Interfacial Tension Sensor for Low Dosage Surfactant Detection

: Currently there are no available methods for in-line measurement of gas-liquid interfacial tension during the ﬂotation process. Microﬂuidic devices have the potential to be deployed in such settings to allow for a rapid in-line determination of the interfacial tension, and hence provide information on frother concentration. This paper presents the development of a simple method for interfacial tension determination based on a microﬂuidic device with a ﬂow-focusing geometry. The bubble generation frequency in such a microﬂuidic device is correlated with the concentration of two ﬂotation frothers (characterized by very different adsorption kinetic behavior). The results are compared with the equilibrium interfacial tension values determined using classical proﬁle analysis tensiometry.


Introduction
The motion of gas bubbles is known to be affected by even the smallest amount of surface-active impurities, as these molecules adsorb at the gas-liquid interface and change the tangential mobility at the bubble surface [1][2][3]. In high-purity water (or surface-active molecule free) electrolyte solutions, in the low shear stress case (i.e., smaller bubbles or gasliquid interface moving slowly), the gas-liquid interface deviates from being tangentially mobile [4][5][6][7][8]. For the higher shear stress (i.e., larger bubbles or gas-liquid interface moving fast) the gas-liquid interface stays tangentially mobile [9,10]. The immobilization of the gas-liquid interface of small bubbles due to adsorption of minute amounts of surface-active impurities makes them sensitive probes for low dosage surfactant detection.
The flotation process is a separation technique mainly used in mineral processing for the separation of valuable minerals from their host rock, and relies on bubbles selectively attaching to valuable mineral particles allowing them to be recovered from a slurry of valuable and gangue mineral particles [11]. Efficient separation is usually maximised by the use of surface-active chemicals (termed collectors and depressants) that preferentially adsorb at solid-liquid interface. These reagents reinforce or produce the required difference in hydrophobicity between the wanted and unwanted minerals, allowing for bubble attachment and recovery. Another group of surface-active flotation reagents are frothers. Frother molecules preferentially adsorb at the gas-liquid interface [12,13] and can be divided into five main subcategories based on their chemical composition i.e., aliphatic, cyclic, and aromatic alcohols, alkoxy paraffins, and polyglycol polymers [14]. Frothers lower gas-liquid interfacial tension affecting both the size and stability of bubbles generated in the flotation tank. Bubble size decreases and stability increases (i.e., bubble coalescence is either delayed or prevented) with increasing frother concentration. This also results in a stable froth phase at the top of the flotation tank [15,16]. Although frothers improve flotation rate and recovery, too high concentration may have negative effects including a lower flotation recovery rate due to the decreased probability of bubble attachment to a hydrophobic particle as well as poorer selectivity [16,17]. Therefore, information about frother concentration could be crucial for more effective control of the flotation process.
The adsorption of frothers at the air-water interface may be studied by interfacial tension measurements. A number of approaches to the study of the kinetics of frother adsorption at the air-liquid interface as well as the equilibrium interfacial tension for different frothers have been reported [18][19][20][21][22][23]. Studies involve the application of various measurement techniques such as Wilhelmy plate [22], Du Noüy ring [23], or profile analysis tensiometry (with both a pendant drop and emerging bubble geometries used) [18,19,21,24]. However, all of these techniques rely on static conditions, in which the adsorption of frother molecules at the interfacial surface happens in the absence of flow, and may not reflect adsorption under dynamic conditions, i.e., such as in the flotation tank [24].
