Electrostatic precursors to granular slip events

Abstract

It has been known for over a century that electrical signals are produced by material failure, for example during crack formation of crystals and glasses, or stick-slip motion of liquid mercury on glass. We describe here new experiments revealing that slip events in cohesive powders also produce electrical signals, and remarkably these signals can appear significantly in advance of slip events. We have confirmed this effect in two different experimental systems and using two common powdered materials, and in a third experiment we have demonstrated that similar voltage signals are produced by crack-like defects in several powdered materials.

Powders and grains—used by the thousands of tons in the processing of polymers, catalysts, pharmaceuticals, and building materials—are well known to exhibit unpredictable jamming to flow transitions (1). On the large scale, these transitions manifest themselves in catastrophic geological slip events (2–4), and on the small scale, they are intimately associated with fracture (5) and material inhomogeneities (6, 7) , causing a documented 50% rejection rate of manufactured ceramics (8, 9). In this letter, we show for the first time that electrical precursors are strongly correlated with—and often precede—any outward sign of a slip event in a powder bed.

Results

In Fig. 1(A), we show a schematic of the first of two experimental systems that we use to investigate powder slip events. This experiment uses a cylindrical tumbler instrumented with a load cell that accurately detects avalanches (10) alongside a noncontact field probe that measures voltage with respect to ground (SI Materials and Methods). Data in this first experiment are acquired by monitoring the tumbler alongside outputs of voltage and load cell sensor with a video camera. Results using automated data acquisition are described shortly; in this first experiment, we obtain readings from the video record twice per second from both voltage and load sensors. A cross-correlation of these voltage and load cell signals exhibits a maximum at 4.8 s, shown in Fig. 1(B), and shifting the voltage signal forward in time by this amount, shown in Fig. 1(C), produces a visible correspondence between steep voltage drops and large slip events. Near coincidences between voltage and load cell spikes are shown as black lines; voltage drops and large slip events are shown as circles and stars respectively, and in Fig. 1(D), we show side-by-side comparisons of large slip and voltage correspondences by moving each slip event to Time = 0. The powder used is an electrically insulating (11) pharmaceutical blend (see figure caption) that has been well studied in powders research (12–14) and exhibits discrete avalanches; the mean size of the blend measured using laser diffraction (Beckman Coulter, model LS 13 320 particle size analyzer) is 90 ± 50 μm. Slip-voltage comparisons using common white flour will be presented in Fig. 2.

Fig. 1.

Experiment demonstrating correlation between electrostatic signals and future slip events. (A) Sketch of apparatus: 25 cm diameter tumbler driven at 5 rpm by onboard DC motor and loaded 50% by volume with powder. Avalanches are detected by load cell shown in blue; electric fields are detected using noncontact voltage probe shown in red (Trek model 6000B-7C). Powder is retained in 10 cm of axial extent of tumbler by foam-core spacer (grey disk in sketch), and available space is filled 50% with powder. The powder used here is a 25/75 blend of acetaminophen [APAP] and microcrystalline cellulose [Avicel 101]. (B) Cross correlation of load cell and voltage signals, showing peak at 4.8 s. (C) Overlapping load cell signal with voltmeter signal advanced by 4.8 s. shows numerous near coincidences (black lines) between avalanches (stars) and voltage spikes (circles) several seconds earlier. (D) Large slip and voltage events transcribed from panel (c), with slip events placed at Time = 0. As described in text, the criterion for a voltage (circle) or slip event (star) is that either drops by one-quarter of the dynamic range within 0.5 s.

Fig. 2.

Experiment removing history dependence by preparing each trial in a uniform tapped initial state. (A) Schematic, showing 10 cm wide acrylic box partially loaded with powder, tapped 20 times, then slowly tipped to produce slip events. (B) Two typical plots of voltage vs. time, with slip events identified by stars, and voltage spikes by circles. The criterion for a voltage spike (yellow spot) is that the voltage changes by more than 15 V within 0.25 s, and the spike time is recorded after the criterion has been reached. The slip event time (black star) is determined by scrutiny of successive, 30 fps, video frames, identifying the time at which motion is first detected anywhere in the bed. (C) Enlargements of slip events and precursors in 8 characteristic cases; typically large slip events are preceded by a precursor 0.5 s previously; an occasional example of a false negatives and a false positive is shown as well. Dark grey lines indicate precursor; green line indicates a duplicate precursor. (D) 23 slip events recorded in nine experiments using APAP/Avicel blend, ordered top-to-bottom by length of precursor. Stars are slip events; yellow circles are earliest voltage criterion attained; green circles are any subsequent criteria observed within 1 s of the slip. Circles at times < 0 represent successful predictions and are colored yellow; circles at times > 0 are prediction failures (false positives) and are colored red; red stars are false negatives. (E) 18 slip events from 10 experiments using bleached white flour, again ordered by length of precursor.

