ph.D. in electrical, computer and telecommunications Engineering at the same university under the guidance of Sergio Palazzo. Since 2002 she is also at the Italian National Consortium of Telecommunications (CNIT), where she worked as a Research Fellow within the VICOM (Virtual Immersive Communications) and the SATNEX Projects. Since November 2010 she is an Assistant Professor at the University of Catania. Her research interests include ad hoc and sensor networks, protocols and algorithms for wireless networks, communication technologies for biomedical applications and network performance analysis. From May to July 2005 she has been a Visiting Scholar at the COMET Group, Columbia University, NY under the guidance of Andrew T. Campbell. She is a member of the Sigmobile, IEEE, ACM N2Women Group and Fondazione Marisa Bellisario. Alfio Lombardo received his degree in electrical engineering from the University of Catania, Italy, in 1983. Until 1987, he acted as consultant at CREI, the center of the Politecnico di Milano for research on computer networks, where he was involved in the Software Environment for the design of Distributed Open Systems (SEDOS) and Conformance Testing Service-Wide Area Networks (CTS-WAN) CEC projects. He was the Technical Coordinator of the Formal Description Techniques (FDT) COST 11 TER project from 1986 to 1988. In 1988 he joined the University of Catania where he is a Full Professor of Telematics. He is currently the coordinator of the project entitled ‘‘MicrOfluidic Switching (MOS): introducing networking technologies in microfluidic systems’’. Presently, his research interests include microfluidic networks, distributed multimedia applications, multimedia traffic modeling and analysis. Giacomo Morabito was born in Messina, Sicily, Italy on March 16, 1972. He received the Laurea Degree in electrical engineering and the Ph.D. in electrical, computer and telecommunications engineering from the Istituto di Informatica e Telecomunicazioni, University of Catania, Catania, Italy, in 1996 and 2000, respectively. From November 1999 to April 2001, he was with the Broadband and Wireless Networking Laboratory of the Georgia Institute of Technology as a Research Engineer. Since April 2001 he is with the Dipartimento di Ingegneria Informatica e delle Telecomunicazioni of the University of Catania where he is currently an Associate Professor. His research interests focus on the analysis and solutions for wireless networks and microfluidic networks.
Contents lists available at ScienceDirect
Nano Communication Networks journal homepage: www.elsevier.com/locate/nanocomnet
Microfluidic networks: Design and simulation of pure hydrodynamic switching and medium access control✩ Lidia Donvito, Laura Galluccio, Alfio Lombardo, Giacomo Morabito ∗ DIEEI, Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, Italy
article
info
Article history: Received 6 June 2013 Accepted 4 August 2013 Available online 30 August 2013 Keywords: Microfluidics Switching MAC
abstract In this paper, we consider the Hydrodynamic Controlled microfluidic Network (HCN) paradigm which is based on purely hydrodynamic microfluidic switching and medium access control. The HCN paradigm can be applied to build programmable microfluidic devices, i.e., Lab-on-a-Chips (LoCs), that by exploiting hydrodynamic effects only, route chemical or biological samples in a microfluidic network, in a controlled way. These microfluidic devices will be highly flexible and inexpensive, and thus are expected to become extremely competitive as compared to the alternative solutions for chemical and biological analysis and synthesis or cheap sensing. This paper provides the design guidelines for the microfluidic circuits implementing the switching function and the medium access control and illustrates through simulations the feasibility of the proposed idea. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction In the last decade, considerable research effort has been devoted to design microfluidic devices where small volumes of fluids are manipulated typically for the purpose of chemical and biological analysis and synthesis (e.g., drug delivery, biomolecule synthesis, diagnostic testing, DNA sequencing, cheap sensing, synthesis of micro-structured materials) [1–5]. To accomplish these goals, microfluidic devices consist of a series of microchannels, usually in silicon, glass or Polydimethylsiloxane (PDMS), where the reagents flow and interact. The advantages of using microfluidic systems come from the specific behavior of fluids at the micro scale, where factors such as surface tension, energy dissipation, and viscosity dominate, so that liquids flow in laminar streams without mixing together. In the recent past a large number of attempts have been
✩ A previous version of this work was presented at IEEE MoNaCom 2013 [24]. ∗ Correspondence to: Viale Andrea Doria 6, 95125 Catania, Italy. Tel.: +39 095 7382355; fax: +39 095 7382397. E-mail addresses: [email protected] (L. Donvito), [email protected] (L. Galluccio), [email protected] (A. Lombardo), [email protected], [email protected] (G. Morabito).
