Low viscosity volcanic systems exhibit a variety of eruption styles with variable intensities within short time periods (Gaudin et al., 2017). Eruption dynamics are primarily driven by the ascent and burst dynamics of gas from within volcanic conduits. Characterising the fluid dynamics of gas bubbles as they ascend within the conduit – particularly their morphologies, velocities, and interaction behaviours – is critical in improving our understanding of surface explosivity and eruptive style transitions. Since we cannot directly observe the inner workings of a volcano, the mechanisms of bubble formation, interaction, and ascent are inferred using observations of eruptions visible at the surface, samples of erupted material, and laboratory experiments designed to imitate known volcanic conditions. Much of what is known about the flow dynamics inside volcanic conduits comes from an extensive series of experimental studies designed to closely replicate in-conduit behaviours in conditions that are safe, controlled, and quantifiable. In the simplest terms, we can think of a basaltic open-vent volcanic conduit as a kilometres-long cylindrical transport pathway for magma and a separated phase of buoyantly ascending bubbles, where eruptions occur as a result of these bubbles bursting at the free magma surface. Indeed, many models for volcano-scale in-conduit fluid dynamics attribute specific eruptive activity to a series of regimes that are also recognisable in two-phase pipe flow in the engineering literature (Vergniolle and Jaupart, 1986). These distinctive bubble morphologies are attributed to specific expressions of surface activity, as shown in Fig. 1, of which there are three broad classifications: passive, effusive, and explosive activity. Passive degassing typically involves low gas volume fractions (GVFs) of small spherical or ellipsoid/deformed bubbles emerging from open-vent conduits, lava lakes, or fumaroles. Effusive activity involves the outflow of lava sometimes accompanied by low-level explosive activity, coming from individual or multiple vents. The transition from effusive to explosive activity can occur gradually or rapidly (James et al., 2008; Maruishi and Toramaru, 2024; Parfitt and Wilson, 1995), and increasing bubble size significantly increases the possibility that more explosive activity is produced (James et al., 2009).

A key factor in the shift from passive or effusive to explosive behaviour is the formation of Taylor bubbles (also known as slugs). Taylor bubble formation begins with the exsolution of a limited gas volume from the melt as pressure decreases towards the surface (Gardner et al., 2022; Sparks, 1978). The exsolved bubbles remain small and compressed until the amount of gas and the surrounding pressure reaches a critical value and bubbles decouple from the magma and rise as a separate phase (James et al., 2004). Small spherical or slightly elongated or deformed bubbles transition into spherical cap and Taylor bubble morphologies by expansion-driven coalescence (Parfitt, 2004; Parfitt and Wilson, 1995), or as a result of the sudden collapse of an accumulated foam layer (Jaupart and Vergniolle, 1989). The bubble diameters become close to conduit (diameter)-filling, with morphologies that can be characterised by the presence of a nose, body and base, or tail, with a surrounding liquid falling film and trailing liquid wake (Llewellin et al., 2012). This change in bubble morphology drives a transition in flow regime to the extent that their governing fluid dynamics also change, and the conduit diameter (in addition to the pre-existing characteristics of the host magma) becomes a major control on bubble ascent. Taylor bubbles are classified as such when their length is greater than 1.5 times the surrounding conduit diameter (Llewellin et al., 2012; Shosho and Ryan, 2001), or when the surrounding liquid falling film has a length larger than or equal to the surrounding conduit diameter (Davies and Taylor, 1950). The ascent of single Taylor bubbles occurs due to sporadic releases of limited gas volumes into the conduit, and continuous Taylor bubble flow occurs due to moderate rates of continuous gas release (Seyfried and Freundt, 2000).