One of the technology platforms that has potential for deployment in industry to allow dynamic, in-line measurement of surfactant concentration is microfluidics. Microfluidic devices are optimized to handle small volumes (from pico-to micro-liters [25,26]) of fluids flowing through the channels (the channel's dimensions are usually in the range of several to tens of microns). The use of micron-sized channels results in laminar flow, which allows for easy and controlled formation of uniform bubbles and droplets [25,27]. In addition, the environment inside the channels is contaminant free, offering another advantage for fluidliquid interfacial studies [28][29][30]. There are a number of considerations regarding the design of such a device to make it viable for interfacial studies. Bubble (or droplet) formation requires the presence of two immiscible phases: (i) the dispersed phase, which could be either gas or liquid and (ii) the continuous phase, which is a liquid that carries the bubbles or droplets. The influx of these two phases into the microfluidic device involves the use of pressure devices such as syringe pumps. After introduction of the phases into the chip, bubble (or droplet) formation depends on the local flow field that is mainly determined by the channel geometry and applied pressure [31,32]. Various microfluidic chip designs have been used for effective bubble or droplet generation. All the designs can be divided, according to the flow area at the contact point of the dispersed and continuous phases, into three categories: (i) cross-flow devices [31], (ii) flow-focusing devices [33], and (iii) co-flow devices [34]. Each of these types of flow categories has been adopted for interfacial tension measurement [35][36][37][38][39], however mostly for droplets. In cross-flow geometry tapered channels with T-junction geometry are often used [35,36]. Nguyen et al. [40] generated droplets at a cross-junction and used an optofluidic sensor detector, consisting of a laser and a photodiode, to measure the droplet formation frequency. However, one of the major drawbacks of using the T-junction configuration for experiments with surfactants is that the surfactant, depending on its nature, may also adsorb to the walls of the channel changing their wettability. Once the channel's walls become hydrophobic the bubbles will attach to them [37]. The current best approach for interfacial tension measurements is a co-flow configuration. Xu et al. [39] studied the effect of surfactant concentration on the liquid-liquid interfacial tension by means of a change in the droplet diameter. A flowfocusing microfluidic device was used by Lee et al. [38], where the authors tried to find the correlation between the liquid-liquid interfacial tension and the deformations of the generated droplets. However, all the reported studies focused on liquid-liquid interfacial tensions and high surfactant concentrations. In addition, the described devices were made of polydimethylsiloxane (PDMS), which makes them unsuitable for deployment in industry to allow dynamic, in-line measurement of the flotation frother's concentration.
In this paper we demonstrate a simple approach, developed for the determination of gas-liquid interfacial tension, using a co-flowing microfluidic geometry for bubble generation, and bubble generation frequency, as a means of frother concentration determination.
The bubble generation frequency as a function of surfactant concentration (for low concentration range) is measured for two commonly-used flotation frothers of different adsorption kinetics, e.g., methyl isobutyl carbinol and DowFroth 250. The influence of the continuous phase flow rate on the bubble generation frequency is also explored. The results obtained in a microfluidic chip are compared with the interfacial tension values obtained using profile analysis tensiometry.

Materials
All solutions were prepared using Milli-Q water (generated by an Advantage system A10, Millipore, USA). The gas-MilliQ water interfacial tension (measured at 22 • C) and the Milli-Q water resistivity were 72.4 mN·m −1 and 18.2 MΩ·cm, respectively. The total organic carbon was less than 4 ppb. Flotation frothers selected for microfluidic interfacial studies were: (i) methyl isobutyl carbinol (MIBC) and (ii) DowFroth 250. MIBC is a branched aliphatic alcohol with a molecular weight of 102.17 g·mol −1 , and was sourced from Sigma-Aldrich (Australia). DowFroth 250 is polypropylene glycol monomethyl ether with an average molecular weight of 250 g·mol −1 (exact value 264.35 g·mol −1 ), and was supplied by The Dow Chemical Company (USA). Both frothers were of reagent grade (98% purity). The hydrophile-lipophile balance (HLB) is 6.05 and 7.83 for MIBC and DowFroth 250, respectively.

