Introduction

Volcanic fissures occur in many types of volcanic settings. In monogenetic volcanic fields, eruptions from long dykes form linear arrays of cones and craters, but isolated cones also result when just a single vent persists (e.g., Hopi Buttes, USA (Muirhead et al. 2016) and Auckland, New Zealand (Houghton et al. 1999)). Fissure systems feed flank eruptions at polygenetic volcanoes, such as Mt. Etna (Geshi and Neri 2014), and they are a principal component of volcanic systems in Iceland (Thordarson and Larsen 2007). Fissure eruptions begin with magma extruding from cracks that can be hundreds of metres to many kilometres long. Within days or weeks, the fissure may evolve by extending laterally, by opening new branches, and/or by localisation of flow so that eruptions become focused to one or a few discrete sites. Spectacular fissure eruptions that have localised from a “curtain of fire” to distinct vents have been observed in Hawaii (Fig. 1a; Richter et al. 1970; Orr et al. 2015; Witt and Walter 2017), Iceland (Fig. 1b; Thorarinsson et al. 1973; Hoskuldsson et al. 2011; Thordarson et al. 2015; Pedersen et al. 2017; Witt et al. 2018), and Réunion Island (Fukushima et al. 2010).

Fig. 1
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Historic fissure eruptions with fountaining from long, linear vent systems (photos accessed via the Smithsonian Global Volcanism Program Image Gallery). a East Rift Zone, Hawaii, 16 November 1979. Photo by Bob Decker, 1979 (US Geological Survey), a Public Domain Work. Fountains are 1-5 m high; b Krafla volcano, Iceland, 6 September 1984. Photo by Michael Ryan, 1984 (US Geological Survey), available under the Creative Commons BY-NC-ND 4.0. Fountains in this eruption reached heights of 20-50 m (Davies 1996). https://volcano.si.edu/gallery/ShowImage.cfm?photo=GVP-06057. c Schematic diagram of a fissure system showing the natural cases for changes to fissure shape, width, and wall-rock temperature to be modelled with our new apparatus. Directional arrows indicate the geometric dimensions and notation we use in our model

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Dyke or fissure opening and initial geometry are principally controlled by the lithostatic pressure, regional stress field, pressure in the crack tip ahead of ascending magma, and mechanical properties of the host rock, including elasticity, yield strength, and consolidation (Buck et al. 2006; Gudmundsson 2006; Keating et al. 2008; Wadge and Burt 2011; Daniels et al. 2012). Once a crack is open, numerous factors can control the localisation process to form a conduit. Here, we investigate the influence of dynamic fissure geometry and host rock temperature on localisation (Fig. 1c). Volcanic fissures do not have simple, planar slot geometries; they narrow and widen, flare, step, and branch (Delaney and Pollard 1982; Gudmundsson 1983; Keating et al. 2008; Parcheta et al. 2015). Moreover, the width and shape may also change during an eruption if a fissure propagates through rocks with different mechanical properties, parts of the host rock melt, or if brecciation and collapse of weak wall-rock locally widens some parts of the fissure while blocking adjacent areas (Delaney and Pollard 1981; Bruce and Huppert 1989, 1990; Geshi and Neri 2014). Thermal variations occur along a dyke or fissure if it propagates into a geothermal area, a new dyke intrudes warm crust that has been subject to recent dyking, or if a dyke intersects an aquifer or wet substrate (Kristjansson 1985; Delaney 1986; Bruce and Huppert 1990; Pansino et al. 2019). Interaction with water can chill magma more quickly or, if magma dynamically interacts with water, cause explosions that excavate surrounding rock and widen the fissure locally (Buchan et al. 1980; Delaney 1986; Valentine and Groves 1996; Ort and Carrasco-Núñez 2009).

Understanding how fissure eruptions evolve and where they may localise to form persistent vents is highly desirable for hazard mitigation. Recent fissure eruptions have produced lava fields of variable volume and extent, in some cases threatening local infrastructure (Pedersen et al. 2017, 2022; Neal et al. 2019; Global Volcanism Program 2021). Focusing of fissures to form a narrower conduit may cause a transition to more violent eruption styles (Genareau et al. 2010), while interaction with water can lead to additional hazards (Németh and Kósik 2020). Surface observations of fissure eruptions, study of eroded plumbing systems, and volcanic deposits do not sufficiently reveal all processes influencing the dyke-conduit transition due to lack of erosion, exposure, or preservation (Keating et al. 2008). Only with experiments can we observe processes of localisation beneath the surface. We built a lab-scale model volcanic fissure, “Artfish”, that can change fissure shape and width, temperature across the fissure wall, and magma flux. Critically, these parameters can be adjusted during an experimental “eruption” to allow investigation of how sensitive the system is to feedback processes occurring when the variables are changed through time. Our aim is to investigate how fissure shape and wall temperature control conduit initiation and development once a fissure eruption is underway. We use polyethylene glycol (PEG) 600, a waxy fluid and herein referred to as wax, as an analogue magma. In this paper, we detail the design and development of the model, the equipment used to monitor experiments, and the results of preliminary tests focused on the functionality of the device. Artfish is housed at the University of Otago, New Zealand, and is intended for use as a facility within an experimental program running for several years.

Previous modelling

Analytical, numerical, and small-scale analogue models have shown that localisation during a fissure eruption is related to the feeder dyke geometry and width, length (depth), magmatic flux, host rock temperature, and magma viscosity, and that these parameters are closely associated (Delaney and Pollard 1982; Bruce and Huppert 1989, 1990; Wylie et al. 1999). Delaney and Pollard (1981) and Bruce and Huppert (1989) showed that an increase in the magma’s volumetric flow rate through wide sections of a dyke causes greater advective heat transfer and maintains or further widens the magmatic pathways. Narrow parts of a dyke become blocked more rapidly due to a reduced volumetric flow rate, cooling, and solidification of magma (Delaney and Pollard 1982; Bruce and Huppert 1989). A positive feedback mechanism is established whereby still molten magma is forced into wider segments, which may become conduits for cone-forming eruptions (Bruce and Huppert 1989, 1990). Bruce and Huppert (1989), focusing on thermal effects, suggest that there is a critical dyke width, dependent on the thermal regime of the wall-rock, that determines whether the dyke will remain open or become blocked, and the time it takes to become blocked.

