Experimental setup

The experimental apparatus comprises a 0.9 × 0.4 m test-section containing a 5 cm deep sediment bed. The test section is inclined at 25° and located inside the Open University’s Mars simulation chamber40, 41 maintained at an average pressure of ~9 mbar. For each experiment, pure water was introduced near the top of the slope at 1.5 cm above the sediment bed and the resulting flow behavior was observed. The water was pumped into the chamber from an external reservoir allowing the temperature to be maintained at ~278 K and the flow rate at ~11 ml s−1 (see Table 1). The sediment consisted of sand (~63–200 μm grain diameter). Each run was performed in triplicate, and all experiments were recorded with three cameras. Digital elevation models (DEMs) of the bed were created both before and after each run using multiview digital photogrammetry. Table 1 provides full details of the experimental conditions.

Table 1 Summary of measured and controlled variables Full size table

Water flow experiments

During the “cold” experiments water flowed over the surface of the sediment and also infiltrated into the sediment. Entrained sediment was transported downslope, depositing a series of lobes that migrated laterally over time, comparable to flows under terrestrial conditions40. The majority of the sediment was transported by overland flow of water (~98%; Fig. 1a–c, Supplementary Movies 1, 2). Boiling of the water was identified by the observation of bubbles at the surface. Occasional millimeter-sized, damp “pellets” of sediment were ejected by the boiling water as it infiltrated the bed. These ejected pellets transported negligible volumes of sediment (~2%). The majority of the sediment transported in the “cold” experiments was by overland flow, confined to a zone with maximum average width of ~9.2 cm and a downslope length of ~36.5 cm (Fig. 1b).

Fig. 1 Image, map, and elevation data at the end-state of experiments. a, d Orthophotographs (0.2 mm pix−1) of “cold” (a) and “warm” (d) experiments. b, e Hillshaded relief from DEM (1 mm pix−1) overlain by process-zone maps giving the spatial extent of the different transport types (blue = overland flow, green = percolation, red = pellets, yellow = dry avalanches/saltation) for “cold” (b) and “warm” (e) experiments, and c, f elevation difference between start and end of “cold” (c) and “warm” (f) experiments. Flow direction is from top to bottom and the same scale is used for all images Full size image

The volume of sediment transported during the “warm” experiments was nearly nine times greater than that during the “cold” experiments, and thus an increase in the sediment transport rate of the flow from ~0.13 cm3 ml−1 for “cold” experiments to ~1.18 cm3 ml−1 for “warm” experiments (Table 1, Fig. 2). Thus to transport the same volume of sediment in the “warm” experiment as the “cold”, only ~11% of the volume of water is required. The increase in the volume transported for a given water volume in the “warm” experiments is caused by three processes: (1) transport of sediment by ballistic ejection of sediment and millimeter-sized sediment pellets, (2) transport of sediment by “levitation” of millimeter-sized to centimeter-sized sediment pellets with very rapid downslope transport, and (3) dry avalanches of sediment triggered by the ejected grains and levitating pellets. The combined effect of these processes accounted for about 96% of the total sediment transport, with overland flow being only a minor component, in contrast to the “cold” experiments.

Fig. 2 Mean volumes of transported sediment. a Mean volumes are divided into “warm” experiments (left bar) and “cold” experiments (right bar), and subdivided into different transport types (blue = overland flow, green = percolation, red = pellets, yellow = dry avalanches/saltation) (see also Fig. 1). The mean of total error (Measurement Error) are presented on top of the bars, errors at the side of the bars represent the mean of total errors (Measurement Error) for each individual transport type. More information on the error calculations can be found in Table 1, the methods section, and in Supplementary Table 3. b Re-scaled “cold” experiments Full size image