To assess the reliability of the precursors, we perform a Fisher Exact Test (FET: see SI Materials and Methods) of the data shown in Fig. 1(C), comparing the number of slip events correctly predicted (within a time period 4.8 ± 1 s), the numbers of false positives, false negatives, and correctly identified “safe” periods (intervals of ± 1 s not preceded by a voltage drop). Doing so, we find the probability that these results are due to random chance is 1.1% (p = 0.011).

We make two clarifying remarks. First, it is crucial that the timescales of slip detection (from the load cell) and voltage measurements (from the probe) are accurately synchronized, and we present results of synchronization experiments in SI Materials and Methods, both for the experiment shown in Fig. 1 and for additional confirmatory experiments described shortly. Second, there are known to be two types of avalanche (15): smaller “cascade avalanches” typically involving flow originating uphill and accumulating material as it propagates downward, and larger “slip events” (also known as slab avalanches in the snow literature), in which material failure occurs within the bulk, and most of the free surface slides downhill. We do not discount the possibility that cascades may exhibit precursors, however, in our experiments we find that the largest events are most predictable (16), and in this letter we neglect smaller avalanches. Correspondingly, the criterion that we use to establish the presence of a voltage or load cell event is that either drops by one-fourth of its dynamic range (maximum-minimum); smaller signals are disregarded. This criterion agrees with visual observations of large avalanches from the video record, however other criteria have been tested as well, and we have found that the FET results are sufficiently strong that nearly any sensible criterion will identify a correspondence between slip and voltage data.

The data shown in Fig. 1 are obtained by placing the voltage probe at the location shown in Fig. 1(A), at about 5 o’clock. We investigated placement of the voltage probe at about 1 and 3 o’clock [cf. Fig. 3(A)], and found that the correlation between voltage and slip signals was then lost. To investigate this dependence on location within the powder bed in greater detail, we moved the probe to the front of the tumbler—again out of contact with the surface—and measured voltage and slip signals at 12 additional spatial locations shown in Fig. 3(A), chosen to approximate locations at which the strongest correlation was seen in the first experiment. In these experiments, we instrumented the apparatus with an automated data collection system (LabVIEW), obtaining both voltage and load cell readings at 1 kHz. Additionally, to discount spurious triboelectrification of the powder or the apparatus, prior to each of these experiments, we discharged the tumbler inside and out with an active eliminator (EXAIR Ion Air Gun), and then loaded the tumbler in 1-cm layers of fresh powder, discharging each layer after loading. Finally, throughout the duration of these experiments, we discharged the exterior of the tumbler with the same eliminator.

Fig. 3.

Association of voltage probe location and future slip events. (A) Front view of apparatus, tumbled again at 5 rpm and here loaded 70% by volume with powder, showing locations at which voltages are evaluated. In the video acquisition approach shown in Fig. 1, measurements are made at R1, R2, R3; data from R3 are shown in Fig. 1(B and C). In the automated data acquisition approach, the voltage probe is pointed axially inward at each of the 12 yellow and red gridpoints shown. (B) False colored snapshot of tumbler, exhibiting train of defects (arrowheads) emanating from gridpoint e6, where precursor correlation is strongest. (C) Overlapping load cell signal with voltmeter signal taken at location e6 advanced by 3.4 s. shows highly significant correlations (black lines) between slip events and voltage signals several seconds before. Data here are taken at 1 kHz and low-pass filtered using a direct form II biquadratic filter to remove high frequency noise. (D) Cross correlation of load cell and voltage signals, showing maximum at 3.4 s. (E) Large slip and voltage events transcribed from panel (C), with slip events placed at Time = 0. As before, the criterion for a voltage (circle) or slip event (star) is that either drops by ¼ of the dynamic range, here within 1.5 s.

These experiments confirm that the correlation between voltage and slip signal depends strongly on probe location. The data shown in Fig. 3(C) are taken at location e6 in Fig. 3(A): At this location, we find that voltages precede slip events by 3.4 s., as shown in the cross-correlation shown in the inset to Fig. 3(C). The voltage precursors at e6 correspond almost one to one with slip events, however, as before, this strong correspondence between voltages and load cell readings is not seen either at location f5 (immediately upstream of e6) or at d6 (downstream). We conclude from this fact that the voltage production mechanism is transient and does not involve persistent charging of, for example, the tumbler surface or a localized region of the bed.