Bruce and Huppert (1990) predicted that magma flow within dykes might persist when intruded into warm host rock, e.g., where recent intrusions or eruptions have occurred. A steady supply of magma through a dyke will also allow it to remain open, while intermittent supply allows time for solidification and closure of narrower dykes when magma flow rate decreases or ceases, especially in cold crust (Taisne and Tait 2011; Chanceaux and Menand 2014, 2016; Pansino et al. 2019). In contrast, Wylie et al. (1999) argued that lateral variations in viscosity leading to localisation by “viscous fingering” is more important than solidification. Since viscosity of magma (and wax) is a function of fluid temperature and heat loss to the surroundings, however, we argue that it is itself controlled by the thermal processes under investigation here; solidification is simply the end member of increased viscosity.

These models provide simple and clear arguments for the behaviour of magma in a dyke and the conditions that lead to localisation, but they are limited. Experiments are required to further investigate the intensity of thermal feedbacks associated with localisation resulting from dyke geometry and wall-rock temperature, and the sensitivity of flow to these feedbacks as they evolve through time.

Larger scale analogue models of a similar size to Artfish have been developed to investigate magma ascent through a fissure, but with a focus on the effect of bubbles within the fluid (Pioli et al. 2017; Capponi et al. 2020). Pioli et al. (2017) conducted experiments to show the importance of conduit geometry by comparing flow dynamics within a slot versus flow within pipes. Capponi et al. (2020) constructed an experimental fissure with the ability to incline the active slot, allowing investigation of the effect of non-vertical ascent of a bubbly magma. Neither of these existing experimental fissures are set up to investigate the thermal evolution of a dyke, nor the influence of wall temperature and fissure shape on localisation within the slot geometry. Analogue experiments by Jones and Llewellin (2021) showed that localisation may develop in a slot geometry during exchange flow of a cooling viscous fluid and/or within a narrow conduit. They did not, however, investigate the feedbacks associated with fissure temperature and width directly and their experiments are focused on the specific case of convecting fluids in a dyke.

Apparatus design, materials, and scaling

Model fissure design

The main goals for Artfish were that with one wall, we could:

  • Change slot width

  • Change slot shape

  • Vary the wall temperature

  • Disassemble and replace or substitute parts.

The active slot of the fissure viewed from the front is 2 m wide and 1.4 m tall. The front of the slot is a 19 mm-thick sheet of glass for viewing the experiments, and the back wall is segmented into 70 panels made of aluminium (Figs. 2 and 3). The panels are 0.2 m × 0.2 m and arranged in a grid with 10 panels horizontally and 7 vertically (Figs. 2, 3, and 4). Side-supports of box steel and a spring-loaded pushing system hold all panels tightly against one another so that there are no leaks of wax through gaps between them (Fig. 2). The two walls are held together by a surrounding box steel frame lined with rubber gasket. Threaded rods run through the frame and are tightened when the device is set up for experiments, pushing the walls tightly together; they can be loosened, and the containment reduced if the panels need to be adjusted. The glass, however, is fixed to the framing because it is too heavy to be removed. Thick glass is required to reduce deflection in the large sheet from the high-pressure head in the wax. Deflection is reduced further by steel rods with rubber pads, which press against the front of the glass. The rods are supported by two lengths of 5 cm-high steel U-channels (Fig. 2 and 3). These two front frames reduce the visibility of the experiment slightly, but they were placed so that they run along the middle of the panels where there is expected to be minimal variation in the solidification behaviour and flow of wax. The fissure has a 2.2 m × 1.5 m basal frame of box steel. Eyelet loops are fixed to the top of the frame, allowing the device to be secured to the lab wall by rope to stabilise it. The whole device is 1.96 m tall and weighs ~ 950 kg. At the widest slot width, the fissure holds 32 kg of wax. The machine is positioned on 4 wooden railway sleepers to distribute its weight across the floor. A wheel is fixed to each corner to allow the device to be moved.

Fig. 2
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Modified from a technical drawing by Farra Engineering Ltd

Principal parts of the model fissure, viewed from the back.

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Fig. 3
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a Drawing and b photo of the front of the assembled model fissure. Dimensions in b are the same as in a. c Fluid recycling system: gutter is fixed to the front of the slot and collects excess molten wax that rises out of the fissure. The wax drains back into the reservoir via the downpipe to be pumped back into the system. d Roto Little-Champ DC Pump with variable speed drives (VSDs) to draw wax from the reservoir and inject into the base of the slot at a controlled rate. Pump is ~ 50 cm long

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Fig. 4
figure 4

a Front view of a panel after powder coating. Temperature sensor not inserted. b Back view of a panel. Three rods are inserted into the back of each plate by a ball joint which allows them to be rotated. The other ends of the rods are threaded for movement back and forwards (see text). Temperature sensor shown here. The wires for every sensor are connected to data loggers. c View of the heat exchanger inside every panel, used to control the panel temperature. d The back view of a row of panels showing how they can be connected to form sections of wall of the same temperature. The brass elbow fittings are the inflow and outflow points for the internal heat exchanger shown in c. The rods are also shown threaded into the box steel bars that support them. The three rods can be rotated simultaneously, keeping the panel square when pushed in or retracted

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Adjustable fissure shape, width, and wall temperature

The segmented wall of water-circulating aluminium panels is the key, novel feature of Artfish that allows for variability in wall temperature and fissure width and shape. Each panel comprises two plates bolted and sealed together with a strong silicone sealant. The front plates are 7 mm-thick aluminium sheets, and the back plates are cast aluminium. A heat exchanger in the form of a 6 mm channel snakes through the interior of each panel, made by cutting 3 mm-diameter U-shaped channels into each plate before sealing them together (Fig. 4). In order to control the temperature of the aluminium panels, water is passed through the heat exchanger. A minimum temperature of 5 °C can be achieved after ice water is flushed through the system for 40–50 min. Higher temperatures depend on the temperature of the water used. Flexible plastic tubing connects neighbouring panels from outlet to inlet points, so that the temperature of large sections of the device can be controlled from one water source. When multiple wall temperatures are desired at the same time, selected panels can be plumbed together as separate groups with water fed from a different tank. This plumbing can be adjusted for each experiment depending on the desired temperature variation across the wall.