Methods
Microfluidic frother concentration determination experiments: The microfluidic device is based on a co-flowing geometry. It was fabricated using borosilicate Pyrex ® glass in the South Australian node of the Australian National Fabrication Facility. The design of the chip consists of a central channel for a dispersed phase (gas) that meets two side channels allowing the flow of the continuous phase (frother solution). All the channels merge to form one large channel ( Figure 1). The width of the dispersed phase channel is 25 µm while the width of the continuous phase channels is 300 µm. The width of the merged channel is 500 µm. The channels were fabricated using deep reactive-ion etching (DRIE). The microfluidic divide was then thermal bonded at 650 • C. Nanoport™ fittings (IDEX Health & Science, USA) made of polyether ether ketone (PEEK) were aligned with and attached to the inlets of the microfluidic device using adhesive rings (IDEX Health & Science, USA) and a curing time of 1 h (at 165 • C). PEEK tubing (IDEX Health & Science, USA) with an inner dimeter of 150 µm was used to connect the Nanoport™ fittings to glass gastight syringes (Hamilton, USA) mounted in programmable and precisely-controlled syringe pumps (Cole-Palmer, USA) allowing for operations at constant and low flow rates of both phases. While the flow rate of the dispersed phase was kept constant (0.4 mL·h −1 ), the flow rate of the continuous phase flow was varied, ranging from 1 up to 10 mL·h −1 . Prior to actual measurement, the flow rates of both phases were allowed to stabilize for at least 15 min. To exclude environmental vibration effects, the experimental set-up was placed on an anti-vibration table Vision IsoStation (Newport, USA). To avoid temperature changes (and gradients) the microfluidic device was side illuminated by a cold light source with a halogen diode lamp (Bruker, USA). All experiments were carried out at 22.0 ± 1.0 • C.
The bubble generation frequency experiments in MilliQ water and in frother solutions of various concentrations were recorded using a high-speed camera SA3 Fastcam (Photron, USA) mounted on an inverted BXFM microscope (Olympus, Japan), as schematically shown in Figure 1. Depending on the surfactant concentration, the videos were recorded at a frame rate of either 250 fps or 1000 fps and with a resolution of 300 pixels × 300 pixels. All videos were recorded in a position capturing the merging of three channels, i.e., the point of bubble formation. Videos were converted to image (*.BMP) sequences and analyzed using ImageJ software [41] to determine the number of bubbles passing through the channel in a given time interval. The average bubble generation frequency was calculated as a function of frother concentration and flow rate ratio from three independent repeats. orded at a frame rate of either 250 fps or 1000 fps and with a resolution of 300 pixels × 300 pixels. All videos were recorded in a position capturing the merging of three channels, i.e., the point of bubble formation. Videos were converted to image (*.BMP) sequences and analyzed using ImageJ software [41] to determine the number of bubbles passing through the channel in a given time interval. The average bubble generation frequency was calculated as a function of frother concentration and flow rate ratio from three independent repeats. Profile analysis tensiometry experiments: Interfacial tension for all studied solutions was determined using profile analysis tensiometer, PAT1-M (Sinterface Technologies, Germany) placed on an anti-vibration table (Vision IsoStation, Newport, USA). The interfacial tension measurements (of static bubbles), as a function of adsorption time, were conducted using an emerging bubble geometry. A U-shaped stainless steel capillary (of a diameter of 2.935 mm) was used to generate air bubbles of a constant volume (17 µ L). A 20 mL square optical glass cuvette was filled with the studied solution and closed with a lid to minimise solution evaporation. Profile analysis measurements were conducted for at least 30 min to ensure that the interfacial tension reached equilibrium. An average value of equilibrium interfacial tension was calculated from at least three independent measurements. A constant temperature of 22.0 ± 0.1 °C was maintained by a heating-cooling circulating bath.
Cleaning protocols: An optical glass cuvette (Hellma Analytics, Germany) used for profile analysis tensiometry. As well, all glassware used for the solution preparation was immersed in 2% aqueous Extran ® (Merck Millipore, USA) solution for 40 min and rinsed with demineralized water. Then, the glassware was placed in a 2M KOH aqueous solution for further 40 min. This was followed by rinsing with copious amount of Milli-Q water until neutral pH and drying at 50 °C in an oven. An optical glass cuvette was additionally exposed to air plasma (Harrick, PDC-OD2, USA) for 90 s prior to the measurement.