Taylor bubbles are most known in volcanology as the drivers of discrete and cyclic VEI 1–3 (mild to moderate) Strombolian explosions that are archetypal to Stromboli, but also observed at Etna, Yasur, Pacaya, and Erebus, among others. Strombolian explosions are one of the most widespread expressions of uninterrupted basaltic sub-aerial volcanism globally (Pering et al., 2016; Pering and McGonigle, 2018). Experimental studies of two-phase flow in conditions that are scalable to volcanic systems are the key to understanding the in-conduit flow dynamics driving these explosions because they facilitate the measurement of key bubble and liquid flow parameters (e.g., bubble velocity, bubble morphology, falling film thickness, and coalescence processes). These parameters influence the overall stability of the flow, the interaction dynamics between bubbles, the circulation dynamics of magma within the conduit, and the volume of gas released at burst, which ultimately enhances our understanding of the mechanisms for eruption periodicity, repose, explosivity, and the transitions between eruptive styles. Indeed, our current knowledge of the fluid dynamics of Taylor bubbles within volcanic conduits – whether ascending in isolation or within a train – is built upon an extensive foundation of experimental studies (Table 1). Taylor bubbles are a subject of broad interdisciplinary interest in both research and industry (Morgado et al., 2016). Outside of volcanology, Taylor bubble flow is relevant to the study of microfluidics and capillary flows (Etminan et al., 2021), buoyancy-driven fermenters, production and transportation of hydrocarbons in the oil and gas industry (Ambrose, 2015), emergency cooling of nuclear reactors, and the boiling and condensing processes in thermal power plants (Aql and Al-Safran, 2024). Understanding how Taylor bubbles flow in pipes is important to many fields, and thus their accurate measurement and analysis is essential. By refining our ability to measure and interpret the experimental dynamics of Taylor bubbles under conditions that suitably scale volcanically, we can improve our capacity to anticipate transitions in eruption behaviour.

In volcanology, the key parameters of interest surrounding Taylor bubble ascent are investigated for their role in governing flow-conditions and ultimately surface eruption dynamics. These parameters include gas volume fraction, gas and liquid slug velocities, bubble length and diameter, falling film thickness, bubble frequency, and the tracking of coalescence or break-up events. The most commonly used experimental techniques for the measurement of Taylor bubble parameters both within and outside of volcanology are described in Table 1. A review of these is also available in Calleja and Pering (2023).

Non-intrusive optical methods such as high-speed imaging, visual observations, and the pulsed shadow technique are typically used to track bubble ascent velocity and morphology in transparent media (Calleja and Pering, 2023; Jaupart and Vergniolle, 1988, 1989; Llewellin et al., 2012; Seyfried and Freundt, 2000). Traditional laser-based approaches like particle image velocimetry (PIV, now widely available as a digital image processing method without lasers) and laser doppler anemometry (LDA) enable precise velocity field and bubble interface measurements using tracer particles. These techniques are more accessible and offer non-intrusive methods for acquiring data at high spatial resolutions. However, their use is limited to transparent media (Calleja and Pering, 2023), and analysis can be computationally intensive at high frame rates. Electrical methods such as wire-mesh sensors and capacitance probes are commonly used to quantify bubble frequency, velocity, and length in opaque systems. These techniques provide real-time data at a low cost, and function well under a wide range of pressure and temperature conditions. However, their reliance on fluid conductivity to function means they are highly sensitive to environmental change and thus require regular recalibration; they are also ineffective in non-conductive fluids and need to be in direct contact with the flow to function. Pressure transducers provide time-resolved measurements of the pressure fluctuations associated with bubble ascent and bursting, while acoustic methods capture bubble dynamics through sound emission; these techniques are useful in optically inaccessible setups. Both methods are sensitive to noise or interference, and have reduced accuracy for bubble size measurements, but are capable of generating high accuracy velocity measurements. They have a wide application range including in extreme environments, and are used in the volcanic literature to experimentally link Taylor bubble ascent velocity and burst dynamics with pulsatory Strombolian eruption dynamics (Del Bello et al., 2015; Seyfried and Freundt, 2000). Magnetic resonance imaging (MRI) provides a 3D reconstruction of internal flow structure but is limited in application by its high cost and low temporal resolution.

We present a novel application of kymography – an existing digital image analysis technique – as an approach that is well-suited to measuring experimental Taylor bubble flow parameters such as gas volume fraction, gas and liquid slug velocities, bubble length and diameter, falling film thickness, bubble frequency, and to track coalescence or break-up events.