An FET analysis produces a 0.8% (p = 0.0075) likelihood that the correlation in this experiment is random. We have performed experiments at different speeds (3 and 5 rpm), fill levels (50% and 70%), and environmental conditions (18–39% RH); additionally, we started and stopped the tumbler for periods ranging from one-half to several minutes to give any charged regions time to relax, and we confirmed that the predictions are not due to possible initial static charge by running the experiment continuously for an hour. Provided that the probe is suitably placed, we find correlations between voltage drops and large slip events persist despite these changes.

We discuss the role of probe location shortly. For the time being, we note from Fig. 3 that both voltage and load signals are contained in an envelope that rises and falls at close to the 12 s period of tumbler rotation. We can identify no evident irregularity in the tumbler, its rotation speed or its loading condition; nevertheless we have been unable to remove this periodicity from the signals measured. To validate our results and eliminate unwanted periodicity, we performed an independent set of experiments using a different apparatus in which we prepare the powder in a nearly uniform initial state prior to each experimental trial.

This second apparatus, shown schematically in Fig. 2(A), is simple enough to be reproduced in any laboratory, and consists of an acrylic box, 46 cm long, 30 cm high, and 4.5 cm wide, that is slowly tipped to produce avalanches. Initially, the powder is stirred with a metal rod to break up any incipient clumps, the box is tipped to the left at about 45°, and the surface is gently flattened. The box is then sharply tapped 10 times each on the bottom and then the left side of the box (17, 18), after which it is slowly tipped to the right (measured at about 1.5 rpm) until avalanches begin. Avalanches are recorded using a 30 frame per second video camera with a stopwatch in the field of view.

We have performed numerous trials of the tipping experiment shown in Fig. 2. We record the times at which the first indication of any kind of bed movement appears on the video, and plot these times in Fig. 2(B) as stars alongside voltage spikes for two example trials. In Fig. 2(C), we enlarge eight typical slip events, including an occasional false negative and a very rare false positive. Unlike the tumbling experiments, there is no evidence of periodicity here, yet as panel (d) shows graphically using the APAP/Avicel mixture, slip events over numerous experiments are more often than not preceded by at least one voltage spike: out of 23 slip events, all exhibit a distinct voltage spike, and 14 of these occur before the slip. The criterion that we use in Fig. 2(D) for a voltage spike is that the voltage must change by at least 15 V within one-quarter s, after which we evaluate the time to the next avalanche. We calculate an FET probability of 0.30% that the precursors are random.

We repeated this tipping experiment 10 additional times using common bleached flour. Flour produces larger voltage excursions and in Fig. 2(E), and we use the criterion that the voltage changes by 500 V within 0.5 s. We then obtain reliable predictions of slip events, with an FET probability of 0.41%, and of the 18 slip events detected, 15 exhibit voltage precursors. We note that the precursor time for slip events in the tipping experiments is less than 1 s—significantly shorter when the bed is tapped than in the tumbler.

Discussion

To make sense of these results, we take note of two facts that are well established, but have not to our knowledge been discussed together. First, it has long been known (19) that solids including crystals (20), glasses (21), rocks (22), and ice (23), adhesives such as on plastic tape (24, 25), and liquids, for example, mercury (26), all produce electrical signals during failure. Second, it has equally long been known (27) that granular materials must dilate before they can flow. Considering these two facts together, a straightforward explanation for our results is that granular materials may also produce a voltage signal when they dilate—and since dilation must precede slip, our data may simply have unveiled electrical signals of dilation. In the context of geophysical granular materials, dilation has been used as an indicator of localized shear stress (28), and indeed dilation in the form of geophysical crack propagation has been proposed as a source of electrical signals (29). Similarly, in our cohesive powder beds, crack-like defects appear as the bed is sheared: these defects can be seen by eye in Fig. 3(B), which shows a false-colored snapshot of the tumbler during rotation. In the enlargement to the right of this panel, we have identified defects in the powder bed (arrowheads), and the video record reveals that slip events occur subsequently, once these defects approach the bed surface (see Movie S1). Moreover, as identified in Fig. 3(B), these defects appear to form a train emanating from the location e6 also shown in the snapshot, and at 5 rpm, it takes about 3 s for regions near e6 to travel to the surface of the bed. No such defects are seen in the tipped bed, which was stirred and then tapped to remove any incipient structure.