The stainless steel capillary (Sinterface Technologies, Germany), polyether ether ketone (PEEK) tubing (IDEX Health & Science, USA), and gastight glass syringes (Hamilton, USA) were sonicated in 2% Mucasol™ (Sigma-Aldrich, Australia) aqueous solutions for 15 min, followed by rising with demineralized water and sonicating in 100% undenatured Profile analysis tensiometry experiments: Interfacial tension for all studied solutions was determined using profile analysis tensiometer, PAT1-M (Sinterface Technologies, Germany) placed on an anti-vibration table (Vision IsoStation, Newport, USA). The interfacial tension measurements (of static bubbles), as a function of adsorption time, were conducted using an emerging bubble geometry. A U-shaped stainless steel capillary (of a diameter of 2.935 mm) was used to generate air bubbles of a constant volume (17 µL). A 20 mL square optical glass cuvette was filled with the studied solution and closed with a lid to minimise solution evaporation. Profile analysis measurements were conducted for at least 30 min to ensure that the interfacial tension reached equilibrium. An average value of equilibrium interfacial tension was calculated from at least three independent measurements. A constant temperature of 22.0 ± 0.1 • C was maintained by a heating-cooling circulating bath.
Cleaning protocols: An optical glass cuvette (Hellma Analytics, Germany) used for profile analysis tensiometry. As well, all glassware used for the solution preparation was immersed in 2% aqueous Extran ® (Merck Millipore, USA) solution for 40 min and rinsed with demineralized water. Then, the glassware was placed in a 2M KOH aqueous solution for further 40 min. This was followed by rinsing with copious amount of Milli-Q water until neutral pH and drying at 50 • C in an oven. An optical glass cuvette was additionally exposed to air plasma (Harrick, PDC-OD2, USA) for 90 s prior to the measurement.
The stainless steel capillary (Sinterface Technologies, Germany), polyether ether ketone (PEEK) tubing (IDEX Health & Science, USA), and gastight glass syringes (Hamilton, USA) were sonicated in 2% Mucasol™ (Sigma-Aldrich, Australia) aqueous solutions for 15 min, followed by rising with demineralized water and sonicating in 100% undenatured ethanol (Chem-Supply Pty Ltd., Australia) for 15 min. Then, all the components were thoroughly rinsed and sonicated in Milli-Q water for 15 min, followed by drying in a nitrogen stream (99.999% purity, BOC, Australia). The cleaned syringes and the capillary were additionally air plasma cleaned for 90 s.
The Pyrex ® glass microfluidic device was cleaned prior to the experiments by pumping 2% Mucasol™ aqueous solution through the channels for 40 min, followed by extensive flushing with Milli-Q water, followed by 2M KOH aqueous solution for 40 min. Then, the microfluidic device was rinsed with Milli-Q water until neutral pH. All solutions were pumped at a constant flow rate of 1 mL·h -1 . Finally, the microfluidic device was dried in a nitrogen stream and exposed to air plasma for at least 90 s.

Interfacial Tension Isotherms
Due to the difference in their molecular weight (and hence differences in surface activity and adsorption kinetics), MIBC and DowFroth 250 were chosen for our study. The equilibrium interfacial tension values as a function of the frother concentration are presented in Figure 2 (panel A for MIBC and Panel B for DowFroth 250). Both frothers' concentrations were chosen to obtain similar values of the air-solution interfacial tension.
ditionally air plasma cleaned for 90 s.
The Pyrex ® glass microfluidic device was cleaned prior to the experiments by pumping 2% Mucasol™ aqueous solution through the channels for 40 min, followed by extensive flushing with Milli-Q water, followed by 2M KOH aqueous solution for 40 min. Then, the microfluidic device was rinsed with Milli-Q water until neutral pH. All solutions were pumped at a constant flow rate of 1 mL•h -1 . Finally, the microfluidic device was dried in a nitrogen stream and exposed to air plasma for at least 90 s.