The panels can be individually moved towards the glass front of the slot, or retracted, to vary the working width of the fissure from 0 (closed) to 15 mm. The working distance is normally 10 mm or less. Each panel is 14 mm thick, with a 35 mm-thick border flange to allow for more stable movement and less leakage of wax when the plates are offset from each other (Fig. 4). Tests have shown that when cooled, the aluminium is very effective at cooling the wax to solidification so that any wax that seeps between panels forms a self-seal before it can leak out. Three aluminium rods are attached at the back of each panel and are supported by steel bars that are fixed horizontally to the framing at the back of the device. The rods are attached to the backs of the panels by ball joints, while the opposite ends are screwed into the supporting bars (Fig. 4). This allows the panels to be moved forwards and back by screwing the rods. Three rods were chosen for stability and to ensure the panels were kept square when moved. A turning mechanism with a chain-wheel allows all three rods to be rotated by the same amount at the same time.

Analogue fluid

We chose wax for the analogue magma because it has a temperature-dependent viscosity and forms a solid crust as it cools; it has commonly been used for experiments to investigate the parameters associated with emplacement, flow dynamics, and morphologies of lava flows and domes (Fink and Griffiths 1990, 1998; Gregg and Fink 1995; Griffiths et al. 2003; Anderson et al. 2005; Cashman et al. 2006; Rader et al. 2017; Rumpf et al. 2018; Peters et al. 2022). The main physical properties of the wax pertinent to these experiments are presented in Table 1. PEG 600 solidifies at ~ 18 °C (Fig. 5), which makes it easier to melt and control its temperature in the laboratory than other grades of PEG with higher melting points. Even so, to maintain a large enough supply of molten wax for the experiments, the laboratory was fitted with additional heaters and window insulation to keep the temperature between 21 and 25 °C at model height all year round (Fig. 6). This warm experimental environment also ensures that the apparatus is warm and limits any heat loss from the wax before it enters the active slot.

Table 1 Values for the variables and dimensionless numbers of the experimental fissure, compared with natural values. The dimensionless numbers for nature are calculated from the variables given here but are also consistent with those given in the cited literature. Experimental values marked with * were determined to optimise the scaling, † were measured, ‡ are from manufacturer’s information
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Fig. 5
figure 5

Plot of measured wax viscosity as a function of temperature. The room temperature is shown; to get lower temperatures the wax had to be actively cooled. During forced cooling, the wax viscosity rose sharply with each ice water injection before stabilising; hence, the data is less smooth than the cooling curve at higher temperatures. Line colours correspond to different barrels; two viscosity measurement curves are shown for each barrel since the wax was heated and cooled between measurements

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Fig. 6
figure 6

Thermal profile of the lab during an experimental cycle. Nine calibrated DS18B20 1-wire thermal sensors are positioned at regular intervals from the floor to the ceiling. The height of each sensor above the floor is annotated against the sensor’s temperature curve. The blue box bounds the sensors that are within the height of the model fissure. During an experiment, the temperature of the room increases slightly, probably due to the number of assisting experimentalists. The sensors that are within the height of the lab door record a sharp decrease in room temperature at the end of an experiment. The lab door is kept open during clean-up after an experiment to keep personnel cool

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We measured the wax viscosity with a calibrated RV-2 T rotational viscometer. During measurement, the wax was placed in a water bath initially at ~ 40 °C. The water bath and wax were left to cool over several hours until they reached room temperature, after which cooling by 1 °C increments was forced by injecting ice water into the water bath and allowing the wax to equilibrate before measuring a stable viscosity. We define the exact solidification point for our batches of wax as the temperature at which the viscosity increases exponentially (Fig. 5). Samples from each of four 200-l barrels were measured twice to ensure consistency of the batch and that there was no change in viscosity after heating and cooling. Our measured viscosity values are consistent with previous studies (e.g., Griffiths et al. 2003). Viscosity measurements are to be conducted as a standard step in the experimental procedure to both determine the precise solidification temperature of each batch of wax, and to monitor any possible changes in a recycled batch over time and repeated heating and cooling.

Scaling

An experiment must be properly scaled for the results to be applied to natural systems (Galland et al. 2015; Merle 2015), but there are limitations to what can be practically achieved in the lab. It is usually impossible to replicate a natural system entirely, but analogue experiments are a powerful tool for understanding the fundamental trends or physical controls of one or a few particular aspects of a system (Kavanagh et al. 2018). We have identified four dimensionless parameters that describe the thermal evolution and flow focusing within a dyke, and which incorporate our key variables, wall-rock temperature and dyke width. These are: the aspect ratio, dimensionless temperature (Θ), Péclet number (Pe), and Reynolds number (Re) (e.g., Delaney and Pollard 1982; Griffiths et al. 2003; Taisne and Tait 2011; Capponi et al. 2020). The dimensionless parameters given here are calculated based on experimental aims and will be refined for each experimental series. It should be noted that Artfish models a dyke half-width because only the aluminium wall is active in terms of adjusting the temperature and shape. The glass wall is fixed and is only for observing the experiments. A schematic diagram showing the experimental case compared to the natural is shown in Fig. 7.