Kymographs – also referred to as time-space plots, dynamic motion analysis plots, rise diagrams, motion-track diagrams, or simply as a reslice – are a way to represent dynamic processes as time-space data in a single image. They are often applied to the visualisation of micron-scale dynamic processes in disciplines outside of volcanology wherein parameters such as the direction, speed, fluxes, and growth dynamics of the object/s of interest can be characterised. Examples include tracking the formation, division, growth, and geometry of cellular components (Mangeol et al., 2016), characterising velocity fields in microflows (Le and Fenech, 2022) and flow characterisation in porous media (Browne et al., 2020; Haward et al., 2021; Pak et al., 2018). In the Earth sciences, traditional kymographs (specifically a revolving paper-wrapped drum on which a stylus recorded motion changes over time) were used in seismography. In contemporary volcanology, kymographs are used to parameterise the frequency, height, and duration of both explosive and effusive eruptions, and to illustrate surface activity transitions over time e.g., for volcanic jets (Eibl et al., 2023; Muñoz et al., 2022; Spina et al., 2023; Taddeucci et al., 2023; Walter et al., 2023), gas emissions (Gaudin, 2017; Vossen et al., 2024), or ash plumes (Walter et al., 2020). Kymographs are also used to capture flow propagation and characterise coherent structures in pyroclastic density currents (Penlou et al., 2023; Trolese et al., 2024; Uhle et al., 2024).

In this paper we demonstrate, for the first time, the use of kymography as an effective digital image processing tool for the analysis of experimental Taylor flow in the context of Taylor bubble-driven volcanism. While kymography does not directly measure physical parameters e.g., pressure or acoustic variations, it effectively captures the motion of Taylor bubbles via identifiable flow features that facilitate the measurement of key flow parameters. Against the backdrop of existing techniques (Table 1), kymography offers a low-cost, accurate, and accessible visualisation tool that is complementary to sensor-based methods but can also be utilised as a stand-alone method in its own right.

The basic setup (Fig. 2) is a simple and cost-effective gas injection system (Calleja and Pering, 2023) consisting of a transparent, vertical, open-ended tube (internal diameter (D): 0.036 m) filled with Newtonian fluids (water-glycerol mixtures, viscosity range: 0.001–0.79 Pa s). The tube is fitted with a voltage-controlled air pump that is capable of varied injection volumes (∼ 0.05–0.25 GVF), all of which form Taylor bubble flow regimes under the listed conditions (Table 2). Gas ascent is recorded against a white background with a SONY RX100-V compact camera at 25 and 100 frames per second (fps), where the camera field of view (FOV) captures a full view of the entire 1.75 m tube length, or a higher resolution close-up view of a 0.15 m segment, respectively. See Table A1 for specific camera settings. With the exception of water, our experimental conditions can be mathematically scaled to represent the low-viscosity basaltic systems that are commonly associated with Strombolian-style volcanism using dimensionless parameters (Table 2). The principle of dimensionless scaling lies in the assumption that physical processes are scale invariant as long as they are geometrically, kinematically, and dynamically proportional. While the characterisation of physical phenomena employs equations in which dimensional quantities (e.g., velocity, viscosity etc.) are described by SI units, dimensionless quantities are obtained from ratios of dimensional quantities (i.e., they are unitless). They thus provide a numerical description of flow that is applicable to both laboratory and volcanic scales. The important dimensionless parameters used here are the Reynolds, Re, Eötvös, Eö, Morton, Mo, Froude, Fr, and dimensionless inverse viscosity, Nf, numbers, and are calculated from a combination of tube, or conduit, liquid, or magma, and characteristic bubble properties (Table 2). The experimental conditions have notably lower Eö (around four orders of magnitude) than the volcano-scale estimates due to the large diameter of volcanic conduits and the large density difference between the ascending large bubbles and the host magma. This disparity is justified because Eö and Mo can be combined to determine Nf (Table 2) when the critical values for gravity dominance are exceeded (Eö > 40, also the minimum required threshold for Taylor bubble formation, and Mo > 10⁻⁶) (Llewellin et al., 2012; Seyfried and Freundt, 2000; Viana et al., 2003), thus overlapping Nf values between experimental and volcanic conditions indicates appropriate scaling. Although water does not scale to volcanic conditions, we include it because its prevalence in the literature and well-documented fluid dynamics facilitate data comparison with existing studies. The primary goal of this paper is to evaluate the viability of kymography as a method for Taylor bubble flow analysis rather than discuss specific implications for volcanic activity, thus justifying the use of water despite its scaling limitations in volcanic contexts.