Interfacial Tension Isotherms
Due to the difference in their molecular weight (and hence differences in surface activity and adsorption kinetics), MIBC and DowFroth 250 were chosen for our study. The equilibrium interfacial tension values as a function of the frother concentration are presented in Figure 2   The adsorption isotherm of MIBC (Figure 2A) resembles that of 1-hexanol, which is unsurprising given the similar carbon chain length and molecular weight [42]. Although there was no drastic reduction in the interfacial tension for the MIBC concentrations, the kinetics of adsorption was very fast, with the equilibrium values of the interfacial tension reached in a fraction of second for all studied MIBC concentrations. Such near-instantaneous adsorption is desirable in the flotation process [43]. It is important to note, that even at its highest concentration (2.5 × 10 −3 mol·L -1 , about 250 ppm), MIBC only lowers the interfacial tension of MilliQ water by 5.3 ± 0.1 mN·m −1 , with the equilibrium interfacial tension of 2.5 × 10 −3 mol·L −1 MIBC being 67.1 ± 0.1 mN·m −1 .
The adsorption isotherm for DowFroth 250, a frother belonging to the polyglycol ether family, is shown in Figure 2B. The isotherm shows that lower concentration of DowFroth 250 is required to achieve a similar decrease in the interfacial tension in comparison to MIBC. The concentration range of DowFroth 250 from 4 × 10 −7 to 4 × 10 −5 mol·L −1 (0.1 and 10 ppm) and resulted in equilibrium interfacial tension values between 72.3 and 67.4 mN·m −1 , while for MIBC a concentration rage of 1 × 10 −5 to 2.5 × 10 −3 mol·L −1 (1-250 ppm) was needed to reach the same values of interfacial tension. In spite of its branched structure, MIBC has a lower HLB in common with other aliphatic alcohols, and will likely The adsorption isotherm of MIBC (Figure 2A) resembles that of 1-hexanol, which is unsurprising given the similar carbon chain length and molecular weight [42]. Although there was no drastic reduction in the interfacial tension for the MIBC concentrations, the kinetics of adsorption was very fast, with the equilibrium values of the interfacial tension reached in a fraction of second for all studied MIBC concentrations. Such nearinstantaneous adsorption is desirable in the flotation process [43]. It is important to note, that even at its highest concentration (2.5 × 10 −3 mol·L −1 , about 250 ppm), MIBC only lowers the interfacial tension of MilliQ water by 5.3 ± 0.1 mN·m −1 , with the equilibrium interfacial tension of 2.5 × 10 −3 mol·L −1 MIBC being 67.1 ± 0.1 mN·m −1 .
The adsorption isotherm for DowFroth 250, a frother belonging to the polyglycol ether family, is shown in Figure 2B. The isotherm shows that lower concentration of DowFroth 250 is required to achieve a similar decrease in the interfacial tension in comparison to MIBC. The concentration range of DowFroth 250 from 4 × 10 −7 to 4 × 10 −5 mol·L −1 (0.1 and 10 ppm) and resulted in equilibrium interfacial tension values between 72.3 and 67.4 mN·m −1 , while for MIBC a concentration rage of 1 × 10 −5 to 2.5 × 10 −3 mol·L −1 (1-250 ppm) was needed to reach the same values of interfacial tension. In spite of its branched structure, MIBC has a lower HLB in common with other aliphatic alcohols, and will likely structure in a semi-organised manner at the bubble surface, resulting in a smaller area per molecule occupied in comparison to the larger (in terms of molecular weight) and more structurally diverse DowFroth 250 [44]. Lower DowFroth 250 concentrations result in slower adsorption kinetics and hence a longer time is required to reach equilibrium interfacial tension (between 2500 and 3500 s for the concentration range used in this study).