Saltation and levitation processes

The following sequence of events were reconstructed from the video footage: in the “warm” experiments, when the water came into contact with the sediment, boiling-induced saltation of the sediment created a continuous fountain of ejected grains until the sediment became saturated (after about 30 s; Fig. 3a–e, k, l; Supplementary Movies 3–5). In the very first seconds of the experiment, numerous saturated sediment pellets detached from the source area and rolled/slide quickly down the test bed (often to the end) with very little direct surface contact (Supplementary Movies 3, 4, 6). These pellets ranged in size from 0.5 to ~50 mm and were observed to travel at average speeds of ~46 cm s−1. This is more than twice the speed of pellets under “cold” experiments (~19 cm s−1; Table 1). We conclude that the pellets in the “warm” experiments partially levitate on a cushion of gas produced by boiling via a mechanism comparable to the Leidenfrost effect (Fig. 3a), which enhances their downslope velocity. The gas released at the base of these pellets causes erosion of loose dry sediment, as shown by tracks leading to isolated pellets, and by the formation of a short-lived transportation channel carved by a rapid series of levitating pellets in the first seconds of the experiment (Fig. 3b–d, i, j; Supplementary Movies 3, 6). The transient channel was approximately 5-cm wide and had a curvilinear shape. Due to the short length of the test bed and the fast material transport, this transient channel was backfilled within the first seven seconds (Supplementary Movies 3, 6).

Fig. 3 Example of transport processes. Frames from video of a “warm” temperature experiment (Run 5). Images after a 1 s, b 3 s, c 4 s, d 10 s, e 44 s, f 60 s, g 122 s, and h 303 s after the start of the experiment. White arrows point to sand saltation plumes, black arrows point to levitated pellets of wet sediment (a, i), to dry material superposing the channel (d), and to the last observed dry avalanche (h). i–l Show detailed excerpts of b–e, respectively. Contrast and brightness was adjusted on all images individually for clarity. Note for scale that the metallic tray is 0.9-m long and 0.4-m wide Full size image

Grain avalanches

In the “warm” experiments, the saltating sediment and levitating pellets triggered grain avalanches that propagated downslope (Fig. 1d–f, Supplementary Movies 3, 4). Grain avalanches and grain ejections occurred over the same time period (up to ~138 s), with some very late grain avalanches observed after 528 s for run 6. During the “cold” experiments no such movements were detectable. About 56% of all transported sediment was by these dry avalanches (Table 1, Fig. 2). The effect of sand saltation and grain flows caused by boiling liquid water was first reported by Massé et al.41, who used a melting ice block as a water source, giving a very low water flow rate of 1–5 ml min−1. They observed the formation of arcuate ridges caused by intergranular wet flow and the ejection of sand grains at the contact of the wet and dry sediment: these phenomena (but not the ridges) were also observed in our experiments. Saltation and flow arrested in their experiments once the water supply was removed41. In our “warm” experiments, though, saltation from the saturated sediment body continued for a mean of ~78 s after the water was stopped. This implies that the sediment in our experiments was supersaturated, and percolation continued after removal of the water source. Supersaturation requires the water release rate to be faster than the infiltration rate (hence flow rates higher than those in Massé et al.41), suggesting this may be a limiting condition for sediment levitation.

Liquid overland flow

Liquid overland flow occurred in both “warm” and “cold” experiments, but only began in the “warm” runs at a mean of ~20 s into the experiments. The total downslope extension of the overland flow in the “warm” runs was ~76% (~8.4 cm shorter, Table 1) and the average width ~80% (~1.8 cm narrower, Table 1) of the “cold” experiments (Fig. 1, Supplementary Movies 2, 4). The average propagation rates were very similar (~0.74 cm s−1 for the “warm” experiments, ~0.61 cm s−1 for the “cold” experiments). The average volume of sediment mobilized by overland flow in the “warm” experiments was about half that in the “cold” experiments due to the shorter time for which this process was active.

Scaling to martian gravity

In our laboratory experiments we were unable to simulate the effect of martian gravity on these processes. Massé et al.41 found that saltation induced by boiling is more effective under martian gravity than terrestrial gravity, resulting in three times more sediment transport. We do not repeat their calculations, but instead focus our attention on the effect of gravity of the levitation of pellets, in order to assess if sediment transport via this mechanism would be more or less efficient than observed in our experiments for otherwise similar conditions. Below we derive equations to describe the levitation force produced by the boiling gas, and then we apply these equations to understand the effect of gravitational acceleration on the levitation duration and the size of objects levitated.