This method utilises the open-source image processing software ImageJ (Schneider et al., 2012). A kymograph is generated by first loading the relevant experimental footage file into ImageJ in .avi format. Audio information is discarded to conserve storage space. Then, a region of interest (ROI) line is traced on the track along which the target object moves; in this case, this is the Taylor bubble. Figure 3 demonstrates simplified schematics of the kymograph generation process using the example of a single ascending Taylor bubble. The initial line ROI positioning determines which parameters can be extracted from the kymograph. The line ROI should be drawn along the central axis of the bubble and parallel to the path of ascent for Taylor bubble and coalescence counts, Taylor bubble velocity, vb, Taylor bubble length, Lb, length of the inter-bubble space,Ll, and liquid level, LL. For measurements of Taylor bubble diameter, Db, and falling film thickness, λ, the line ROI should be drawn so that it is perpendicular to the path of ascent. The kymograph generation process is initiated using the in-built “image > stacks > reslice” command in ImageJ's GUI. An intensity line (a “slice”) is generated for each time point, i.e., each frame, along the line ROI and then plotted along the x-axis. This process repeats so that the intensity lines are stacked vertically along the y-axis for all frames. The resulting image is a time-space plot (the kymograph), where pixel width corresponds to distance, and pixel height corresponds to time. Real (annotated) kymograph samples generated using this method are shown in Fig. 4. Examples of unedited kymographs can be accessed through the links appended at the end of the paper.

Taylor bubble noses and tails appear on the kymographs as lines with high image contrast in the x-direction. The space in between these lines (the low-contrast region) represents the body of the Taylor bubble. We refer to these features as they appear on the kymograph as bubble bands. The spaces in between the bubble bands i.e., between the lines representing the base of a leading bubble and the nose of the next bubble ascending in the train, are the inter-bubble spaces, or liquid slugs. We refer to these features as they appear on the kymograph as liquid bands. Bubble bands are differentiated from liquid bands by the flow direction of the small (< 1 cm) entrained bubbles and how they appear on the kymograph as a result of the way they interact with the reslice line ROI (Fig. 4Ai). They can also be identified by the merging of two bubble bands, which indicates a coalescence event (Fig. 4Ai). The number of bubble bands present on the kymograph indicates the number of ascending Taylor bubbles present in the footage sample. Bubble and coalescence event counts can be extracted by simply counting these bands.

The kymographs generated from close-up footage (Fig. 4Ai and B) capture a limited (∼ 15 cm) segment of the tube, provide high resolution (captured in 1920 × 1080 pixels at 100 fps, 60 Mbps) data and are well-suited for measurements of Taylor bubble velocity, length, and diameter, liquid slug length, and falling film thickness (depending on the orientation of the selection ROI). In this case the target segment captures bubbles that have reached steady state, with the exception of low viscosity mixtures with localised turbulence. The full-view kymographs (Fig. 4Aii) capture all bubble and liquid behaviour (for the parallel selection ROI) from injection to burst: Taylor bubble velocity and length, liquid slug length, liquid level (needed for the calculation of GVF), and all coalescence events. Full-view kymographs can be divided into three regions: the injection instability region, the steady state region, and the burst instability region. The injection instability region begins at the initial injection point and ends at the approximate location along the tube where bubbles tend to enter steady state, and the steady state region begins. The start of the steady state region corresponds to the distance along the tube where Taylor bubbles are observed to stabilise, equivalent to ∼ 16D (Taitel et al., 1980), around 0.57 m along the tube. The majority of recorded coalescence occurs in the injection instability region immediately after injection. Bubble bands in this region are labelled as sub-divisions of the bubble they coalesce into upon reaching the steady state region (e.g., B6a–c in Fig. 4Aii). The burst instability region describes the approximate distance along the tube where the bubbles destabilise before burst.