Microfluidic Determination of Interfacial Tension
Our first target in the microfluidic experiments was the determination of microfluidic device working conditions for MilliQ water. All experiments were performed in the dripping flow regime, i.e., at low flow rates of dispersed (0.4 mL·h −1 ) and continuous (1 up Colloids Interfaces 2021, 5, 9 6 of 12 to 10 mL·h −1 ) phases with the periodic generation of an individual bubble detaching from the tip of the dispersed phase channel [45].
The relation between viscous forces and capillary forces is described by a dimensionless number-the capillary number, Ca, as: where µ c is the continuous phase viscosity, U c is the continuous phase velocity, and γ is the interfacial tension [45]. The bubble pinches off from the tip when the viscous drag forces overcome interfacial tension forces with the balance between these forces governing the size of the detaching bubble. Figure 3A presents pictures of air bubbles formed in the microfluidic channel flowing Milli-Q water at different flow rates of the continues phase, while the air bubble generation frequency as a function of Milli-Q water flow is plotted in Figure 3B. As can be seen in Figure 3A the size of the generated air bubbles decreases with increasing flow rate of the continuous phase (Milli-Q water). This is because the increase of the continuous phase flow rate leads to increased shear stress, causing formation of smaller air bubbles. At the same time, the generation frequency of air bubbles is higher. For the experiments with frothers, in order to avoid the situation when the bubble is 'squeezed' between the walls of the channel (and hence affecting uniform frother adsorption at the air-solution interface), we will focus on the following three continuous phase flow rates: 5, 7, and 9 mL·h −1 . Figure 4 presents the pictures of air bubbles generated in Milli-Q water and various concentrations of MIBC. The flow rates of both phases were From data plotted in Figure 3B one can see that the frequency of generated air bubbles increases from 1.8 to 12.3 Hz as the continuous phase flow increases from 1 to 10 mL·h −1 , and that the relation between the frequency and the flow rate is linear (the coefficient of determination, R 2 , is 0.9969). The results are reproducible with the relative standard deviation, RSD, for three independent measurements not exceeding 3%. Hoeve et al. [46] predicted that the formation frequency, f, in a flow-focusing microfluidic device under the jetting regime and for constant flow rate is proportional to the flow rate of the continuous phase (Q c ), the radius of the dispersed phase channel (r d ), and the main channel, f ∝ Q c /πr d r 2 . However, in the dripping regime and for constant dispersed phase flow rate, the bubble generation frequency increases in a linear manner with increases in the continuous phase flow rate, as the viscosity is constant [47].
For the experiments with frothers, in order to avoid the situation when the bubble is 'squeezed' between the walls of the channel (and hence affecting uniform frother adsorption at the air-solution interface), we will focus on the following three continuous phase flow rates: 5, 7, and 9 mL·h −1 . Figure 4 presents the pictures of air bubbles generated in Milli-Q water and various concentrations of MIBC. The flow rates of both phases were kept constant with the dispersed phase flow rate being 0.4 mL·h −1 and the continuous phase flow rate being 5 mL·h −1 . The presence of frother in the continuous phase results in adsorption of its molecules at the air-solution interface, which decreases the interfacial tension forces that keep the air bubble at the tip of the dispersed phase channel [19,45]. As a result, smaller bubbles (generated at the higher frequency) detached in surfactant solutions compared to the bubbles generated in Milli-Q water. The bubble size decreased and the bubble generation frequency increased with increases in the frother concentration, with the smallest and most frequently generated bubbles for 50 ppm MIBC solution (from the examples presented in Figure 4). Moreover, for higher concentrations (50 ppm and above) the generated air bubbles were 'pushed in contact' in downstream parts of the channel but we observed no coalescence. This is not surprising as 50 ppm is~4.5-5 times higher than the critical coalescence concentration for MIBC [25,48].  The bubble generation frequency in MIBC and DowFroth 250 solutions of different concentrations for three different flow rates of the continuous phase is presented in Figure  5A,B, respectively. For the same continuous phase flow rate, as the concentration of MIBC and DowFroth 250 increased (and the interfacial tension counteracting viscous drag decreased), the bubble generation frequency increased. For both MIBC and DowFroth 250, when the frother concentration was kept constant but the continuous phase flow rate increased (and the viscous drag counteracting constant interfacial tension increased) the bubble generation frequency increased.