We follow the reasoning and calculations of Diniega et al.43 who considered the levitation of a sublimating CO 2 ice block on Earth and on Mars. We assume that the wet sand pellet can also be treated as a block with a width D = 2 R (m), a thickness H (m), and an aspect ratio of D/H lying on the dry sand test bed (Fig. 4). The temperature at the surface of the wet sand pellet is set at the temperature of evaporation of the liquid water T e for the relevant atmospheric pressure p. We assume that the temperature of the test bed T 0 exceeds the evaporation temperature. We assume that the gas escapes uniformly from the bottom of the object, perpendicular to the surface of the test bed. The object experiences two opposing forces (Fig. 4). The force W due to weight of the object

$$W = g{\rho _{{\rm{ws}}}}HA,$$ (1)

where g is the local gravity, \({\rho _{{\rm{ws}}}}\) is the wet sand density, H is the height of sand pellets, and A is the area in contact with the test bed. As in Diniega et al.43 we consider two shapes: (I) rectangular, if R<<L (length in m), then the problem can be solved in 2D and A = 2RL or (II) cylindrical, the problem is solved in 3D and A = πR 2. The contact between the block and the sand bed results in frictional forces that prevent the block from falling. The friction force F T is proportional to the normal force N z

$${F_{\rm{T}}} = \mu {N_{\rm{z}}},$$ (2)

where the coefficient of proportionality μ is the Coulomb friction coefficient. Moreover, there is no motion of the pellet if \({F_{\rm{T}}} >W\,\sin \,\theta \). To determine if motion can start, we need to consider the normal force N z , which is the resulting force between the weight W and the levitation force F e , defined in the normal direction z as follows:

$${N_{\rm{z}}} = W\,{\rm{cos}}\,\theta - {F_{\rm{e}}},$$ (3)

where θ is the slope angle and F e is the force due to the gas escape by evaporation of liquid water during boiling43 and defined as:

$${F_{\rm{e}}} = {C_{\rm{f}}}A\frac{{R\,{u_0}\,v}}{k}.$$ (4)

Fig. 4 Schematic representation of a block over an inclined plain. The block represents a wet sand pellet in contact to dry sand with T 0 > T e . The block is subject to three forces in competition: the weight W, the friction force F T , and the levitation force F e . The z-axis is oriented so that z ≥ 0 indicates increasing depth into dry sand and the x-axis is oriented parallel to the sand surface so that absolute values of x less than 1 represent the interior of the wet sand pellet43 Full size image

The levitation force F e is therefore proportional to the dynamic pressure \(R{u_0}

u /k\) (described below), the surface area A, and an aerodynamic coefficient C f . The aerodynamic coefficient is complex to evaluate because it depends on both the shape of the object (rectangular, spherical, oval, etc.), its roughness and the slope angle. By making some simplifying assumptions, Diniega et al.43 have shown that this coefficient can be deduced from the calculation of the total force of the fluid exerted on the sublimating CO 2 block placed on a flat floor. Thus, for a rectangle (A = 2LR), their calculation of the force after integration gives \({F_{\rm{e}}} = 2\,LR.\left( {\frac{\pi }{4}} \right).\left( {\frac{{R\,{u_0}\,v}}{k}} \right)\), which makes it possible to deduce that \({C_{\rm{f}}} = \pi /4\) for a rectangular object and \({F_{\rm{e}}} = 2LR.\left( {\frac{{4\pi }}{3}} \right).\left( {\frac{{R\,{u_0}\,v}}{k}} \right)\) is \({C_{\rm{f}}} = 4/\left( {3\pi } \right)\) for a cylindrical object.

In our case the determination of C f is non-trivial. The pellets consist irregular objects of cohesive sand supersaturated with water. The surface of the pellets is not smooth as could be reasonably assumed for a block of CO 2 ice. Moreover, the shape of our objects depends on the experiment considered and can be very variable according to the temperature conditions of the experiment. Finally, we must consider the slope that will favor the levitation effect and will tend to increase this coefficient, but increasing roughness will decrease this coefficient.

For these reasons we have chosen to estimate the value of the aerodynamic coefficient C f using our experimental results. We estimated the size and shape of the pellets from the videos and orthophotos of the experiments at 297 and 278 K. The pellet sizes range from 0.5 to 50 mm. They have irregular shapes and are often flattened with an aspect ratio H/D = ~0.75.

Therefore we know that for experiments at a sediment temperature of 297 K, the boiling effect is strong enough to move centimeter-sized pellets for the duration of several seconds. At 278 K, centimeter-sized pellets are not levitated while millimeter-sized pellets are observed to levitate for a few seconds. We tuned the aerodynamic coefficient to match these experimental observations. We find that C f ranges from approximately 1.45 to 7.3. We then used the corresponding value of the aerodynamic coefficient C f in our calculations for Mars to evaluate the influence of Mars’ reduced gravity on pellet levitation.