Detailed information on camera calibration, distortion correction, pixel-to-meter calibration, error calculation, and filtering and thresholding processes is provided in the Appendices. Pixel to world unit (m s⁻¹, m) calibrations are performed using objects in the image with a known distance e.g., the tube diameter, to determine a scale factor that is later applied to the relevant data. The clarity and readability of the generated kymographs and the data that can be extracted from them are dependent on the frame rate and resolution of the recorded footage, the FOV of the camera, the setup and lighting, and the stability of the recorded flow. Footage showing stable flow produces more coherent kymographs and thus reduced error relative to data from lower viscosity media, even at low framerates. In turbulent flows, such as in water, the larger dispersed bubbles present in the surrounding liquid and the more chaotic flow behaviour generate noisier kymographs and increased precision error. This behaviour is demonstrated in the trends observed in all the measured parameters in water as shown in Sect. 2.4–2.6; the glycerol data demonstrate strong precision between methods and less variation within the same experimental conditions because the overall flow stability is much greater than in water. Measurement precision decreases with increasing kymograph resolution because selection variability increases when pixel coverage is higher, as reflected in the data plots herein.

The precision of pixel selection by the user (“human error”) and the distortion caused by the camera lens are combined to give the root-mean-square error (RMSE). Human error was quantified as the standard deviation of repeat measurements of a single feature in millimetres (converted from pixels) for each generated kymograph i.e., based on experiment condition, camera FOV, and the initial ROI selection (parallel or perpendicular to the direction of bubble ascent). The camera has in-camera automatic distortion correction (as determined by performing checkerboard calibration) with calculated mean reprojection errors of 0.91 and 0.14 pixels, equivalent to 0.013 and 0.79 mm, for the close-up and full-view footage FOVs, respectively. Refraction at the curved boundaries along the tube cross section is found to affect all measurements taken perpendicular to the direction of bubble ascent, i.e., bubble diameter and falling film thickness measurements. A correction can be applied to the data retroactively to account for this (see Appendix D), or it can be corrected for during ROI selection as described in Sect. 2.6. Distortion along the tube length is negligible and primarily driven by the lens distortion in the camera; it is thus accounted for in the calculated error.

Image filtering and thresholding techniques including Gaussian, median, and Fourier-transform filters were applied in an attempt to enhance kymograph accuracy but ultimately failed, as they eroded critical features and reduced measurement precision. Automation attempts were also unsuccessful for similar reasons (see Appendix E). As kymography is further refined, particularly through advances in imaging and AI, its utility for the automated collection of Taylor flow parameters is likely to expand.

The ascent velocity of volcanic Taylor bubbles (along with conduit geometry and magma viscosity) is a key control on flow stability and overpressure, and thus surface explosivity. Bubble coalescence influences eruption periodicity and repose, and is similarly modulated by magma viscosity and conduit conditions, in addition to bubble and liquid velocities. The ability to observe and measure these parameters experimentally is essential for understanding the in-conduit flow processes that drive surface explosivity and activity transitions. On a kymograph, objects moving with constant velocity appear as straight lines, where the slope of the line is directly proportional to the velocity of the moving object. The velocity of Taylor bubbles rising in steady state is determined by drawing an unsegmented line ROI along the edge of the relevant bubble band on the kymograph, then utilising the “Velocity Measurement Tool” (VMT) macro for imageJ (https://github.com/avmann/Velocity_Measurement_Tool_askScale/blob/main/Velocity_Measurement_Tool_askScale_0.3.2.ijm, last access: 25 July 2025) to measure the velocity of the line segment in pixels, and scaling to the appropriate unit (m s⁻¹) using calibrated measurements. Taylor bubbles ascending in non-steady state appear on the kymographs as non-linear bands, such as during coalescence (Fig. 4Ai) or in turbulent flow. The oscillating movement of Taylor bubbles ascending in a turbulent regime appear as irregular bubble bands which expand and contract in the y-direction on the kymograph. The acceleration of the trailing bubble is illustrated on the kymograph as a slight curvature in the corresponding bubble band as it is captured into the leading bubble wake, up to the point of coalescence. This can also be measured using the VMT with a segmented line instead, so that velocity values are calculated for each line segment.

