Melt polymer drawn single and multi-capillary fibre-based electroosmotic pumps

Microfluidic devices have been employed in micro-analytical systems and microelectronics using inexpensive, customisable fluid-handling automation at the microliter scale. Here we utilise a well-established fibre drawing technique, which offers a range of materials and capillary conformations, that can be utilized within microfluidic devices to control fluid movement via electroosmotic processes to produce a simple electroosmotic pump (EOP). Single capillary EOPs were fabricated from drawn PU capillary fibres with internal diameters ranging from 73 to 200 µm and were shown to be capable of actively transporting a buffer solution using an external driving electric potential. A maximum flow rate of 0.8 ± 0.1 μL/min was achieved for a 73 ± 2 µm diameter PU capillary fibre at an applied potential of 750 V/cm. This flow rate was successfully increased up to 5.3 ± 0.3 μL/min by drawing a multi-capillary array consisting of 4, 5 and 7 capillaries.


Introduction
Microfluidics (Whitesides 2006) is a technology that enables the manipulation of small volumes of fluid in a precise manner with applications across diverse fields such as DNA analysis (Hosokawa et al. 2004;Wainright et al. 2003), high-throughput screening (Guo et al. 2012), cell biology (Whitesides 2006;Koster et al. 2008), chemical synthesis (Gunther and Jensen 2006), proteomics (Lion et al. 2003) and medical diagnostics (Yager et al. 2006). Underpinning all integrated microfluidic systems is a range of core generic components which include sample delivery capabilities, pumps to move fluid around the device, as well as various other units for combining, mixing, purifying and ultimately detecting of an analyte of interest (Aryasomayajula et al. 2017). An essential function underpinning all of these components is the ability to pump fluid. Micro-pumps with two-or three-dimensional microchannels are frequently utilized in microfluidics as these devices typically have small overall volumes, laminar flow, and a large surface-to-volume ratio. Pumps that utilise electrokinetic flow, such as the electroosmotic pump (EOP), leverage the surface charge which has been described by von Helmholtz (1853) using an electric double layer (EDL) theory (Fig. S1). This surface charge spontaneously develops when a liquid comes in contact with a confined surface within the microchannel or microcapillary and can be used to control fluid movement 1 3 45 Page 2 of 11 by controlling the applied electrical field (Xuan 2008;Ghosal 2004Ghosal , 2006. Direct current (DC) and alternating current (AC) EOP designs leverage the electroosmotic flow (EOF) process to achieve a laminar pulseless flow profile in a pump configuration which has no moving parts (Wang et al. 2009a(Wang et al. , 2009b. The simplicity of the EOP design makes it appealing in applications such as chromatographic separation (Chen et al. 2004) and drug delivery (Chen et al. 2007). The types of EOP designs and their respective applications by other research groups is summarised in Table 1. In these EOP design approaches, microchannels or capillaries are utilised to achieve controllable flow rates (or flow velocity) which are directly controlled via an applied voltage. The majority of these approaches focus on silicon, glass and PDMS for the device fabrication, although there have been reports utilizing thermoplastic polymers (Kirby and Hasselbrink 2004;Nge et al. 2013) such as PU, poly(methyl methacrylate) (PMMA), polycarbonate (PC) and poly(ethylene terephthalate) (PET). The method of fabrication is clearly dominated by lithography (soft lithography and photolithography), involving etching, casting, and bonding, while methods such as hot imprinting and laser ablation have been used to a lesser extent. While there have been extensive developments in the EOP field, both the limitations of material type and fabrication approaches, to some extent, curb the development of EOPs in microfluidic systems.
In this study, for the first time, we develop a cost-effective fibre-based EOP using thermally drawn thermoplastic PU capillary structures fabricated by a well-established fibre drawing technique. This fibre drawing technique has been used previously to produce complex multi-microstructured fibres for photonic devices (Hayashi et al. 2019;Atakaramians et al. 2012;Singh et al. 2012;Tuniz et al. 2013;Eijkelenborg et al. 2001Eijkelenborg et al. , 2004. The approach is based on rigid polymers and soft glasses, but it can also be used to produce flexible capillary structures with thermoplastic polymers Farajikhah et al. 2021Farajikhah et al. , 2019Cheng et al. 2015). Here, PU was chosen here as it is flexible, elastomeric and provides an active surface-charged interface. Furthermore, PU has been used in microfluidic devices as a replacement of substance such as silicon, glass and PDMS (Wu et al. 2012;Domansky et al. 2013;Fan et al. 2020). Using the fibre drawing technique, PU capillary fibres with internal diameters ranging from 73 to 200 µm, have been produced and utilised in single capillary and multi-capillary configurations for microfluidic pumping.

