# Secure Air Traffic Control at the Hub of Multiplexing on the Centrifugo-Pneumatic Lab-on-a-Disc Platform

## Abstract

**:**

## 1. Introduction

^{TM}(CD), Digital Video Disc (DVD), or Blu-ray formats (or sections thereof) with their standard 12 cm diameter, thickness of about 1.2 mm, and a central, 15 mm diameter hole for coupling to the spindle. The disc shape is also commensurate with the rotational symmetry of the centrifugal field. While centrifugal microfluidic devices have been implemented on many other shapes, e.g., circular segments, semicircle, standard (rectangular) microscope slides, and even tubes, for the sake of this work, the popular term “disc” will represent all types of chip formats attached to a rotor.

## 2. Basics of Rotational Flow Control

#### 2.1. Centrifugal Field

#### 2.2. Pressure Contributions

#### 2.3. Angular Acceleration

#### 2.4. Critical Spin Rate

#### 2.5. Siphon Valving

#### 2.6. Centrifugo-Pneumatic Siphon Valving with Dissolvable-Film Membranes

## 3. Performance Metrics

#### 3.1. High Field Strengths for LUOs

#### 3.2. Radial Space

#### 3.3. Spatial Footprint

#### 3.4. Volume Definition and Loss

#### 3.5. Reliability and Band Width

## 4. Multiplexing

#### 4.1. System-Level Robustness

#### 4.2. Frequency Corridor

#### 4.3. Configuration in Real and Frequency Space

#### 4.4. Exemplary Bioassay Panel

#### 4.5. Assay Parallelization

## 5. Advanced Rotational Flow Control

#### 5.1. Event Triggering

#### 5.2. Logical Flow Control

#### 5.3. Delay Elements

#### 5.4. Pulsing of Spin Rate

## 6. Conclusions and Outlook

## Funding

## Conflicts of Interest

## Appendix A. Default Geometry of CP-DF Siphon Valves

**Table A1.**Default geometrical parameters and relationships of CP-DF siphon valves (Figure 1). The resulting critical spin rate $\mathsf{\Omega}\left(R,\mathsf{\Gamma},{U}_{0}\right)/2\pi \approx 22\mathrm{Hz}$. Minimum lateral dimensions are given by the smallest practical diameter of milling tools (200 µm). As tools for injection molding are often adopted from optical data storage (e.g., CD, DVD, Blu-ray), a central, 1.5 cm diameter hole and a disc radius of 6 cm with thickness around 1.2 mm, fluidic structures $\mathsf{\Gamma}$ may need to stay within the radial interval between ${R}_{\mathrm{min}}=1.5\mathrm{cm}$ and ${R}_{\mathrm{max}}=5.5\mathrm{cm}$, and an upper limit for the depth of about 1 mm. The lowest depth of cavities is often restricted by the sealing technology; for large lateral extensions or small aspect ratios, sagging of the lid, which is often a foil, may significantly change the nominal volume capacity, also in response to the pressure, and might even lead to sticking to the bottom of the cavity.

$R=3\mathrm{cm}$ | ${R}_{\mathrm{min}}=1.5\mathrm{cm}$ | ${R}_{\mathrm{max}}=5.5\mathrm{cm}$ | ${R}_{\mathrm{DF}}=3.15\mathrm{cm}R$ |

${A}_{0}={d}_{0}\cdot {w}_{0}$ | ${d}_{0}=1\mathrm{mm}$ | ${w}_{0}=5\mathrm{mm}$ | |

${U}_{0}=100\mu \mathrm{L}{\mathrm{A}}_{0}\cdot \left(R-{R}_{\mathrm{min}}\right)$ | |||

${U}_{\mathrm{iso}}={d}_{0}\cdot h\cdot L\ll {U}_{0}$ | ${d}_{\mathrm{iso}}=1\mathrm{mm}$ | ${h}_{\mathrm{iso}}=1\mathrm{mm}$ | ${L}_{\mathrm{iso}}=15\mathrm{mm}{w}_{0}+w$ |

${U}_{Z}=d\cdot w\cdot Z$ | $d=500\mu \mathrm{m}$ | $w=800\mu \mathrm{m}\ll {w}_{0}$ | $Z=10\mathrm{mm}$ |

${V}_{\mathrm{C},0}={d}_{\mathrm{C}}\cdot {w}_{\mathrm{C}}\cdot {h}_{\mathrm{C}}\gg {U}_{Z}$ | ${d}_{\mathrm{C}}=1\mathrm{mm}$ | ${w}_{\mathrm{C}}=20\mathrm{mm}$ | ${h}_{\mathrm{C}}=10\mathrm{mm}$ |