Fig. 7
figure 7

Schematic diagram to show the relationship between a natural dyke and the experimental fissure with an aluminium wall after establishment of a thermal boundary layer of solidified wax has formed. The temperature curve shows schematically the change in temperature across the solidified magma/wax boundary in two endmember conduction regimes (solid and dashed lines correspond to arrows showing conduction in the experimental and natural cases). The experiment models a dyke half-width

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The aspect ratio is an important dimensionless parameter to use for ensuring geometric similarity, in particular similar boundary effects between the model fissure and natural fissures (Capponi et al. 2020). Like Capponi et al. (2020), however, we find that an analogue fissure with the same aspect ratio as a natural fissure is impractical, being either far too wide for a laboratory space or with a slot width of less than 1 mm that would make it impossible to meaningfully vary fissure shape. Following Capponi et al. (2020), we have designed the largest possible slot suitable for ease of use, while maintaining a geometry that ensures the effects from the end walls are small. The range of aspect ratios of our model is larger than the natural range, but the model can be considered as a segment of dyke, rather than a full-length dyke, and the results may be extrapolated laterally when scaling up to the natural case. In the literature, “dyke length” is variably referred to as the horizontal dimension parallel to the strike or the vertical dimension (e.g., Wylie et al. 1999; Taisne and Tait 2011; Capponi et al. 2020), and there is inconsistency over which aspect ratio is used. Similarly, in referring to an analogue model of a dyke, there is room for confusion in whether the term “width” means the lateral extent of the model/dyke, or the size of the opening (e.g., Delaney and Pollard 1982). Here, we term the vertical dimension, depth (z), the horizontal dimension that is parallel to the strike, length (l), and the dyke opening, width (w) as shown in Fig. 1c. Our aspect ratio (A) of interest is the ratio between width and length:

$$A=\frac{2w}{l}$$
(1)

The range of aspect ratios given in Table 1 are for short, wide dykes to long, narrow dykes. The depth of the model is appropriate since field evidence suggests that the transition from intrusion to eruptive conduit occurs in the shallow subsurface at 100–350-m depth (Keating et al. 2008; Muirhead et al. 2016).

The dimensionless temperature Θ is a ratio of the temperature contrasts between the solidification temperature of magma Ts, magma temperature at source Tm, and wall temperature Tw (Delaney and Pollard 1982; Fink and Griffiths 1990; Griffiths et al. 2003):

$$\theta =\frac{{T}_{s}- {T}_{w}}{{T}_{m}- {T}_{w}}$$
(2)

The natural wall temperatures we model here range from ambient crustal temperatures to crustal temperatures surrounding previously intruded dykes (Delaney and Pollard 1982; Bruce and Huppert 1989). The range of Θ given in Table 1 are for fluids injected into cold host rock versus warm host rock. If Θ is close to 1, the magma temperature is close to its solidification temperature, and only a low degree of cooling causes a change in rheology (Griffiths 2000). We use this ratio to calculate the range in wall temperatures and initial wax temperatures that will scale the experiments appropriately (Table 1).

When modelling the thermal evolution of dykes and fissures, a parameter is needed that describes the ratio of advective to conductive heat flux. Heat is introduced to the system by advection as new magma enters from the source and ascends the dyke, while conduction removes heat laterally into the host rock via the dyke walls. Aluminium has a conductivity that is two orders of magnitude higher than for rocks and so by controlling its temperature, the rate of heat transfer from wax to the wall can be very effectively controlled. The large contrast in conductivity with the natural case causes very high initial heat loss when the wall temperature is well below the melting point of wax. The rapid solidification of a thin layer of wax, however, establishes a thermal boundary layer that effectively controls the heat loss (Fig. 7). The relevance of this for shallow intrusions is discussed in the section on the test experiments (see below). Since the heat exchanger within the aluminium panels acts as a very efficient cooling system and the temperature at the back of the wall is maintained throughout an experiment (see fissure thermal profiles below), we can treat the wall as a constant thermal boundary. We follow previous models, which simplify the ratio of advection and conduction of heat down to a dimensionless flux parameter (Delaney and Pollard 1982; Taisne and Tait 2011; Chanceaux and Menand 2014) or a form of the Péclet number (Griffiths 2000; Galland et al. 2006) using only the heat transfer parameters within the slot:

$$Pe= \frac{v\rho {C}_{p}w}{k}$$
(3)

where v is the fluid ascent velocity, ρ is the magma density, Cp is the specific heat capacity, and k is the thermal conductivity of the fluid. The range of Pe given in Table 1 are for a slowly ascending fluid in a narrow dyke to a fast-moving fluid through a wide dyke. The range of Pe for the experiments is 1–2 orders of magnitude below that of the natural range, but they are well into the advection-dominated regime, meaning that physical equivalence is achieved (Galland et al. 2015).

Our final dimensionless parameter is the Reynolds number Re:

$$Re=\frac{v\rho w}{\mu }$$
(4)

where μ is the fluid viscosity (Pa∙s). The range of Re given in Table 1 are for slow moving fluid in a narrow dyke to fast moving fluid in a wide dyke. The Re must be low such that the flow within the fissure is laminar. At the ascent velocities, fissure widths and fluid viscosity used in these experiments, this model is well within the laminar regime and within the limits for natural dykes (Delaney and Pollard 1982; Kavanagh et al. 2006; Capponi et al. 2020).

Prototype testing and cross-fissure thermal profile

Before building the full size Artfish, we first made a smaller prototype with four panels to test the materials and function of the device, as well as various monitoring equipment. One key aim was to determine the magnitude of heat loss through the back wall of panels, and also the degree to which the glass front cools before an experiment at different slot widths. A too-cold glass pane is undesirable since it could cause solidification against the glass that would block observations of wax flow in the slot, and because it could cause significant unmeasured heat loss from the wax to the glass pane. We carried out tests by placing thermal sensors at the back and front of every panel, and the back and front of the glass at the same height so that a horizontal thermal profile could be drawn in each quadrant of the prototype. This was only possible in the smaller prototype, and not in the full-scale model. Measurements were taken while the prototype was sitting at ambient temperatures in the lab, during the cooling of the back panels, wax entry, and with continued flux of wax through the slot as the wax also cooled and solidified against the actively cooled panels. In the first test, the slot width was varied with one half of the slot at 4 mm and the other at 10 mm. A second test was conducted with the slot uniformly 8 mm wide. Thermal profiles across the fissure were drawn at different stages in the test to show how the panels and glass respond to cooling and wax injection (Fig. 8). Since the 4- and 10 mm slots were in two sides of the same experiment (two panels each), there are two profiles for these slot widths, and four for the 8 mm slot.