Figure 5 presents Taylor bubble velocity data from 5–30 s of experiment footage where Taylor bubbles ascend in steady state in water or a solution with 0.95 glycerol fraction in continuous flow (GVF = 0.25). Results compare well to a sample of 10 point-to-point measurements from the raw footage i.e., where average velocity is calculated from the time taken for the Taylor bubbles to cover a known distance, and data from existing literature. We refer to the point-to-point measurements as “manual measurements” herein. The kymograph data show good agreement to the manual measurements in all cases, especially where flow conditions are more stable. Data from existing literature for similar experimental conditions under continuous flow are scarce, though there is good agreement with data from (James et al., 2006). There are, however, many publications exploring a broad range of isolated Taylor bubble ascent parameters (see Calleja and Pering, 2023; Morgado et al., 2016, reviews and references therein) to which we compare our results. Manual and kymograph measurements were performed for isolated Taylor bubble injections only for comparison to studies where D=0.036 ± 5 mm and in water. The processed data from the kymographs show good agreement with the studies, within a margin of 0.03 m s⁻¹ or 12 %. We also compare our results to the theoretical prediction of the ascent velocity of volcanic slugs, vsl, assuming isolated Taylor bubble ascent within a stagnant Newtonian fluid in a vertical tube: 1vsl=0.345gD where g is the gravitational constant and D is the internal tube diameter (Viana et al., 2003). Measurements in water show greater variation both within the same dataset and between the different methods because of the natural instabilities and turbulence that occurs in this media. Data form stable ascent conditions i.e., the higher-viscosity glycerol data show very little variation between the kymograph and manual measurements. This highlights the efficacy of kymography in this use case, especially in efficiently processing large bubble samples.

Taylor bubble length influences the volume of gas released at burst, and longer Taylor bubbles are linked to increased overpressure and stronger eruptions at burst (Del Bello et al., 2012; Suckale et al., 2010). Understanding the in-conduit controls on Taylor bubble length during ascent via flow experiments improves our understanding of in-conduit gas-liquid dynamics and eruption behaviour at true scale. On a kymograph, the height of the bubble bands and the liquid bands correspond to the length of the Taylor bubbles and the inter-bubble spaces (or liquid slugs), respectively. Taylor bubble length is calculated by first drawing a vertical line ROI which starts at the band line that corresponds to the bubble nose, and ends on the band line that corresponds to the bubble base (Fig. 4Ai) and extracting its time coordinates, then multiplying the converted y-coordinates in seconds by the known ascent velocity as follows: 2Lb=vbtbase-tnose where tbase and tnose are the time coordinates, in seconds, which correspond to each point of the vertical line ROI. The length of the inter-bubble space is calculated using an almost identical method where the vertical line ROI is instead positioned to cover the liquid band and the following equation is used: 3Lb=vbtnose-tbase where vb now refers to the nose ascent velocity of the bubble rising below the inter-bubble space within the train. Figure 6 shows Taylor bubble length data for a sample of 10 bubbles ascending in steady state in continuous flow (GVF = 0.25) compared to manual measurements in identical conditions. Taylor bubble length varies in all cases due to both the liquid properties and the coalescence rates, as expected for continuous flow. The greatest difference between the manual and kymograph measurements occurs in water because the low-viscosity-driven instabilities in the flow generate lower resolution kymographs and thus increased precision error, as discussed in Sect. 2.3. The manual and kymograph measurements are shown to agree well where flow conditions are stable.