Capillary sample preparation
Continuous PU capillary fibres were drawn from a large thermoplastic PU preform tube (Grayline Inc., USA), having a 6.4 mm outside diameter, using a fibre draw tower shown in Fig. 1. The drop-off temperature was set to 215 °C while the subsequent drawing was performed at 200 °C. The large PU preform was fed downwards into a furnace at rates between 4 and 25 mm/min, and fibres were drawn with a capstan wheel at rates between 0.5 and 2 m/min. The ratio between the feed and drawing determines the final dimension of the PU capillary fibres. Multi-capillary PU fibres were fabricated using the "stack-and-draw" method, where multiple PU tubes were first arranged into a preform stack, heated to 120 °C for two days and then drawn to fibre as before (Kaysir et al. 2017).

Characterisation
An optical microscope (Leica M205A) associated with Image J software was employed to measure the cross-sectional and dimensions of the capillary structures. A USB microscope AM4113T-GFBW (Dino-Lite Premier, Clarkson, WA, Australia) equipped with a blue light-emitting diode was used to record the fluid height changes in glass capillary tubes to determine fluid pump rates. A thermal camera (ThermoIMAGER TIM160) was used to record the temperature changes of PU fibres during the tests.

PU capillary EOPs characterization
A schematic overview of the experimental setup for an EOP is shown in Fig. 2. The EOP design consisted of two reservoirs, the bridging capillary structure and glass capillary tubes for electrode insertion and fluid level determination. The reservoirs consisted of sealable 600 µL microcentrifuge tubes. A Tris-CHES buffer solution, pH 8.83, consisting of 1.0 mM or 5.0 mM Tris-(hydroxyl methyl) amino-methane (Tris) and 1.0 mM or 5 mM N-cyclohexyl-2-aminoethanesulfonic acid (CHES) (Sigma-Aldrich) was used. To accurately determine the flow volumes generated by the EOP, each test was run over 60 s and the head height displacement of the buffer solution was visually observed in the capillary glass tubing recorded over time using a previously reported approach (Hamblin et al. 2007). Flow rates were determined by measuring the change in head height (corresponding to volume) in the glass capillary tubes with respect to time. These capillaries were not involved in controlling electroosmotic flow as no electric field was passed through them. Rather, these capillaries simply measured reservoirs displacement (volume) by changes in capillary head height with respect to time which relates to flow rate. A schematic diagram of the fluid flow in capillary-based EOP was described in our previous work (Wu et al. 2021). Platinum (Pt) wires (30 µm in diameter) were inserted into the top of the capillary tubing in each reservoir to serve as polarizing electrodes. The PU capillary was primed by pressurized Cell transport Witek et al. (2004) injections of the buffer solution into the reservoir to ensure removal of air blockages within the capillary channel. A LabSmith HVS448 High Voltage Sequencer (3 kV ± 0.05%) was used to apply an electric field of up to ± 1500 V. PU capillary of 20 mm in length were tested in triplicate at applied fields up to the 1500 V supply limit.

PU single-capillary fibres
PU capillary fibres with inner diameters ranging from approximately 73-200 µm were successfully fabricated, as shown in Fig. 3. The resultant micro-channels (capillaries) were observed to have mainly ovoid-circular cross-sectional capillary shape. Deviations from circularity result from the original preforms being non-circular due to manufacture and/or storage deformation. The data describing the characteristics of the capillary area and structures for these PU capillary samples are given in Table 2. The inner diameters Fig. 1 Schematic of fibre drawing process (inset: a typical temperature profile inside a fibre drawing furnace with respect to the preform position) of the capillary structures were in the range of 73-200 µm, while the outer diameters of these samples were between 172 and 523 µm. The cross-section area of the PU capillary was from 4 to 33 × 10 3 µm 2 , compared with the whole structure cross-sectional area 22-420 × 10 3 µm 2 . The area ratio of the inner capillaries to the whole fibre structures was between 15.4% and 18.7%.