1878-7789/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.nancom.2013.08.002
made to define a framework, including hardware and software features, for realizing programmable microfluidic systems able to execute a large number of different elementary analyses within a single device [6–9,4]. A number of problems have prevented this very ambitious goal to be reached; however recently the introduction of an emerging approach denoted as droplet-based microfluidics [3,10], first, and the introduction of the innovative concept of bubble logic [2] later, have shown that the design of microfluidic networks aimed at supporting flexible, low-cost and scalable programmable microfluidic systems is feasible. In particular bubble logic paves the way to the introduction of both communication and networking functionalities in microfluidic devices. A first step in this direction has been proposed in [11] where the possibility of encoding information in the distance between consecutive droplets and/or bubbles has been introduced; later on [12–14] this encoding methodology has been used to represent the address information in a microfluidic networked system where the flow of bubbles is driven into a microchannel network by means of other properly timed bubbles.1
1 In the rest of this paper we will refer to the droplet case; however the same concepts and discussions apply to the bubble case.
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The availability of such solutions may foster a paradigm shift in the microfluidic domain similar to the introduction of the network-on-a-chip concept in the systemon-a-chip domain [15]. Today’s programmable droplets microfluidic chips, in fact, rely on the active droplets manipulation methods, such as the electrowetting-ondielectric method, requiring a complex multilayer microfabrication process for the chip, external instrumentation for the operation and sometimes are not suitable for some biological settings due to the problems of biocompatibility of electrical signals on cells or biomolecules [1,16,17]. On the contrary the approach proposed in our work is to use purely hydrodynamic technologies to support networking capabilities in a network of microfluidic devices. Accordingly we consider the Hydrodynamic Controlled microfluidic Network paradigm (HCN). To this purpose, we address a system architecture consisting of a physical ring topology implementing a logical star topology as shown in Fig. 1. All packets are generated by or delivered to the central hub connected to the same ring; the hub performs a managing role which incorporates both the system logic necessary to perform job scheduling, and the sorting functionalities among the individual elements. For this reason we will name this hub microfluidic router µR. It is evident that the µR is connected to other boundary elements, such as pumps, by using standard electrical/electronic interfaces in order to control the injection of reagents into the system. Similar to what is done in the network-on-chip domain, we assume that a networking element that we call Microfluidic Network Interface (MNI) is attached to each element to perform the operations required for efficient, flexible and reliable exchange of samples with the other elements. More specifically, basic objectives of the i-th MNI are:
165
Fig. 1. HCN system architecture.
• to detect droplets that must be delivered to the i-th element and switch them accordingly,
• to appropriately insert droplets generated by the i-th element in the shared microfluidic channel only when this is ‘‘possible’’. In other words, the MNI is responsible for switching and medium access control. In this paper we will describe how these functionalities can be implemented and provide a validation for both. The rest of this paper is organized as follows. In Section 2 we describe the design of the switching functionalities and assess these through simulations. In Section 3 we focus on the medium access control performed by the MNI. Finally, in Section 4 conclusions are drawn. 2. Switching droplets in HCN Let us suppose that the samples which should be chemically treated or analyzed by the HCN are included in a payload droplet. In order to route the payload droplet appropriately, our HCN switching scheme exploits another droplet, which is called header droplet, used for network signaling only and, in particular, for encoding the destination address. The destination address is encoded in DHP , that is the distance between the header droplet and the payload
Fig. 2. HCN switching block of the i-th MNI.