Fig. 8
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Thermal profiles across the prototype fissure at different slot widths and times during an experiment. a Empty fissure at ambient laboratory temperatures. b After the wall has been brought to the desired temperature, but before wax entry. c 50 seconds after wax entry. d 3.5 minutes after wax entry. e 7 minutes after wax entry. f 10 minutes after wax entry. The start of the profiles (0 mm) show the temperature of the backs of the panels. The vertical dotted lines show the position of the glass at different distances from the wall-slot interface (i.e., the front of the panels). The solidification point of the wax (~ 18 °C) is shown by the horizontal orange dashed line

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Figure 8 shows that once the panels had cooled, the back remained at a constant temperature for the duration of the test due to the continuous flux of ice water through the cooling system. This supports our treatment of the heat exchanger as a constant thermal boundary. One of four sensors at the back of the 8 mm slot recorded a consistent temperature of 10 °C, while all others at all fissure widths were ~ 5 °C. The 10 °C sensor may not have been fixed securely to the panel, such that it was partially measuring the air temperature at the back of the fissure. The profile for the 8 mm slot also shows a warmer fissure at the start and during the first few minutes of wax flow than the others. This is probably because it was the second test of the day; after each test, hot water is passed through the heat exchanger to melt the solid wax and empty the fissure, and so it started out warmer.

For all slot widths, the back of the glass cooled significantly as the panels were cooled down and before any wax entered the slot; the 4 mm-wide fissure had the coolest glass temperature at this point. The front of the glass had also cooled, but to a lesser degree (Fig. 8b). Once wax entered the slot, the glass warmed in contact with the warm wax, as did the front of all panels. During the test, the front of the panels cooled as the wax cooled and solidified, and a steady state was reached between the front and back of the panels. Although the glass did cool before the test due to its proximity to the cooling system in the back wall, the continued flux of wax warms the glass above the solidification temperature of the wax and remains warm while the back wall remains cool. There should, therefore, be no major heat loss through the glass while an experiment is underway.

Design limitations

Artfish was designed to investigate the thermal controls and feedbacks on flow localisation in a dyke or fissure. It is an advanced model in that the shape and wall temperature can be changed, but it does not replicate all features of a dyke or all processes that occur during magma ascent. The model simulates a crack that is already open with an eruption underway; it does not reproduce crack opening and hence does not address effects of rock yield strength or fracture toughness. It also does not model the effects of a pressure gradient through the depth of the dyke. Initial experiments will focus on the changes in viscosity and solidification of a single-phase fluid, but bubbles and solid particles representing crystals may be added later. The influence of the wall-rock properties on thermal focusing are investigated in isolation from these other variables. There is, however, room for adaptations to the design as the apparatus can be dismantled for features to be added or replaced, except for the front pane of glass.

Experimental procedure and methods for data collection

Prior to an experiment, the aluminium panels in the active wall are individually moved into position to achieve the required fissure width and shape. The heat exchangers in each panel are plumbed together in groups, with each group circulating water close to the desired wall temperature for that sector of the fissure. The circulation system is left for about 1 h to allow the panels to come to temperature. A 200 l barrel of wax is melted using heat mats beneath and surrounding the barrel. The liquid wax is stirred to ensure even heat distribution and to prevent re-solidification before being pumped from the barrel with a progressive cavity pump (Roto Little Champ DC-41, Fig. 3). Variable speed drives (VSDs) in the pump enable flow rates to range from 0.2 to 0.6 l/s. The wax enters the slot at the base via a manifold consisting of five branches of PVC pipe. The five injection pipes are equally spaced and feed a channel along the base of the fissure, from which the wax rises into the slot (Fig. 2). The multiple injection points ensure even pressure distribution in the incoming wax and even flow from the beginning of the experiment. As molten wax exits the top of the slot, it is collected in a gutter that runs through a downpipe into the reservoir, from whence it is cycled back into continued flow through the slot for the desired duration of the experiment. Each experiment is monitored by video and with thermal sensors. The videos supplement real-time visual observations and are used for particle image velocimetry (PIV).

Visual observations

A Sony Cyber-shot DSC-RX10 IV digital camera is positioned 2 m from Artfish to fit the active slot in the image frame and record videos of each experiment. The aluminium panels are powder-coated in matte black to remove their shine and reduce reflection in the videos. Only the front surface is coated so that the panels are still able to slide past each other with minimal friction. Dark blinds were also installed in the lab, and a black polyester sheet backdrop is set up behind the camera to reduce reflection in the glass. Additional cameras were used for close-up videos to record details in selected areas of the fissure. Lights can be mounted when and wherever needed for better illumination.

Particle image velocimetry (PIV)

Particle image velocimetry (PIV) is a computer-assisted, image-based, pattern-matching technique, which visualises and quantifies the velocity fields of flows by comparing subsequent video frames. PIV is widely applied in volcanology to measure velocities and visualise patterns within flows of different sorts (e.g., Andrews et al. 2014, 2016; Dürig et al. 2015; Witt and Walter 2017; Kavanagh et al. 2018). We chose poppy seeds for tracer particles to image the flow patterns in the wax and determine flow velocity in the fissure. The grey seeds contrast well with both the transparent-white wax in various stages of solidification and the black powder-coated panels. The seeds are ~ 1 mm in size and have a density of 1060 kg/m3 (Mesbah Oskui et al. 2017), making them suitable passive tracers. The density of the seeds is slightly below that of the wax, but tests show that on the timescale of the experiment, the seeds remain in stable suspension rather than floating to the top of the reservoir. We used a ratio of 100 ml of seeds to 60 l of wax. The close-up videos were used for the PIV analysis as the poppy seeds are more easily discernible in these than in videos of the full fissure. Areas for the close-up videos were selected for their potential in showing interesting flow patterns, predicted locations for localisation, and/or areas where the flow rates were to be quantified. The interrogation window size is the camera’s field of view: ~ 55 × 35 cm. Since experiments are long-lasting and the full video files are large, shorter 10-s clips equating to ~ 300 frames are used for PIV analysis based on observations of interest during the experiments, or for calculating the flow rates at particular fissure widths and pump speeds. The PIV analysis was carried out on PIVlab, a toolbox for MATLAB (Thielicke 2014; Thielicke and Stamhuis 2014; Thielicke and Sonntag 2021).