PU multi-capillary fibres
PU capillary fibres with different numbers of capillaries were also investigated. The cross-sectional images of these samples with 4, 5 and 7* capillaries are shown in Fig. 4. These capillaries were distributed based on the preform stacking configuration resulting in triangular (Fig. 4A), rectangular (Fig. 4B) and hexagonal formats (Fig. 4C). The structural analysis of the resultant cross-sections of the drawn capillary structures is given in Table 3. As a consequence of the drawing process, a clear distortion of the capillaries was noted resulting in a range of non-circular capillary shapes. For example, the width of these capillaries in Fig. 4A was 54 ± 16 µm, while the height was between 36 ± 12 µm. The cross-section area of the capillaries was 7379 µm 2 , compared with the cross-sectional area of the whole fibre 39,000 µm 2 . The area ratio of the multi capillaries to the whole fibre structures was between 10.7 and 18.9%. The number of functional capillaries in the multi-capillary structure in Fig. 4C was actually 13, with 7 large and 6 small capillaries. However, here the six smaller capillary channels were considered to have a negligible effect on the overall flow rate due to their relative size when compared to the larger seven capillaries. Therefore, the number of functional capillaries was considered to be 7* in this configuration.

Flow properties of PU capillary EOP
PU capillary EOPs of 20 mm in length were tested over a 60 s period using a 1 mM Tris-CHES buffer at ± 200 to ± 1500 V. Electrical current is typically used to monitor the EOF in microfluidic devices (Locascio et al. 1999;Pittman et al. 2003;Huang et al. 1988), as it reflects the realtime EOF within the capillaries under different experimental conditions. Here, the resultant device currents were observed to increase with an increasing voltage, Fig. 5. Similar current trends were also observed for EOPs with different diameters, Fig. S2A-C. Furthermore, the observed currents increase as the diameter (or area) increase when the same voltage was applied as seen in Fig. S2D. In addition, the observed current was related also to the concentrations of buffer where Capillary area (× 10 3 µm 2 ) 33 20 7 4 Capillary/structure area ratio 15.4% 18.7% 18.0% 18.2% Capillary inner diameter (µm) 200 ± 5 160 ± 2 93 ± 6 73 ± 2 Capillary outer diameter (µm) 523 ± 8 368 ± 10 224 ± 6 172 ± 3 Fig. 4 Optical micrograph of the PU multi-capillary structures A′ 4-capillary before melting, B′ 5-capillary before melting, C′ 7-capillary before melting, A 4-capillary after melting, B 5-capillary after melting C 7*-capillary after melting (the scale bar is 200 µm) the higher the concentration resulted in a higher current response, Fig. S2D.
The current responses observed for various voltages, geometries, and buffer solutions in the EOP can be described by EDL theory. The electrical current, I , can be expressed by the relationship in Eq. 1; where E is the electrical field strength applied to the capillary, is the ionic conductivity in the solution, A is the cross section of the capillary ( A ∝ d 2 ) , where d is the diameter of capillary) and L the length of capillary. A lower current would be expected with decreasing capillary area, increasing capillary length, reducing voltage and conductivity of buffer solution. Importantly, in a practical device, a lower current would be advantageous as it would assist in minimising localised Joule heating which would result in non-linear flow behaviour by inducing viscosity and ionic mobility changes (see discussion below) (Xuan 2008;Ghosal 2006;Grushka et al. 1989). PU-EOP samples with a 73 µm diameter gave a relatively stable performance with respect to current variations observed during operational tests, Fig. S2A.