${V}_{\mathrm{int}}={d}_{\mathrm{int}}\cdot {h}_{\mathrm{int}}\cdot {L}_{\mathrm{int}}\ll {V}_{\mathrm{C}}$ | ${d}_{\mathrm{int}}=200\mu \mathrm{m}$ | ${h}_{\mathrm{int}}=300\mu \mathrm{m}$ | ${L}_{\mathrm{int}}=1\mathrm{cm}2w$ |

${V}_{\mathrm{DF}}=0.25\pi \cdot {d}_{\mathrm{DF}}\cdot {D}_{\mathrm{DF}}^{2}\ll {V}_{\mathrm{C}}$ | ${d}_{\mathrm{DF}}=190\mu \mathrm{m}$ | ${D}_{\mathrm{DF}}=3\mathrm{mm}$ | $\alpha =0.45,\beta =0.5$ |

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**Figure 1.**CP-DF siphon valving. The measures of the default geometry $\mathsf{\Gamma}$ (linearized display, not to scale) are compiled in Appendix A, Table A1. The structure consists of an inlet reservoir of cross-section ${A}_{0}={d}_{0}\cdot {w}_{0}$ with depth ${w}_{0}$ and width ${w}_{0}$, which is connected through a (narrow) isoradial channel of volume ${U}_{\mathrm{iso}}={d}_{\mathrm{iso}}\cdot {L}_{\mathrm{iso}}\cdot {h}_{\mathrm{iso}}$ positioned at $R$to an inbound section of radial extension $Z$ and cross-section $A=d\cdot w$ of depth $d$ and width $w$. (For the sake of simplicity, ${d}_{0}={d}_{\mathrm{iso}}=d=1\mathrm{mm}$ is chosen in this rudimentary layout.) During retention, the outer part represents the gas-filled compression chamber, with a main compartment of volume ${V}_{\mathrm{C},0}$, isoradial and radial sections of aggregate volume ${V}_{\mathrm{int}}$ (with ${V}_{\mathrm{int}}\ll {V}_{\mathrm{C},0}$) connecting to a shallow round chamber of volume ${V}_{\mathrm{DF}}$ (with ${V}_{\mathrm{DF}}\ll {V}_{\mathrm{C},0}$) centered at ${R}_{\mathrm{DF}}$. This outer compartment of volume ${V}_{\mathrm{DF}}$ features a dissolvable-film (DF) membrane. This DF intermittently covers a centrally placed vertical via leading to an outlet in a lower layer until a liquid volume ${U}_{\mathrm{DF}}=\beta \cdot {V}_{\mathrm{DF}}$ with geometry-dependent coefficient $0<\beta <1$ (here: $\alpha =1/2$) has arrived. A fraction $\alpha \cdot {V}_{\mathrm{DF}}$ with $\alpha <\beta $ remains in the receiving chamber after transfer.

**Figure 2.**Variation of retention rate $\mathsf{\Omega}$ (11) and its standard deviation $\mathsf{\Delta}\mathsf{\Omega}$ (20) with (

**a**) the volume of the main, permanently gas-filled compartment of the compression chamber ${V}_{\mathrm{C},0}$ and (

**b**) the radial position $R$ while leaving (the remainder of) the structure $\mathsf{\Gamma}$ unchanged. The retention rate $\mathsf{\Omega}$ sharply increases towards shrinking compression volumes ${V}_{\mathrm{C},0}$ and central placements $R$; this comes at the expense of widening the tolerance $\mathsf{\Delta}\mathsf{\Omega}$. The gridlines represent the default volume ${V}_{\mathrm{C},0}=200\mu \mathrm{L}$, at a radial position $R=30\mathrm{mm}$ and retention rate $\mathsf{\Omega}/2\pi \approx 22\mathrm{Hz}$. (

**c**) $\mathsf{\Omega}$ and $\mathsf{\Delta}\mathsf{\Omega}\mathrm{vs}.R$ while maintaining the field strength ${f}_{\omega}$ (1), originally evaluated for its default geometry $\mathsf{\Gamma}$ (Table A1), critical spin rate $\mathsf{\Omega}/2\pi =30\mathrm{Hz}$, $\varrho =1000{\mathrm{kg}\mathrm{m}}^{-3}$ and $R=3\mathrm{cm}$, while varying the radial position $R$.