Temperature

The temperature at the wax-wall interface is measured across the fissure by 70 thermal sensors (DS18B20 1-wire type), which are calibrated against a platinum thermal sensor. The sensors have an error of ± 0.3 °C and read data every 1.5 s. Each sensor is sealed into a hole in the middle of a panel, so it sits flush with the panel’s front face, allowing the panel to be closed against the glass. A cone was cut into the panel front, around the sensor, allowing as much wax to contact the sensor as possible and limit interference from the panel. The sensors are also isolated from the panel by a collar of plastic tubing. Additional thermal sensors are placed in the inflowing and outflowing wax.

Preliminary tests

We conducted two initial tests on the functionality of the device and the use of the monitoring equipment. These tests did not simulate a particular natural scenario but show the range of capabilities of Artfish. Around 120 l of wax was used in each test. Videos, a timeline of events during each test, and the thermal data from each plate and the wax on entry and exit are provided in the “Supplementary information”.

Test A: varying fissure shape and width

The aims of this test were to vary the width across the slot, to include an “obstacle” created by some panels closed against the glass front, and to move some panels mid experiment. The experimental configuration is shown in Fig. 9 T1. Each panel is labelled based on its position in the grid. Rows are labelled 0–6, and columns are labelled A–J. Rows 0 and 6 were 4 mm from the glass, column A was 2 mm from the glass, and column J was 1 mm from the glass. Five panels (C3, D2, D3 and D4, and E3) arranged in a “cross” shape and a single panel (G4), were closed against the glass. The rest of the fissure was 10 mm wide. Six minutes into the test, panel B4 was moved forward to close against the glass after a layer of wax had already solidified against this panel. The pump speed was also reduced in steps during this test from 800 to 400 RPM at ~ 9:30 min, and then to 200 RPM ~ 12 min into the experiment. The pump was turned off 14 min into the experiment for 6 min to simulate pulsating flow (“Supplementary information”).

Fig. 9
figure 9

T1 Schematic of the fissure shape set up for test A. The black tiles are column and row labels for the panels. In the rest of the grid, numerical values are the width of the fissure at each panel in mm. Panel B4 was closed during the test. T2–6 Frames taken from the video showing the response of the wax to changes made during the test. The wax turns from colourless to white as it solidifies, and so the progression of solidification can clearly be seen across the fissure. Yellow arrows trace flow patterns. White and black arrows show areas affected by shadow and a spotlight, respectively, rather than changes in the wax

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Results of test A

Figure 9 shows frames from the video at key times during the test, and the progress of the flow and solidification of wax at these points. The change in transparency of the wax as it solidified clearly shows where cooling, solidification, and closure occurred. At T2, the wax had reached the top of the slot and had begun to cool and solidify against the panels. The gradual cooling of the wax resulted in streaky flow lines, which show well the flow pattern of the wax. Most of the flow was clearly diverted around obstacles and channelled into open pathways in the slot. Some wax was seen to flow across and solidify against the panels that were meant to be closed against the glass.

By T3, 10 min after the start of the test, the wax solidified against columns A and J had built out to the glass and blocked the fissure at these points, which were initially the narrowest parts. Almost no solidification had occurred against the panels on row 0 at this time, but white wax was seen in the flow lines here, and wax was solidifying against the panels in row 1. Panel B4, which already had a layer of solid wax frozen against it, had been moved forward by T3 and wax flow was seen to divert around the new obstacle (Fig. 10). Flow velocities were ~ 0.01–0.04 m s−1, but locally increase to 0.05–0.06 m s−1.

Fig. 10
figure 10

a Frame from close-up video focused on panel B4 during test A. The panel has been closed against the glass. Tracer particles (poppy seeds) can clearly be seen as dark specks against the white wax. Arrows indicate flow direction of seeds and wax. Panels are 200 x 200 mm. b Mean particle image velocimetry determinations from 300 frames at the same view as a showing the flow velocity and pattern of the wax and seeds around the closed parts of the fissure

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While the pump was switched off (Fig. 9 T4–T5), solidification advanced in all areas that remained open in the fissure, including row 0. Since wax in the fissure was stagnant, advective heat transfer shut down, but cooling of the wax by conduction continued. When the pump restarted, flow resumed in the wider parts of the fissure, which had not yet become blocked during the period of stagnation. Flow persisted here until the pump was switched off at the end of the test, 26 min from the start (Fig. 9 T6).

The data from the thermal sensors placed in the panels at the wax-wall interface are shown in maps of the fissure wall (Fig. 11) at the same time slices as those in Fig. 9. Figure 11 shows the thermal evolution across the wall, relative to the pre-experiment state (T1). At T2, the wall was warm in response to the entry of wax. It was warmest at row 0, consistent with the lack of solidification shown in Fig. 9, and cooler at row 6. From T3 to T6, the wax-wall interface generally cooled down across the whole fissure length, and row 0 reached a temperature more consistent with the rest of the fissure after the pump was switched off. At T2, panels C3, D2, D3 and D4, E3, and G4, which started closed against the glass, were slightly cooler than the wider parts of the fissure.

Fig. 11
figure 11

T1 Measured temperature (°C) at the plate-fissure interface after cooling and before wax input. T2–6 Temperature difference maps of the wax-wall interface at the same points in time as shown in Fig. 9. Each map shows the change in temperature recorded by the thermal sensors placed in each panel relative to the temperature recorded before the wax entered the slot (T1). Note changes in colour bar scale between T1 and others. White and black numbering is used only for clarity against the square colour

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Test B: varying wall temperature and shape

The aim of this test was to see if localised variation in the temperature of the active wall could be achieved. Two columns of panels were left uncooled (H and I), while all other panels were cooled with ice water. Some shape variation was also tested; lateral widening was simulated with columns A to D increasing from 2 to 8 mm from the glass in the initial set up. A central column of panels (E), and the rightmost column (J) were closed against the glass. Columns F to I were initially set 4 mm from the glass. Panels F1-6, G5 and G6, H5 and H6, and I3-6 were pushed to close against the glass partway through the test, while panels B5 and B6 were pulled out to 8 mm (Fig. 12 T1; “Supplementary information”). The pump was operating at its lowest recommended speed of 200 RPM for the entire test.