EOP flow rate
The flow rate (or electroosmotic velocity) of the electrolyte within the PU capillary EOP was determined by measuring the changes in the liquid head height in microcapillary glass tubes with respect to time. The dependence of the flow rate with respect to the applied voltage, Fig. 6, ideally should increase linearly with electric field as predicted by Eq. 5 (see ESI Sect. 1.1), where velocity (u) was influenced by the electric field (E) . However, EOPs with a larger capillary cross section, such as the 200 µm-EOP, were significantly affected by the operational temperature (as a result of Joule heating) as well as the presence of electrolysis bubbles that were generated at higher voltages which could travel more readily inside the larger capillary sizes. As a result, the larger capillaries exhibited a more unstable and non-linear performance when compared to the 73 µm EOP (with respect to the  Fig. 6 The flow rates of PU-EOPs with different diameters versus voltages observed current at the same applied voltage, Fig. 5 and Fig. S2). There was also a clear trend of the flow rate decreasing with respect to the increase in capillary diameter, Fig. 6. This behaviour is not predicted by Eq. 5 (see ESI Sect. 1.1) where the flow rate is proportional to the cross-sectional area of the capillaries. One reason for this may be due to an influencing competitive and counteractive siphon effect. This is in line with the report of Wim Kok that siphoning is not a problem with diameters of ≤ 50 µm, but is stronger in wider capillaries ≥ 100 µm (Kok 2000). This effect can dramatically offset the driven force generated by the electric field when the diameter of capillary increased. Significantly, the PU EOP of 73 µm in diameter exhibited a significant pumping performance (0.8 µL/min at 1500 V or 5.33 ×10 −4 µL/min V) when compared to a reported silica-based EOP (Dasgupta and Liu 1994) with a flow rate of 3.33 ×10 −5 µL/min V and PDMS-based EOPs (Gao and Gui 2014) with a flow rate of 4.56 ×10 −5 µL/min V, as shown in Table 1.

Thermal properties of PU capillary EOP
Joule heating resulting from the passage of electric current through a capillary filled with a resistive electrolyte media, is problematic, particularly when higher voltages are applied. The impact of Joule heating on the PU capillary was investigated over 400-1500 V, Fig. 7. In Fig. 7C, D, the temperature of PU-EOPs upon the application of a driving voltage at 20 s increased dramatically-reaching a relatively steady rate until the end of the experiment (at 80 s). The heat generated was observed to decrease rapidly to the ambient temperature once the driving voltage was removed. The maximum temperature change ( ΔT = 3 • C ) was observed using a thermal imaging camera for the 200 µm-EOP at 1500 V, while the 160 µm-EOP was slightly lower at 1.2 °C. Significantly, there was no observable temperature change ( ΔT ) for the 73 µm and 93 µm EOP. The observed temperature differences were directly related to the observed current during the EOP operation. Here, the current was related to the inner diameter, d, (or area) of the capillary, where I ∝ d 2 . Therefore, a smaller volume capillary will result in lower Fig. 7 The temperature difference of PU-EOPs with different diameters at different voltage (400-1000 V). A 73 µm-EOPs; B 93 µm-EOPs; C heat generation. This also indicated that it could be advantageous to use small inner capillaries, when the temperature is the key factor that dramatically influences the performance of EOPs.