The dynamic pressure \(R{u_0}

u /k\) is dependent of the length R, the sand permeability k, the gas viscosity v, and the mean gas velocity u 0 escaping from the surface A of the block, which is defined as follows:

$${u_0} = \frac{q}{{{E_{\rm{v}}}\,{\rho _{\rm{g}}}}},$$ (5)

where q (W m−2) is the heat flux by thermal conduction, E v is the enthalpy of evaporation for water, and \({\rho _{\rm{g}}}\) is the volatile gas density. The heat flow is obtained by solving the heat equation44. The integration of the solution gives us the heat flux q from the sand bed to the block by conduction

$$\left. {q\left( t \right) = \lambda \frac{{\partial T}}{{\partial {\rm{z}}}}} \right|\begin{array}{*{20}{c}}\\ {} \\ \\ {z = 0} \\ \end{array} = \left( {{T_0} - {T_{\rm{e}}}} \right)\sqrt {\frac{{\lambda {C_{\rm{p}}}{\rho _{\rm{s}}}}}{{\pi t}}} ,$$ (6)

where λ is the thermal conductivity of the sand, C p is the heat capacity of the sand, \({\rho _{\rm{s}}}\) is the sand density, and t is the time (s).

Along a slope, a block will move if the friction force is overcome by the weight force in the x-direction (Fig. 4):

$$\mu \left( {W\,{\rm{cos}}\,\theta - {F_{\rm{e}}}} \right) < W\,\sin \,\theta \to \tan \theta \, >\, \mu - \frac{{\mu {F_{\rm{e}}}}}{{W\,\cos \theta }}.$$ (7)

Determination of the Coulomb friction coefficient μ is non-trivial. There is no empirical method to determine this coefficient and we have no experimental measurements that allow us to calculate it directly. As μ is a coefficient, its sign is imposed, so the sense of the inequality depends only on the sign of \(\left( {1 - \frac{{{F_{\rm{e}}}}}{{W\cos \theta }}} \right)\) and therefore on the ratio \({F_{\rm{e}}}/W\,{\rm{cos}}\,\theta \). Under the angle of repose of the sediment, if \({F_{\rm{e}}} >W\,{\rm{cos}}\,\theta \) then the pellets will move. Increasing slope will tend to reduce the threshold value F T required to start movement.

We calculated the evolution of the ratio of the levitation force F e to the weight force W cos θ of a block over a slope of 25° with time for both the low pressure environment of our chamber experiments at different temperatures and for equivalent conditions, but using martian gravity. The parameters used for these calculations are presented in the Supplementary Table 1. We assume that not all the heat flux due to conduction is used for the change of state of the water contains in pellets. Figure 5 shows that the levitation force produced by boiling is about 4.6 higher at 297 K than 278 K, which is consistent with our experimental results. For pellets with an aspect ratio of 0.75, circular basal area (results are similar for a rectangular base), and a sand temperature of 278 K, our calculations predict that levitation should not occur for pellets of R = 1 cm and should persist for about 2 s for R = 0.1 cm, and these predictions are consistent with our experimental observations (Supplementary Movies 1, 2). For the same aspect ratio, at sediment temperature of 297 K, our calculations predict that levitation should persist 5 s for R = 1 cm, which is of the same order of magnitude as the levitation duration observed in our experiments (Supplementary Movies 3, 4, 6). For R = 0.1 cm, we predict that levitation can last for 51.5 s, but many pellets of this size hit the end of the tray, therefore this prediction cannot be validated by our experimental data.

Fig. 5 Evolution in the ratio of the levitation force to the weight force. The ratio of the levitation force F e to the weight force W cos θ of a block over a slope of 25° with time is calculated for the physical parameters of the martian surface and of our experiments in the Mars simulation chamber (Supplementary Table 1) and use a cylindrical geometry. The levitation of the block occurs when the ratio is greater than 1 (dashed black line). a Ratio calculated for different sand temperatures T s and sizes of block for parameters of the Mars simulation chamber and H/D = 0.75. b Ratio calculated for different temperatures T s for parameters of martian surface and of the Mars simulation chamber and H/D = 0.75 with R = 0.01 m Full size image