droplet. The HCN switching block of the i-th MNI consists of the T-junction circuit shown in Fig. 2. This circuit has one inlet coming from the previous MNI in the ring, i.e. the (i − 1)-th MNI. The inlet is connected to a pipe which bifurcates in B in two opposite pipes denoted as pipe 1 and pipe 2. The points at the end of pipe 1 and pipe 2, denoted as A and C , respectively, are connected by a channel characterized by a very low hydrodynamic resistance, which we denote as bypass channel. Then, pipes 1 and 2 continue into pipes 3 and 4, respectively. At the end of pipes 3 and 4 there are two outlets: the outlet out ′i at the end of pipe 3 is connected to the i-th el(Σ )
ement, Ei , while the outlet out ′′i at the end of pipe 4 is connected to the inlet of the (i + 1)-th MNI. The bypass channel connecting A and C is used as a pressure shunt to equalize the pressure at these two points [18]. Accordingly, the pressure difference between (BA) points B and A, which we denote as 1Pi , is equal to the pressure difference between points B and C , which we de(BC ) note as 1Pi . This occurrence makes the droplet behavior
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(a) Microfluidic equivalent circuit of the MNI.
(b) Electrical equivalent circuit of the MNI.
Fig. 3. Equivalent microfluidic and electrical circuits for the MNI represented in Fig. 2.
in the MNI microfluidic circuit represented in Fig. 2 dependent only on the geometric characteristics of pipes 1 and 2 only. In the following we derive the HCN design parameters which allow the MNI to correctly decode the destination address and therefore to switch the payload droplet accordingly. More specifically, in Section 2.1 we will first identify the conditions in which the header droplet works appropriately, that is, it enters pipe 2 at the bifurcation B. Then, we will identify the conditions in which the payload droplet appropriately implements the switching functionalities: it enters pipe 1 if its distance from the header droplet is such that the latter is still in pipe 2 when the payload droplet arrives in B, while enters pipe 2 when the header droplet has already left pipe 2:
• in the first case, the payload droplet will be processed (Σ )
by the i-th element, Ei ; • in the second case, the payload droplet follows the header droplet in the ring, and is forwarded to the next MNI. In Section 2.2 we will assess the switching functionalities through simulations. 2.1. Controlling the droplets We will study the microfluidic circuit shown in Fig. 2 by exploiting the Hagen–Poiseuille’s law 1P = Rhyd Q , where 1P is the difference in pressure at the end points of a pipe, Rhyd represents the hydrodynamic resistance of the pipe, and Q is the flux in the pipe. Accordingly, to completely describe the circuit we need to solve the microfluidic circuit represented in Fig. 3(a). An analogy with the Ohm’s law (1V = RI) can be easily drawn [19] where the pressure difference 1P is equivalent to the voltage difference 1V , and the flow rate Q is equivalent to the electric current I. In both Fig. 3(a) and (b), note that R1 and R2 represent the equivalent resistance of pipe 1 and 2, respectively, R3 represents the equivalent resistance (Σ ) at the end point of pipe 1, A, towards the element Ei , and R4 represents the equivalent resistance at the end point of pipe 2, C , towards the next MNI in the ring. A droplet arriving at a bifurcation always enters the pipe with higher flow rate [11,20]. Therefore, to appropriately address the (Σ ) element Ei , initially we should guarantee that Q2 > Q1 (or analogously I2 > I1 ) when the header droplet arrives at the bifurcation point. By applying the Kirchhoff laws and considering that we can assume Pout,2 ≈ Pout,1 , Rby ≪ min{R3 , R4 } and R3 and
R4 very large as compared to the other hydrodynamic resistances involved in the circuits, we can further approximate as follows
(Q1 − Q2 ) ≈ k(R2 − R1 )
(1)
where k is an appropriate constant. In Eq. (1) the sign of Q1 − Q2 depends on the sign of R2 − R1 . Accordingly, if R2 < R1 and thus Q2 > Q1 , then the header droplet enters pipe 2 when arrives at the bifurcation point B, as desired. By using the results in [19] to impose that R2 < R1 , and recalling that the hydrodynamic resistance R of a rectangular microchannel with length L, height h, and width w , traversed by a monophase flow can be written as R=α