Flow rates of PU multi-capillary EOP
The flow rates of PU multi-capillary EOPs (based on fibres whose cross-sectional images are shown in Fig. 4) of 20 mm in length were investigated, Fig. 8. Here, the flow rates of the EOP experienced a significant increase with increasing voltage and demonstrated behaviour similar to the single capillary EOP configuration (Sect. 3.2.1). The maximum flow rate for EOP with an equivalent of 7* capillaries was 5.3 µL/min at 1500 V, which was approximately double the rate of the 5-capillary EOP and nearly 7 times for 1-capillary EOP. The number of capillaries significantly affects the flow rates of EOP where the higher flow rates were achieved by the higher number of capillaries. The flow rates achieved here (5.3 µL/min at 1500 V or 3.53 ×10 −3 µL/min V were greater than the reported Si-based microchannel devices with a flow rate of 6.00 × 10 -4 µL/min V (Heuck and Staufer 2011), similar to PDMS based microchannels with a flow rate of 2.84 × 10 -3 µL/min V (Ye et al. 2019), and lower than a reported PU microfluidic device with a 76.8 µL/min V (Piccin et al. 2007) as shown in Table 1. It should be noted that the manufacturing techniques required to produce these Si-related, PDMS and PU devices were far more complex, compared to the simple fibre drawing approach adopted here. From Eq. 5 (see ESI Sect. 1.1), the flow rate is related to the applied electric field ( E ), the cross-sectional dimensions ( r ), the working liquid, the surface charge density of the channel as well as the temperature. Increasing the number of capillaries increases the cross-sectional area (dimensions), which increases the flow rate. Figure S4 shows the relationship between the flow velocity and the number of the capillaries (or the cross-sectional dimensions). For a given voltage, a working liquid and a well-distributed capillaries configuration, the flow velocity of PU multi-capillary EOP (m/min) was similar. As a result, increasing the number of capillaries did not boost the flow rate per capillary (area) but resulted in an increase in mass flow rates.
Additionally, the slight non-linear behaviour observed for the 7* capillary EOP was likely due to the non-uniform capillaries sizes and the difficulty in determining the actual flow contribution from the number of smaller capillaries. The cross-sectional area of each capillary shown in Fig. 4C was very different in this configuration, particularly where one capillary in the middle of the structure was calculated to have a cross-sectional area of 11 × 10 3 µm 2 which was three times the size of other capillaries in this layout. This non-uniformity likely resulted in the differing flow rates. Compounding this, Joule heating which arises from resistive heating of the multi-capillary with increasing capillary area also contributes to non-linear flow behaviour.

Further potential applications
In this study, simple, cost-effective, and scalable thermoplastic PU capillary fibre-based electroosmotic pumps were successfully demonstrated to be feasible and reproducible. The results were very promising, however, at this proof-ofconcept state, it leaves scope for optimisation, in particular, the potential applications.
One main application of using the PU capillaries to control fluid flow is for sample acquisition and analysis. Particularly, PU capillaries here can be an alternative to a reported polymethylmethacrylate (PMMA)-based microfluidic device with complex microchannels (Jubery et al. 2012) to process bio-separation and concentration tests based on isotachophoresis (ITP). Furthermore, the fabrication techniques required to produce PMMA channels were far more complex than the simple fibre drawing approach adopted here. Another aspect that PU capillaries and EOPs can be applied is to manipulate biological cells. E. coli and S. cerevisiae cells, for example, were used to study the electrokinetic transport in polymerbased microfluidic devices (Witek et al. 2004). Due to the fact that cells can be driven separately using electrophoretic/ electroosmotic forces in a microchannel, PU capillary EOPs could be used as a microdevice for cells separation. In addition, due to the flexibility and stretchability of PU capillaries (microchannels) structures, PU capillary EOPs have great potential to be used into many areas including flexible microfluidic devices and flexible wearable electronics (Fallahi et al. 2019).

Conclusions
Simple, cost-effective and scalable capillary fibre-based electroosmotic pumps where successfully produced utilising a thermally drawn thermoplastic PU fibre drawing technique. Single capillary EOPs with internal diameters ranging from 73 to 200 µm were fabricated and were shown to be capable of actively transporting a buffer solution using a driving electric potential. Results show that a maximum flow rate of 0.8 μL/min was achieved for a 73 µm diameter PU fibre at an applied potential of 750 V/ cm. Furthermore, this flow rate was successfully increased up to 5.3 μL/min by the drawing of a multi-capillary array consisting of up to 7* capillaries. Overall, the concept of creating PU capillary structures, using a simple and lowcost approach, for EOPs was shown to be feasible and reproducible, thereby opening up more opportunities in development of microfluidic devices.

Acknowledgements
The authors would like to acknowledge funding support from the Australian Research Council Centre of Excellence Scheme (CE 140100012) and the Australian Research Council Discovery Project DP170103537. The authors thank the Australian National Fabrication Facility (ANFF)-Materials Node and NSW Nodes for access to the facilities hosted at the University of Wollongong and the Research & Prototype Foundry Core Research Facility at the University of Sydney. The ANFF is funded through the National Collaborative Research Infrastructure Strategy (NCRIS) providing nano-and micro-fabrication facilities for Australia's researchers. We also gratefully acknowledge the technical assistance of Peter Henry and Justin Digweed.
Funding Open Access funding enabled and organized by CAUL and its Member Institutions.

Conflict of interest
The authors declare that they have no conflict of interest.
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