Fig. 12
figure 12

T1 Schematic of the fissure shape set up for test B. The black tiles are column and row labels for the panels. In the rest of the grid, numerical values are the width of the fissure at each panel in mm. Panels that are moved during the test are shown with their initial and final position from the glass separated by > . Blue panels are cooled, while yellow panels have not been cooled. T2–8 Frames taken from the video showing changes in the solidification and flow of the wax over time and, in the case of T7, in response to panels being moved. The wax turns from colourless to white as it solidifies, and so the progression of solidification can clearly be seen across the fissure. Yellow arrows trace flow patterns. White and black arrows show areas affected by shadow and a spotlight, respectively, rather than changes in the wax

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Results of test B

It took 2 min 40 s for the wax to fill the fissure after the start of the test corresponding to an overall initial ascent rate of 0.01 ms−1. Figure 12 shows that at T2, 1 min after wax entry, the wax had risen just two-thirds of the way up the fissure. Some wax had squeezed between the closed panels of column J and the glass, and some wax also penetrated between the glass and the closed panels of column E. This occurred from the sides as the wax was rising. T3 shows that wax continued to pass between the glass and these panels, but it solidified quickly in the narrow gap, sealing the fissure at these columns. At column J, the wax never managed to penetrate fully across the upper panels.

All time slices of Fig. 12 show that the warm panels (columns H and I) maintained a conduit of molten wax throughout the test; wax did not effectively solidify against the warm wall. This shows that temperature variation can be created and maintained during an experiment and that warm panels were not being substantially cooled by their contact with surrounding cold panels. Wax and poppy seeds were seen to flow straight up this part of the fissure.

Time slices T3 to T6 show solidification against the cool panels on the left side of the fissure and closure in the narrower parts, particularly column A, which gradually diverted molten wax to flow into columns C and D. At T4, column A was nearly completely sealed, but column B was still open such that flow was only weakly diverted into columns C and D. By T6, the solidification front had progressed towards the glass, and the wax was being more strongly diverted into the open conduit that persisted at column D. The poppy seeds were concentrated into column D by T6 and moving relatively fast, indicating that wax was moving faster in column D than B and C (Fig. 13). Wax did not cross the sealed column E. As in test A, the bottom row of panels stayed warm during the test. This meant that solidification occurred more slowly in the bottom rows, and the flow of wax began to localise mid-ascent (Fig. 12 T4-T6).

Fig. 13
figure 13

a Frame from close-up video focused on the upper part of columns B–D during test B. Solid wax has blocked column B and seeds there are fixed in place. Seeds are concentrated to column D. b Mean particle image velocimetry determinations from 300 frames at the same view as A showing the vertical flow of wax moving relatively fast in column D and not at all in column B

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By T5, panels F1-6, G5 and G6, H5 and H6, and I3-6 had been moved closer to the glass. This did not cause an obvious visual change in the solidification of wax, but the seeds were observed to move more slowly in the fissure around these panels, indicating a decrease in the wax flow rate due to closure. At T7, panels B5 and B6 were pulled out and caused the wax to flow laterally into this now-wider conduit.

The rise of wax into the system initially warmed the active wall of the fissure (Fig. 14). The rise of wax and warming in contrast to an empty slot is shown well at T2, where the wax had only risen past the lower 3 rows. Columns E and J showed little to no change in temperature in response to the wax because they were closed. By T3 the wax had filled the fissure and the entire back wall had risen in temperature. By T4 the fissure was cooling down as wax solidified against the back wall, except for columns H and I, which were kept warm and continued to warm up as wax flowed upward. These two columns maintained a warm temperature relative to the rest of the fissure throughout the test, consistent with the observed lack of solidification shown in the video. T5 shows increased cooling in the panels, which was in response to the cooling system being replenished with more ice. This replenishment was necessary in this long-running test to maintain effective cooling since the system unfortunately leaked but has now been fixed. A slight increase in temperature was measured at T7 at panels B5 and B6 and C5 and C6 after these panels were pulled out to 8 mm and warm wax flowed laterally from column D into this widened area. After this, the fissure maintained a fairly uniform temperature until the end of the test, ~ 80 min from the start.

Fig. 14
figure 14

T1 Measured temperature (°C) at the plate-fissure interface after cooling and before wax input. T2–8 Temperature difference maps of the wax-wall interface at the same points in time as shown in Fig. 12. Each map shows the change in temperature recorded by the thermal sensors placed in each panel relative to the temperature recorded before the wax entered the slot (T1). NA = thermal sensor not available. Note changes in colour bar scale between T1 and others. White and black numbering is used only for clarity against the square colour

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Discussion

Overall, the tests show that our key variables, fissure shape, wall temperature, and fluid flow rate can be controlled and changed during an experiment. A wide range of simple to complex experimental configurations can be achieved. The tests show that the injection system produces stable and planar fluid ascent, that the recycling system successfully replenishes the slot with fluid, and that the instruments all record different key aspects of solidification, thermal focusing, and flow localisation. Initial thermal changes, which track with thickening and solidification of the wax, are recorded by the thermal sensors at the wax-wall interface. Solidification and flow localisation are observed in the videos. The transition of wax from a colourless fluid to a white solid is clearly visible, along with the advance of the solidification front towards the glass, and diversion of the flow around obstacles and into open parts of the fissure by flow lines and the tracer particles. The tests show air bubbles occasionally rising through the fissure, which seem to be formed by air entering the system at the injection pipes. Since these may affect the flow behaviour of the wax, work is ongoing to prevent these bubbles forming. We find that few or no bubbles are generated when volumetric flow rates are low and stable, and we can thus proceed with quantitative analyses under those conditions. In later stages of the experimental programme, we would like to introduce bubbles in a controlled way to investigate their influence.