L
with h < w (2) w where µ denotes the fluid viscosity and α is defined as α = 12 µ/[h3 (1 − 0.63 h/w)], it follows that to have R2 < R1 , the length of pipe 2 must be smaller than the length of pipe 1. When the header droplet is in pipe 2, it is needed that (Σ ) the payload droplet enters element Ei if it is addressed to it. Otherwise, it should go on along the ring. To this purpose, the presence of the header droplet in pipe 2 should invert the sign of the difference between the hydrodynamic resistances of pipes 2 and 1, respectively. This is reasonable by remembering that the presence of a droplet in pipe 2 increases the hydrodynamic resistance of such pipe [21–23]. We denote the increased resistance as R′2 . By recalling the results in [21–23], the condition R′2 > R1 can be equivalently rewritten as
L2 < L1 ζ [µc L2 + LD (µd − µc )] > ζ µc L1
(3)
where ζ = µα , µc is the viscosity of the continuous phase, c µd is the viscosity of the dispersed phase and LD is the length of the droplet. Accordingly the MNI design must satisfy the following condition: 0 < L1 − L2 < LD
µ
d
µc
−1 .
(4)
2.2. Switching functionalities validation In this section, we report the simulation results obtained to assess both the support of the MNI receiving functionalities and its design as described in the previous paragraph of this section.
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where δMargin is a confidence margin utilized to absorb fluctuations in the actual value of the distance between the header and the payload droplets at the receiving MNI which could cause errors in the delivery of the payload droplet. The value of δMargin must be set by considering that the distance between droplets changes as they move forward in the microfluidic channels. In our simulations we (i) have chosen δMargin = 100 µm and DHP = 600 µm which satisfy the relationship in Eq. (5). We show two snapshots of the simulation output representing:
• the situation immediately before the header droplet arrives at the bifurcation point B of the i-th MNI (Fig. 5(a)); • the situation immediately after the payload droplet left the bifurcation point B of the i-th MNI (Fig. 5(b)). (i)
Fig. 4. MNI configuration considered for simulations. Table 1 Parameters characterizing the geometry illustrated in Fig. 4. (i)
(i)
Parameter
w
wby
L1
L2
h
Value (µm)
100
300
1200
600
33
For the worth of clarity and brevity we have chosen to report only the simulation results obtained upon considering one MNI as shown in Fig. 4.2 As we already explained, the bypass channel is a crucial element in the circuit. Note that it must be large enough to guarantee very low hydrodynamic resistance while it must be designed in such a way that droplets do not enter it. In Table 1 we give the values of the parameters characterizing the geometry used in Fig. 4, where wby is the width of the bypass channel. For the sake of conciseness, in these simulations we only illustrate the case in which there are oil droplets dispersed in water continuous phase. Accordingly, the viscosities of the dispersed and continuous phases are µc = 1 mPa s and µd = 10 mPa s, respectively. The parameters characterizing the geometry given in Fig. 4 must satisfy Eq. (4), where LD = 150 µm. We have considered two cases. In the first case, the (Σ ) payload droplet must be delivered to Ei , whereas in the second case the payload droplet must be forwarded to the (i + 1)-th MNI. Accordingly, in the first case the distance between the droplets entering the i-th MNI must be such that when the payload droplet arrives at the bifurcation point the header droplet is still in pipe 2. To this end, it has been shown (i) in [24] that by applying the current divider analogy DHP (i.e. the distance between two droplets entering the i-th MNI) must satisfy the following relationship: (i)
DHP <
(i)
(i)
L1 + L2 (i)
L1
· L(2i) − δMargin = 800 µm
(5)
2 We omitted here the results in the case of more than one MNI only because more complex microfluidic dynamics are met which cannot be intuitively understood as in the case of only one MNI.