In Figure 5A (MIBC concentration ranged between 1 and 250 ppm or 1 × 10 −5 and 2.5 The bubble generation frequency in MIBC and DowFroth 250 solutions of different concentrations for three different flow rates of the continuous phase is presented in Figure 5A,B, respectively. For the same continuous phase flow rate, as the concentration of MIBC and DowFroth 250 increased (and the interfacial tension counteracting viscous drag decreased), the bubble generation frequency increased. For both MIBC and DowFroth 250, when the frother concentration was kept constant but the continuous phase flow rate increased (and the viscous drag counteracting constant interfacial tension increased) the bubble generation frequency increased.
The bubble generation frequency in MIBC and DowFroth 250 solutions of different concentrations for three different flow rates of the continuous phase is presented in Figure  5A,B, respectively. For the same continuous phase flow rate, as the concentration of MIBC and DowFroth 250 increased (and the interfacial tension counteracting viscous drag decreased), the bubble generation frequency increased. For both MIBC and DowFroth 250, when the frother concentration was kept constant but the continuous phase flow rate increased (and the viscous drag counteracting constant interfacial tension increased) the bubble generation frequency increased.
The relationship between bubble formation frequency and interfacial tension in a T-junction microfluidic device was formulated by Nguyen et al. [49]. In their proposed model, the bubble formation frequency can be calculated using the following equation: where ρ c is the continuous phase density, D c is the diameter of the continuous phase channel, D d is the diameter of the dispersed phase channel, and C D and C S are the coefficients for drag and interfacial tension, respectively. In the T-junction geometry, the flow rate and the formation frequency is characterized by non-linear dependency, as the bubble detachment is also affected by the interaction of the dispersed phase with the wall of microfluidic channel [34]. However, Nguyen et al. reported that for surfactant solution flowing through the microfluidic channel bubble formation frequency depended linearly on the interfacial tension, provided the continuous phase density was kept constant [40,48].
We cannot apply this equation to our data due to the different geometry of the channels, but we expect that there will be a similar dependency between bubble formation frequency and interfacial tension. Figure 6A,B present bubble generation frequency as a function of the interfacial tension for MIBC and DowFroth 250, respectively. For both frothers, at the constant continuous phase flow rate, the bubble generation frequency decreased linearly with increasing air-solution interfacial tension with R 2 for MIBC data being higher than 0.9978, and R 2 for DowFroth 250 data being higher than 0.9971. When the air-solution interfacial tension was kept constant, the bubble generation frequency increased with increasing continuous phase flow rate.
for drag and interfacial tension, respectively. In the T-junction geometry, the flow rate and the formation frequency is characterized by non-linear dependency, as the bubble detachment is also affected by the interaction of the dispersed phase with the wall of microfluidic channel [34]. However, Nguyen et al. reported that for surfactant solution flowing through the microfluidic channel bubble formation frequency depended linearly on the interfacial tension, provided the continuous phase density was kept constant [40,48].