**Figure 3.**Multiplexing of concurrently loaded valves in frequency vs. time domain. High- and low-pass valving takes place at points in time $\{{T}_{i}\}$. With each step $i$, a certain frequency corridor (green) that is available for LUOs rearranges. (

**a**) For rotational actuation, reliable opening of valves $\{i,j\}$ in a given step $i$ is triggered by fully crossing their linked frequency bands $\{{\mathsf{\Omega}}_{i,j}\pm M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i,j}\}$. (

**b**) In venting mode, the concurrently loaded valves serially release according to the order of opening their compression chamber, i.e., ${V}_{\mathrm{C},0,i}\mapsto \infty $ and ${p}_{V}\mapsto {p}_{0}$.

**Figure 4.**Representative scenarios underpinning multiplexing. The critical retention rates $\{{\mathsf{\Omega}}_{i,j}\}$ (11) of concurrently loaded (high-pass) valves $\{i,j\}$ to be rotationally actuated at a time ${T}_{i}$ may be preserved while shifting the radial positions $\{{R}_{i,j}\}$ of the structures $\{{\mathsf{\Gamma}}_{i,j}\}$. This might be, for instance, required to meet spatial needs towards more crowded disc layouts, by adjusting the (permanently gas-filled part) of the compression chamber of volume ${V}_{\mathrm{C},0,i,j}$, while observing proper arrangement in the frequency domain $\mathit{\omega}$, e.g., to avoid overlapping bands by ${\mathsf{\Omega}}_{i}+M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i}<{\mathsf{\Omega}}_{i+1}-M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i+1}$.

**Figure 5.**Distribution of bands in frequency space $\omega $ with required volumes of the main compression chamber ${V}_{\mathrm{C},0,i}$ for the different radial staggering and release scenarios as portrayed in Figure 4. CP-DF siphon valves $\{i,j\}$ to be released simultaneously, i.e., ${T}_{i}={T}_{i+1}$, or sequentially, i.e.,${T}_{i}{T}_{i+1}$; the valves, which have similar geometries ${\mathsf{\Gamma}}_{i,j}$ of their liquid-occupied sectors and downstream compression volumes ${V}_{C,0,i,j}$, are placed isoradially, i.e., at $R=3\mathrm{cm}$, or staggered over radial positions $R=\{2,3,4,5\}\mathrm{cm}$. The reliability factor is $M=4$. (

**a**) A set of radially staggered valves $\{i,j\}$with ${R}_{i,j}>{R}_{i,j-1}$ has been tuned through their ${V}_{\mathrm{C},0,i,j}$ to simultaneously burst in the same step $i$ once $\omega >{\mathsf{\Omega}}_{i}+M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i}$ with ${\mathsf{\Delta}\mathsf{\Omega}}_{i}=\mathrm{max}\{{\mathsf{\Delta}\mathsf{\Omega}}_{i,j}\}$. There are three representative cases for sequential actuation with ${\mathsf{\Omega}}_{i}-M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i}>{\mathsf{\Omega}}_{i-1}+M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i-1}$ for successive steps $i$ according to ${\mathsf{\Omega}}_{i}>{\mathsf{\Omega}}_{i-1}$. (

**b**) For identical ${\mathsf{\Gamma}}_{i,j}$ and ${V}_{\mathrm{C},i,j}$, the valves will open according to their radially inbound order ${R}_{i}<{R}_{i-1}$. (

**c**) For isoradial alignment ${R}_{i}=R=\mathrm{const}.$, the valve with the largest ${V}_{\mathrm{C}}$ opens first: ${V}_{\mathrm{C},i}<{V}_{\mathrm{C},i-1}$. (

**d**) Further, a radially outbound opening sequence ${R}_{i}>{R}_{i-1}$ can be achieved, for which ${V}_{\mathrm{C},i}$ needs to be drastically reduced along successive steps $i$ to suppress premature release from by the high pressure ${p}_{\omega}$ (2) at distal locations $R$, which comes at the expense of huge bandwidth $\mathsf{\Delta}\mathsf{\Omega}$ (20).