In Fig. 5(a) we observe that the distance DHP satisfies the condition in Eq. (5), whereas in Fig. 5(b) we observe that (Σ ) the payload droplet enters the pipe leading to Ei . In this case the header droplet will be eliminated by the sink at the end of the HCN. In the second case in order for the payload droplet to go towards the (i + 1)-th MNI, we must guarantee that the distance between the header droplet and the payload droplet before they arrive at the bifurcation point B of the i-th MNI should not satisfy Eq. (5), namely: (i)
DHP >
(i)
(i)
L1 + L2 (i)
L1
(i)
L2 + δMargin .
(6)
In Fig. 6 we represent the corresponding simulation re(i) sults by setting DHP = 1.1 mm, which satisfies the condition in Eq. (6). More specifically we show two snapshots of the simulation output representing:
• the situation immediately before the header droplet arrives at the bifurcation point B of the i-th MNI (Fig. 6(a)); • the situation immediately after the payload droplet leaves the bifurcation point B of the i-th MNI (Fig. 6(b)); 3. Droplet sense multiple access In this section we present the design of another important network element that provides a channel access control mechanism to avoid the coalescence, due to undesired collisions, between droplets that come from different microfluidic elements and flow into the same shared channel. More specifically, in Section 3.1 we describe the rationale of the proposed scheme and an overview of the device which implements it. In Section 3.2 we derive a model of the proposed device which can be used to set the design parameters. Finally, in Section 3.3 we verify that the proposed device works as expected through simulations. 3.1. Rationale and overview of the device The approach that we propose here, is inspired by the medium access control (MAC) protocol used in communication networks when a number of transmitting stations
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(a) Condition before the header droplet arrives at B.
(b) Condition after the payload droplet leaves B. (Σ )
Fig. 5. Simulation results for the case in which the payload droplet is addressed to the i-th element Ei
(a) Condition before the payload droplet arrives at the point B of the i-th MNI.
.
(b) Condition after the payload droplet leaves the point B of the i-th MNI.
Fig. 6. Simulation results for the case in which the payload droplet is forwarded to the (i + 1)-th MNI.
share the communication medium (i.e. bus, ring, etc.) to coordinate their transmissions so that they do not interfere with each other. Networks with this kind of topologies, typically apply a Carrier Sense Multiple Access (CSMA) mechanism to share the communication medium. In CSMA before transmitting, a node senses the medium to detect if this is already occupied by another transmitting node. If a carrier signal from another connected device is detected, the device attempting to transmit identifies the medium as busy; accordingly it will wait and try again sensing the channel after a random time interval. If no carrier signal is detected, the device can transmit its data. This mechanism avoids data collisions on the medium. In microfluidic networks the carrier signal is a droplet and the shared channel is the ring that connects the mi(Σ ) crofluidic elements Ei to each-other and to the microflu(Σ )
idic router. When a microfluidic element, Ei , completes the needed set of operations on a droplet, the latter will flow through the output channel of this element again on the ring. Then, if needed, the droplet could be addressed towards another element. So, when an element has to transmit a droplet over the ring, a mechanism is necessary to manage the medium access because a collision can occur if another droplet is in the proximity of the junction
(Σ )
and the between the output channel of the element Ei shared channel. In analogy with the CSMA mechanism, the (Σ ) that has a droplet to send on the channel element Ei must listen the channel before transmitting it. If the device detects a droplet on the ring that comes from a previous (Σ ) element, Ej , where j = 1, . . . , i − 1, near its output junction, it must wait and slow down or stop its output droplet as long as the area close to the junction is not busy. When there is no other droplet detected on the ring, the device releases its one. In Fig. 7 we show the device we propose for executing the medium access control functionalities and in the small plot we sketch its scheme in detail. To ensure that no collisions occur between the droplet that has to be inserted into the shared channel and the other droplets that flow through it, we exploit two ‘‘sensing channels’’ upstream and downstream of a junction, respectively. We denote as ‘‘sensing zone’’ the part of the shared channel between the two sensing channels; we also denote as ‘‘trapping zone’’ the part of the output channel of the microfluidic element between the two sensing channels. If a droplet that travels along the shared channel is in the sensing zone and another droplet simultaneously comes in the trapping zone, the latter will be slowed
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is calculated according to Eq. (2). Using this model, we set the channel sizes that would result in the desired behavior. To simplify the circuit we make some assumptions. We assume that the flow rates at the inlet 1 and 2 are equal. This can be achieved by configuring the flow paths to provide uniform resistances to fluid flow.3 We consider the droplet moving in the sensing zone as an additive resistance and take it into account by representing R2 and R5 as two variable resistors. We analyze four situations which can be met in the sensing zone: Case 1: no droplets are available in the sensing zone. Case 2: there is a droplet in branch 2: the resistance of branch 2 is set to R′2 = R2 + RD . Fig. 7. Device implementing medium access control for droplets.