We cannot apply this equation to our data due to the different geometry of the channels, but we expect that there will be a similar dependency between bubble formation frequency and interfacial tension. Figure 6A,B present bubble generation frequency as a function of the interfacial tension for MIBC and DowFroth 250, respectively. For both frothers, at the constant continuous phase flow rate, the bubble generation frequency decreased linearly with increasing air-solution interfacial tension with R 2 for MIBC data being higher than 0.9978, and R 2 for DowFroth 250 data being higher than 0.9971. When the air-solution interfacial tension was kept constant, the bubble generation frequency increased with increasing continuous phase flow rate. This frother sensing system based on bubble generation frequency is very sensitivea drop in air-solution interfacial tension of 0.1 mN·m −1 causes an increase of 13-14% in bubble generation frequency, making it suitable for the detection of even minute amounts of frother molecules. Figure 7 presents the scaled data from Figure 6 A,B. The relative bubble generation frequency, fr (i.e., the bubble generation frequency for frother solutions, ff, normalised with respect to the bubble generation frequency for Milli-Q water, fw, at a given flow rate: fr = This frother sensing system based on bubble generation frequency is very sensitive-a drop in air-solution interfacial tension of 0.1 mN·m −1 causes an increase of 13-14% in bubble generation frequency, making it suitable for the detection of even minute amounts of frother molecules. Figure 7 presents the scaled data from Figure 6A,B. The relative bubble generation frequency, f r (i.e., the bubble generation frequency for frother solutions, f f , normalised with respect to the bubble generation frequency for Milli-Q water, f w , at a given flow rate: , is plotted as a function of the drop in interfacial tension from Milli-Q water ∆γ = γ w − γ f , with γ w being the interfacial tension of Milli-Q water and γ f being the interfacial tension of the frother solutions. The black closed circles are for MIBC while the red closed circles are for DowForth 250. The scaled frequency data for two frothers and bubbles generated at three different continuous phase flow rates can be fitted with a straight line (R 2 of 0.9979) for the entire range of considered frother concentrations. Therefore, after normalising with the bubble generation frequency for Milli-Q water, the bubble formation frequency is independent of the continuous phase flow rate and is only affected by changes (with respect to Milli-Q water) in the interfacial tension. Despite different adsorption kinetics, the relative bubble generation frequency is the same for MIBC and DowForth 250 solutions of the same interfacial tension.
continuous phase flow rates can be fitted with a straight line (R 2 of 0.9979) for the entire range of considered frother concentrations. Therefore, after normalising with the bubble generation frequency for Milli-Q water, the bubble formation frequency is independent of the continuous phase flow rate and is only affected by changes (with respect to Milli-Q water) in the interfacial tension. Despite different adsorption kinetics, the relative bubble generation frequency is the same for MIBC and DowForth 250 solutions of the same interfacial tension.

Conclusions
In this work we present a microfluidic-based approach to determine gas-liquid interfacial tension for two flotation frothers of very different adsorption kinetics using bubble generation frequency measurements. We show that, in the dripping regime and at the constant dispersed phase flow rate, the bubble formation frequency in Milli-Q water linearly depends on the continuous phase flow rate. A drop in the air-solution interfacial tension as small as 0.1 mN·m −1 causes the bubble generation frequency to increase by 13−14%, making it a suitable device for the detection of even minute amounts of frother molecules. Moreover, for MIBC and DowFroth 250 solutions, despite the very different adsorption kinetics, the bubble generation frequency increases linearly with decreases in the equilibrium interfacial tension and increases in the continuous phase flow rate. Upon data scaling, all curves collapse onto a single line, despite different adsorption kinetics for MIBC and DowFroth 250. This is likely due to the continuous supply of the frother molecules to

Conclusions
In this work we present a microfluidic-based approach to determine gas-liquid interfacial tension for two flotation frothers of very different adsorption kinetics using bubble generation frequency measurements. We show that, in the dripping regime and at the constant dispersed phase flow rate, the bubble formation frequency in Milli-Q water linearly depends on the continuous phase flow rate. A drop in the air-solution interfacial tension as small as 0.1 mN·m −1 causes the bubble generation frequency to increase by 13−14%, making it a suitable device for the detection of even minute amounts of frother molecules. Moreover, for MIBC and DowFroth 250 solutions, despite the very different adsorption kinetics, the bubble generation frequency increases linearly with decreases in the equilibrium interfacial tension and increases in the continuous phase flow rate. Upon data scaling, all curves collapse onto a single line, despite different adsorption kinetics for MIBC and DowFroth 250. This is likely due to the continuous supply of the frother molecules to the gas-liquid interface. Moreover, a flow-focusing device offers a directional flow onto the bubble surface upon its generation, providing continuous supply of frother molecules.