The falling film refers to the thin layer of liquid flowing downwards along the boundary between the Taylor bubble and the tube walls (Llewellin et al., 2012). The thickness of the falling film has implications for bubble stability, shape, velocity, wake behaviour and coalescence dynamics. In a volcanic conduit, the thickness of the falling magma film surrounding Taylor bubbles influences the development of overpressure and thus eruption explosivity (Del Bello et al., 2012). To measure bubble diameter and falling film thickness, the kymograph must be generated from the close-up FOV footage and using a line ROI that is perpendicular to the bubble ascent path. The resulting kymograph provides a stretched view of the target bubbles and the features needed for measurement (Fig. 4B). Differentiation of the bubble boundaries from the regions of shadow or contrast caused by the refraction of light through the tube and the liquid is crucial for accurate measurements. Misidentification of the bubble boundaries leads to underestimating falling film thickness, and overestimating bubble diameter beyond the known internal diameter of the tube. By using the known tube dimensions, it is possible to accurately identify the bubble boundaries. Once these features are correctly identified, bubble diameter and falling film thickness are measured using horizontal line ROIs as shown previously in Fig. 4B, then converting to the appropriate unit. This method of ROI selection negates the need to mathematically correct the data for the effects of refraction at the curved boundaries along the tube cross-section, as evidenced by agreement with experimental and theoretical data from the literature. An alternative approach for measuring bubble diameter and falling film thickness which requires post-processing corrections to account for image distortion by diffraction is available in Appendix D.

There are several empirical correlations in the literature that estimate dimensionless film thickness, λ′, as a function of Re or Nf, that are valid for isolated Taylor bubble ascent under our experimental conditions (de Azevedo et al., 2017; Karapantsios and Karabelast, 1995; Lel et al., 2005; Llewellin et al., 2012). The theoretical λ′ for each correlation was calculated and then used to determine predicted λ: 4λ=λ′r as rearranged from Llewellin et al. (2012). Under the assumption of an axis-symmetric laminar falling film, the predicted film thickness can be used to calculate theoretical bubble diameter for the same experimental conditions: 5Db=D-2λ The plots in Fig. 7 demonstrate good agreement between the kymograph and manual measurements of diameter and falling film thickness, and also between the kymograph measurements with the available theoretical and experimental data for the diameter and falling film thickness of isolated Taylor bubble ascent. Where flow is stable, the single injection predictions agree well with the kymograph data for continuous Taylor flow. This is not always the case for unstable flow, where film thickness is underpredicted by the literature correlations compared to both manual and kymograph single injection measurements.

In gas-rich basaltic systems, the gas volume fraction (GVF) within the conduit plays a fundamental role in modulating the style, periodicity, and intensity of eruptive activity. GVF serves as both a diagnostic parameter for in-conduit flow conditions and a first-order control on explosivity and surface eruption dynamics. The critical GVF required for stable slug formation and ascent defines the onset conditions for Strombolian activity, where the coupling between the Taylor bubble and the overlying magma determines whether sufficient overpressure can accumulate to generate an explosion at the surface. As such, it is vital that we are able to determine the GVF within the experimental system to ensure volcanic scalability (Table 2).

Liquid level fluctuations can be quantified on a kymograph to calculate the GVF within an experimental system, and to determine the full gas injection capability of a pump (Fig. 8). To measure liquid level fluctuations throughout an experiment run, the line ROI used to generate the kymograph must pass through the end of the tube. Once generated, the tube end appears on the kymograph as a vertical line. Numerous measurement ROIs can then be drawn to span the distance between the liquid level line and line representing the top of the tube. GVF is calculated by extracting the time coordinates and line length in pixels, performing appropriate unit conversions, and then inputting the values into the following equations: 6Lg=LL+g-LLL7VL+g=πr2LL+g8Vg=πr2Lg9GVF=VgVL+g where LLL is the length of the liquid level in the tube without bubbles, i.e., before the pump is active, LL+g is the fluctuating liquid level in the tube in meters during gas injection, Lg is the length in the tube in meters that is made up of gas only, VL+g is the volume of liquid and gas in the tube during the gas injection process in meters cubed, Vg is the volume of gas only in meters cubed, and ris the internal radius of the tube in meters. We demonstrate the use of this method to determine the injection capability of a Delaman^® 12 V DC miniature diaphragm pump for a range of liquid viscosities in Fig. 8A, then show how these data be can used to develop a model that predicts GVF within an experimental system where pump voltage and liquid viscosity are known Fig. 8B. Gas volume fraction is shown to increase with increasing pump input voltage as expected. The model predicts GVF peaks with an R2 of 0.863 and a root mean square error of 1.5 %; individual predictions have uncertainty of approximately ±3.1 % at the 95 % confidence level. Full details are available in Appendix F.