Case 3: there is a droplet in the branch 5; the resistance of branch 5 is set to R′5 = R5 + RD . Case 4: there is a droplet in branch 2 and another in branch 5, so we set R′2 = R2 + RD and R′5 = R5 + RD . The system must be designed in such a way that a droplet in the trapping zone enters the shared channel only in Case 1. The droplet, once in the trapping zone, can take two pathways: along the branch 4 or along the branch 6. The latter is designed with pillars at one end to prevent droplet from entering it. We solved the circuit using the Symbolic Math Toolbox to evaluate the voltage drops across RD1 and RD2 that represent the differential pressures across the droplet when this is in the trapping zone. By studying the sign of the difference between these two voltage drops ϵ = 1VRD − 1VRD we find the 2 1 conditions for trapping. In fact, if ϵ > 0 the droplet is trapped because it is forced to take the branch 6 but it is blocked because this branch is designed in such a way that droplets cannot enter it; if ϵ < 0, the droplet goes along branch 4 and enters the shared channel. We found that the desired behavior is obtained for the values of resistances listed in Table 2, for which we have:
Fig. 8. Electrical equivalent circuit of a device for MAC.
down or stopped until the sensing zone is empty of other droplets. The length of the sensing zone is such that the droplet is inserted not too close to other droplets to avoid interaction and coalescence between them. The basic idea is to exploit the increase in resistance due to the presence of droplets in the sensing zone to affect the pressure field and modify the flow fields around the droplet that is in the trapping zone so as to stop it. In fact, an increase in resistance in the sensing zone results in an increase of flow rate in the sensing channels and thus in a pressure field hindering the droplet motion in the trapping zone. 3.2. Design of the device To design the device in detail, we modeled it as the equivalent Ohm circuit shown in Fig. 8. The trapped droplet is represented as two fluidic resistors (RD1 , RD2 ) for the two branches of the circuit that it directly affects. We focus on a static model in which the droplet is in the trapping zone in order to find the conditions for which this droplet is trapped or not. We assume that RD1 = RD2 = RD , where RD is the resistance introduced in a channel by a droplet and
Case 1 ϵ < 0 ∀RD . Case 2 ϵ > 0 for RD > 3.9α . Case 3 ϵ > 0 for RD > 1.19α . Case 4 ϵ > 0 for RD > 0.97α . Therefore, when choosing RD > 3.9α , all the four cases can be satisfied. In fact, although it is difficult to predict exactly the droplet resistance, a suitable rule of thumb is that each droplet will increase the resistance of the segment of the channel it occupies by about 2–5 times [25]. 3.3. MAC functionalities validation To test the theoretical results we perform a set of numerical simulations by setting the viscosities of the dispersed and continuous phases to µd = 1 mPa s, µc = 1.3 mPa s and densities to ρd = 1000 kg/m3 , ρc = 1820 kg/m3 with the interfacial tension between the two phases given as σ = 12 mN/m. By using the values given in Table 2 we have verified that the system works properly.
3 Observe that in the case of a cascade of two MAC elements the assumption that the two flow rates at the inlets 1 and 2 are equal does not hold. However, also in this case, it can be proved that the condition on the resistance RD discussed in the following still holds.