**Figure 6.**Exemplary bioassay implementing the loading of blood sample, plasma separation, and mixing with three prestored liquid reagents $\{{\mathrm{L}}_{i}\}$. Flow is controlled by five high-pass valves with release rates ${\omega}_{\mathrm{min}}<{\mathsf{\Omega}}_{i}<{\omega}_{\mathrm{max}}$ located at ${R}_{\mathrm{min}}<{R}_{i}<{R}_{\mathrm{max}}$ and opening for $\omega >{\mathsf{\Omega}}_{i}$at points in time ${T}_{i}$. (

**a**) Plasma (P) is extracted from the sample (S) in a peripheral position ${R}_{\mathrm{P}}$ at high field strength ${f}_{\omega}\propto {R}_{\mathrm{P}}\cdot {\omega}^{2}$ (1). While owing to the unidirectional nature of the centrifugal field ${f}_{\omega}$ (1), the course of the assay requires ${R}_{\mathrm{S}}<{R}_{\mathrm{P}}<{R}_{\mathrm{D}}$ and ${R}_{\mathrm{L}1}<{R}_{\mathrm{P}}$, a radially inbound staggering ${R}_{\mathrm{L}1}>{R}_{\mathrm{L}2}>{R}_{\mathrm{L}3}$ (Figure 5b) has been chosen for the serial release of $\{{\mathrm{L}}_{i}\}$ through their high-pass valves opening at ${\mathsf{\Omega}}_{\mathrm{L}1}<{\mathsf{\Omega}}_{\mathrm{L}2}<{\mathsf{\Omega}}_{\mathrm{L}3}$. (

**b**) A blood sample S is loaded and released at ${\mathsf{\Omega}}_{\mathrm{S}}<\omega <{\mathsf{\Omega}}_{\mathrm{P}}$. Separation of plasma P proceeds at ${\mathsf{\Omega}}_{\mathrm{P}}<\omega <{\mathsf{\Omega}}_{\mathrm{L}1}$. Onboard liquid reagent L1 is then forwarded at ${\mathsf{\Omega}}_{\mathrm{L}1}<\omega <{\mathsf{\Omega}}_{\mathrm{L}2}$ into the separation chamber where it is mixed with the plasma P within ${\omega}_{\mathrm{min}}<\omega <{\mathsf{\Omega}}_{\mathrm{L}2}$. The mixture P&L1 then progresses to the final detection chamber for ${\mathsf{\Omega}}_{\mathrm{P}}<\omega <{\mathsf{\Omega}}_{\mathrm{L}2}$, followed by addition of and mixing with L2 within ${\mathsf{\Omega}}_{2}<\omega <{\mathsf{\Omega}}_{3}$ and ${\omega}_{\mathrm{min}}<\omega <{\mathsf{\Omega}}_{\mathrm{L}3}$, respectively. Finally, L3 is added at ${\mathsf{\Omega}}_{3}<\omega <{\omega}_{\mathrm{max}}$ and blended to obtain S&L1&L2 within ${\omega}_{\mathrm{min}}<\omega <{\omega}_{\mathrm{max}}$. The green background marks the allowed frequency corridor at each point in time $t={T}_{i}$, with its upper limit expanding according to ${\omega}_{\mathrm{min}}<{\mathsf{\Omega}}_{\mathrm{S}}<{\mathsf{\Omega}}_{\mathrm{P}}<{\mathsf{\Omega}}_{\mathrm{L}1}<{\mathsf{\Omega}}_{\mathrm{L}2}<{\mathsf{\Omega}}_{\mathrm{L}3}<{\omega}_{\mathrm{max}}$. Note that, for the sake of simplicity, the frequency thresholds $\{{\mathsf{\Omega}}_{i}\}$ are meant to refer to their associated bands ${\mathsf{\Omega}}_{i}\pm M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i}$.

**Figure 7.**Rotational automation of an exemplary bioassay featuring sequential release of sample and separated plasma as well as pre-stored liquid onboard reagents L1, L2, and L3 with high-pass CP-DF siphon valves of release rates $\{{\mathsf{\Omega}}_{i}\}$ with ${\mathsf{\Omega}}_{\mathrm{S}}/2\pi =15\mathrm{Hz}$ and ${\mathsf{\Omega}}_{\mathrm{P}}/2\pi =30\mathrm{Hz}$. The release rates $\{{\mathsf{\Omega}}_{i}\}$ are tuned by the dead volumes of the main compression chamber $\{{V}_{\mathrm{C},0,i}\}$, as displayed on the vertical axis. (a) Radial positions (blue) ${R}_{i}$=$\{3,4,3.5,3,2.5\}\mathrm{cm}$ and (orange) ${R}_{i}^{\prime}={R}_{i}+0.5\mathrm{cm}$mimick concurrent processing of the same bioassay protocols requiring identical $\{{\mathsf{\Omega}}_{\mathrm{i}}\}$ for concurrent valving ($M=3$), while increasing their spatial packing density towards microfluidic LSI.