Deflection in the glass front

Flow of wax in parts of the fissure that were meant to be closed indicate that the glass had deflected due to the pressure head created by the rising column of wax, even with supports holding it back. Despite this deflection, the flow of wax and tracer particles was still predominantly controlled by the shape of the back wall of the fissure. Wax that flows past panels that were meant to be closed also freezes rapidly and reseals the fissure. This is probably because the gap is very narrow and when the panels were closed, they would have cooled the glass front where they were in contact with it. A small volume of wax flowing through this part of the slot would therefore lose heat very quickly. This is evident in the closed columns in test B, particularly column J where wax cannot completely fill the column before it self-seals. In test A, the closed “cross” of panels also showed some flow of wax, but cooler temperatures than the surrounding panels because this part of the slot would have been cooler and narrow. Work is underway to reduce the deflection in the glass. Measurements to determine the range of deflection are to be carried out in future tests and can be used to adjust the initial slot back-wall geometry to counter the pre-determined deflection in different parts of the fissure.

Thermal evolution

In both tests, the first row of panels remained relatively warm at the beginning because it is just above the injection slot where fresh warm wax was entering the system. Thermal sensors in row 6 recorded cooler temperatures in the wax that had cooled on its ascent through the slot. The individual thermal features for each test are described and discussed above. For both tests, however, with time the variation in solidification and flow observed in the videos is not reflected in the temperature data at the wax-wall interface. We infer that once the initial layer of wax solidified against the panels, it isolated the thermal sensor from the rest of the fissure, and so only the temperature at the interface was recorded. The actively cooled wall continued to cool the wax that solidified, but visually observed evidence of thermal focusing was not captured in this wall-temperature data. This indicates that the cooled aluminium wall set-up resembles natural surroundings. Observations of thermal effects of natural intrusions in the shallow crust (Gudmundsson 1983; Kristjansson 1985; Baker et al. 2015) suggest that as magma cools and solidifies against a dyke wall, conductive heating in the country rock is often limited. This is attributed to effective cooling by the presence of groundwater in the permeable country rock (Kristjansson 1985; Baker et al. 2015). Heat transfer in this setting is controlled by the thickness of the solidified magma at the dyke margin and the distance over which heat is conducted from molten magma in the dyke interior to the boundary would increase as the solidified layer widens. Although cooling remains faster than in a fully conductive setting (e.g., Carrigan 1986), this leads to a reduction in heat transfer as the interior of the dyke is gradually “insulated” from the surrounding rock (Delaney and Pollard 1982). In terms of monitoring the processes of localisation, the videos are more helpful in this case than are the thermal data.

Additional tools or instruments that can monitor temperature changes in the wax in the interior of the fissure are desirable. Thermochromic pigments were tested and could be used as a visual indicator of the temperature change as the wax rises and solidifies or re-melts. The change is discrete, however, and occurs only at the temperature at which a particular pigment changes colour. In this case, it was 22 °C, so only limited information can be obtained. We find the colour change of the hot clear wax, which gradually turns opaque white as it solidifies, more useful for monitoring the rate of solidification and for resolving tracer particles. Infrared thermal cameras were also tested, but they only show the temperature of the front face of the glass window.

Summary and future work

We have built the first model fissure for investigating the influences of fissure geometry and wall-rock temperature on flow localisation. Initial tests show proof of concept as well as showcasing the capabilities of the apparatus and the types of instrumentation used to monitor thermal and flow evolution within the fissure. In these first tests, we were able to change the shape and width of the fissure both in the initial set up and during an experiment. We also created temperature variations in the active wall and could change the flow rate of wax from the pump or shut it off for a period of time. These changes were translated into variations in the solidification and flow behaviour of the wax. Video-recorded visual observations made during the tests and the poppy seeds as particle tracers could be picked up for PIV to determine flow patterns and velocities within the fissure. Thermal sensors recorded initial thermal evolution at the wax-wall interface, and then showed the development of an insulating boundary. The wax injection system successfully delivered a stable, planar flow of wax into the slot that was recycled back into the system until the fissure closed or the end of the test. With this recycling system, we can conduct experiments that last hours, though more typical durations are in the 30-min range.

We observed that at narrow fissure widths, the solidification of wax progresses from the cooled panels to the glass and completely seals the fissure so that flow is diverted into wider areas. At greater slot widths, the fissure is partially closed by a solidified layer of wax forming against the panels, but it does not close completely, even after over an hour of continuous cooling. This observation suggests that the initial layer of solid wax forms an insulating boundary between the interior of the fissure and the wall. At small widths, this fills the fissure. For greater fissure widths, this layer reduces the loss of heat by conduction into the fissure wall; advection from inflowing warm wax, shielded from heat transfer to the wall by the solidified layer, is dominant, and flow persists for as long as there is a steady supply. If flow ceases, the wax filling the fissure will probably eventually completely solidify if it is not drained back. Bruce and Huppert (1990) identified a threshold fissure width controlling fissure sealing or persistence, consistent with the observed behaviour here. Other models have also shown that sealing or persistence is related to magma flux (Taisne and Tait 2011; Pansino et al. 2019). We also show that solidification is slowed or does not occur in areas of the model where the wall is kept warm. The observed behaviour proves the use of this apparatus in achieving a range of desired experimental scenarios and that the effect on flow behaviour is appropriate.

The ongoing experimental program will systematically test the influence of each variable before advancing to increasingly complex thermal, geometric and wax-flux configurations, including ones that are changed during the experiment. Observations of flow behaviour and localisation may be used to draw general trends based on the dimensionless parameters calculated for each experiment. Modelling of natural scenarios will assist in determining the likely areas where a vent will persist during a natural fissure eruption, enabling hazard planners to prepare. Artfish is being adapted as work progresses with, for example, relocation of the coolant reservoir to a height midway up the device to minimise coolant circulation gradients. With little or no additional modification, the device can be used for other analyses of fluid flow through a non-planar slot and/or in variable temperature conditions.