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(a) Time 0.01 s.
(b) Time 0.11 s.
(c) Time 0.154 s.
(d) Time 0.203 s.
(e) Time 0.235 s. Fig. 9. Simulation results that assess the correct MAC functioning.
Table 2 Parameters characterizing the geometry illustrated in Fig. 7. Parameter
L1
L2
L3
L4
L5
L6
L7
L8
L9
L10
L11
Value
5
1
2
1
1
0.8
2
5
6.5
15
5
w
w
w
w
w
In Fig. 9 we plot the snapshots of the simulation output representing:
• the case in which two droplets flow in the sensing zone and the droplet in the trapping zone is stopped and released only when the last droplet leaves the sensing zone; • the case in which no droplets flow in the sensing zone so the droplet is not trapped and flows into the shared channel. The small plots in Fig. 9 show the system behavior in the case the device implementing the medium access control is not available. Observe that in
w
w
w
w
w
w
Fig. 9(b) and (d) the small plots show droplets collisions which will be incurred if no MAC functionalities are implemented. 4. Conclusions In this paper, we have discussed the Hydrodynamic Controlled microfluidic Network (HCN) paradigm which is based on a pure hydrodynamic switching and medium access control of droplets in microfluidic devices. Major objective of HCN is to support a new family of programmable LoCs
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Lidia Donvito received her the Laurea Degree in telecommunications engineering from the University of Catania, Italy, in 2012. Currently she is a Ph.D. student with the Dipartimento di Ingegneria Elettrica, Elettronica ed Informatica of the University of Catania. Her research interests include microfluidics, nanomachine communications and large-scale information networks analysis.
Laura Galluccio received her Laurea Degree in electrical engineering from the University of Catania, Catania, Italy, in 2001. In March 2005 she received her Ph.D. in electrical, computer and telecommunications Engineering at the same university under the guidance of Sergio Palazzo. Since 2002 she is also at the Italian National Consortium of Telecommunications (CNIT), where she worked as a Research Fellow within the VICOM (Virtual Immersive Communications) and the SATNEX Projects. Since November 2010 she is an Assistant Professor at the University of Catania. Her research interests include ad hoc and sensor networks, protocols and algorithms for wireless networks, communication technologies for biomedical applications and network performance analysis. From May to July 2005 she has been a Visiting Scholar at the COMET Group, Columbia University, NY under the guidance of Andrew T. Campbell. She is a member of the Sigmobile, IEEE, ACM N2Women Group and Fondazione Marisa Bellisario. Alfio Lombardo received his degree in electrical engineering from the University of Catania, Italy, in 1983. Until 1987, he acted as consultant at CREI, the center of the Politecnico di Milano for research on computer networks, where he was involved in the Software Environment for the design of Distributed Open Systems (SEDOS) and Conformance Testing Service-Wide Area Networks (CTS-WAN) CEC projects. He was the Technical Coordinator of the Formal Description Techniques (FDT) COST 11 TER project from 1986 to 1988. In 1988 he joined the University of Catania where he is a Full Professor of Telematics. He is currently the coordinator of the project entitled ‘‘MicrOfluidic Switching (MOS): introducing networking technologies in microfluidic systems’’. Presently, his research interests include microfluidic networks, distributed multimedia applications, multimedia traffic modeling and analysis. Giacomo Morabito was born in Messina, Sicily, Italy on March 16, 1972. He received the Laurea Degree in electrical engineering and the Ph.D. in electrical, computer and telecommunications engineering from the Istituto di Informatica e Telecomunicazioni, University of Catania, Catania, Italy, in 1996 and 2000, respectively. From November 1999 to April 2001, he was with the Broadband and Wireless Networking Laboratory of the Georgia Institute of Technology as a Research Engineer. Since April 2001 he is with the Dipartimento di Ingegneria Informatica e delle Telecomunicazioni of the University of Catania where he is currently an Associate Professor. His research interests focus on the analysis and solutions for wireless networks and microfluidic networks.