**Figure 8.**Principle of event-triggered flow control. (

**a**) Basic valve configuration with the control film (CF), which is opened by a first liquid to vent the compression chamber of a pneumatic valve. Consequently, a second liquid is released through the load film (LF) (Adopted from [81] with permission from The Royal Society of Chemistry). (

**b**) Extended corridor for the spin rate $\omega \left(t\right)$ in case of the event-triggered versus the rotationally actuated (Figure 6a) high-pass valves. After the sample is released at $\omega >{\mathsf{\Omega}}_{\mathrm{S}}$, the upper boundary is defined by the, e.g., common, retention rate $\stackrel{=}{\mathsf{\Omega}}$ shared by all LUOs. Release from their chambers is prompted by event-triggered venting, rather than raising the spin rate $\omega $.

**Figure 9.**Event-triggered flow control in exemplary bioassay protocol. (

**a**) The set of valves $\{{\mathsf{\Gamma}}_{i}\}$ at their default (blue) positions $\{{R}_{i}\}$, and radially shifted outwards by $0.5\mathrm{cm}$ (orange), which is a common requirement towards microfluidic LSI. All frequency bands $\{{\mathsf{\Omega}}_{i}\pm M\cdot {\mathsf{\Delta}\mathsf{\Omega}}_{i}\}$ are centered at identical rates ${\mathsf{\Omega}}_{i}=\mathsf{\Omega}$. (

**b**) The same radial distribution $\{{R}_{i}\}$ is operated at different spin rates ${\mathsf{\Omega}}_{i}={\mathsf{\Omega}}_{\mathrm{P}}$, showing that event triggering is advantageous for enabling high spin rates $\omega $, e.g., for improving and accelerating plasma separation.

**Figure 10.**Pulse-actuated CP-DF valving (Adopted from [82]). (

**a**) Photo and concept of the fluidic structure. (

**b**) Spin protocol $\omega \left(t\right)$ and (

**c**) decrease of the retention frequency $\mathsf{\Omega}\left({U}_{0}\right)$ with the arrival of the liquid volume ${U}_{0}\left(t\right)$. In conventional CP-DF siphon valving (Figure 1), a group of liquids is sequentially released through stepping up the spin rate $\omega $ across their critical burst frequencies $\{{\mathsf{\Omega}}_{i}\}$. Digital pulse actuation considers the time $\mathsf{\Delta}{T}_{i}$ it takes a liquid volume ${U}_{0}$ to advance through the outlet channel between valve opening at the burst frequency ${\mathsf{\Omega}}_{i}$, and its arrival at the following valve featuring ${\mathsf{\Omega}}_{i+1}$. During this interval $\mathsf{\Delta}{T}_{i}$, which is primarily determined by the centrifugally induced pressure head ${p}_{\omega}$ (2), the flow resistance of the connecting channel on the viscosity of the liquid, and the dissolution time of the DF, the subsequent valve $i+1$ is only partially loaded, so its effective retention rate ${\mathsf{\Omega}}_{i+1}({T}_{i}<t<{T}_{i+1})$ is transiently be lifted above ${\mathsf{\Omega}}_{i+1}\left({U}_{0}\right)$ that is nominally calculated after the arrival of the full volume ${U}_{0}$ (

**c**). The spin rate $\omega \left(t\right)$ can thus be spiked well above ${\mathsf{\Omega}}_{i+1}\left({U}_{0}\right)$ during this interval $\mathsf{\Delta}{T}_{i}$, and also allow ${\mathsf{\Omega}}_{i+1}<{\mathsf{\Omega}}_{i}$ to squash the requirement of steadily growing retention rates ${\mathsf{\Omega}}_{i+1}>{\mathsf{\Omega}}_{i}$for the high-pass valves along the serial assay protocol $\omega \left(t\right)$.

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**MDPI and ACS Style**

Ducrée, J. Secure Air Traffic Control at the Hub of Multiplexing on the Centrifugo-Pneumatic Lab-on-a-Disc Platform. *Micromachines* **2021**, *12*, 700.
https://doi.org/10.3390/mi12060700

**AMA Style**

Ducrée J. Secure Air Traffic Control at the Hub of Multiplexing on the Centrifugo-Pneumatic Lab-on-a-Disc Platform. *Micromachines*. 2021; 12(6):700.
https://doi.org/10.3390/mi12060700

**Chicago/Turabian Style**

Ducrée, Jens. 2021. "Secure Air Traffic Control at the Hub of Multiplexing on the Centrifugo-Pneumatic Lab-on-a-Disc Platform" *Micromachines* 12, no. 6: 700.
https://doi.org/10.3390/mi12060700