Thus we propose that in the tumbler, these defects may produce slip after they have been transported to the bed surface, while in the tipped bed, longstanding defects have been prevented by consolidating the bed, so that defect formation precipitates a more immediate slip event. This description remains only qualitative pending a more definitive mechanistic analysis, however it appears to account for the results that we have seen. We note that structural precursors to slip have been reported previously, for example, an experimental study (16) has revealed that disorder within a granular bed increases significantly in advance of large avalanches, and a recent computational study of cohesive particles (30) reports that the mean gap between particles begins to grow several seconds before evidence of slip.

The role of defects in the inception of slip events has previously been documented in studies of grains and colloids (31, 32), in models of earthquake dynamics (33), and in research into disorder transitions in a broad range of glassy materials (34). The hypothesis engendered by the present work is that the initiation of these defects precedes large slip events, and that the formation of defects in powder beds produces distinctive voltage spikes. To close the loop in this line of reasoning, we have performed a final set of experiments to confirm that the formation of defects by itself in the materials used in this work does produce the hypothesized voltage spikes.

As shown in Fig. 4(A), this last experiment consists of a vertically oriented shear cell loaded with sifted powder. Because the cell is vertical and the powder is loosely packed, powder can settle downward, leaving a sizeable gap between the powder bed and the top of the upper chamber. This gap in turn allows crack-like defects to develop as the upper and lower chambers shown in the figure are sheared left to right (see enlargement to right of panel).

Fig. 4.

Experiment demonstrating that opening and closing of a crack-like defect in a powder bed produces repeatable voltage signals. (A) Overview of experiment, showing two powder chambers oriented so that sliding either upper or lower chamber causes cracks to open and close. Thus the crack circled in red opens when the Upper chamber is slid to the Right, and closes when it is slid to the Left. ; The voltage probe is held about 1 cm from the front surface of the upper chamber and is moved with the chamber to maintain its focus on the crack of interest. The chambers are sheared by a distance required to open and close the crack, about 1 cm. (B) Data from experiment using unbleached wheat flour; thickness of “open” and “close” bars represent approximate time spent opening and closing the crack shown in the enlargements to the Right of the panel; chambers are not moved during periods of time colored dark gray. Lower trace shows voltages with probe near large crack about 4 cm from the upper chamber’s rightmost edge; Upper trace shows control, with probe at center of upper chamber, far from cracks. Red data show raw voltages sampled at 1 kHz; black curve is smoothed over nearest 100 data points (i.e. data rate reduced to 10 Hz). (C) Comparison data from cracks using APAP-avicel blend (“APAP”) and sheetrock patching compound (“Patching compound”). Insets to Right show patching compound; APAP crack appearance is similarly multifaceted.

Importantly for our purposes, individual cracks can be repeatedly opened and closed as the chambers are sheared back and forth: this is shown in the enlargements to the Right of Fig. 4(B). By pointing the voltage probe at a particular crack and acking the crack with the probe as the chambers are sheared, we obtain voltage signals as shown in Fig. 4(B and C) for various powders. In Fig. 4(B), we show voltages in chambers loaded with unbleached white flour and sheared left and right every 5 s. The shearing time is brief, about 0.25 s, and no motion of either chamber occurs between shearing events (see Movie S2). We have replicated these experiments several times, and we find that the voltage signals near cracks are invariably very abrupt and persist at relative humidities at least up to 70%. As shown in Fig. 4(B), the voltage near the crack (lower trace, labeled “Defect”) drops abruptly every time the crack opens, and jumps abruptly every time the crack closes. A control experiment, using exactly the same system but with the probe near the center of the upper chamber where cracks seldom change, shows little voltage variation (upper trace, labeled “Control”).

We emphasize that the repeatability shown in Fig. 4(B) depends strongly on the crack morphology: In Fig. 4(B) the crack (see upper right inset) is large, well-defined, nearly linear, and does not change perceptibly with multiple shearing events. In multiple trials for this and a variety of other powders, we find that smaller, more irregular or transient cracks produce more variable voltages. Exemplar voltage traces are shown in Fig. 4(C) for the APAP-avicel blend discussed earlier (upper trace) and for sheetrock patching compound (lower trace). Alongside these plots we show snapshots of the crack that we focus the probe on before and after the experiment using patching compound; the APAP crack is similar in appearance. In the cases shown in Fig. 4(C), the crack is small, irregular and multifaceted, and while the voltages still spike sharply at most shear events, more variability is seen during both shearing and stationary periods.

Notwithstanding this variability, we find in our trials that with few exceptions, voltages decrease abruptly during periods of crack opening and increase abruptly during closing. For large and stable cracks [e.g. Fig. 4(B)], these voltage features are repeatable, while for smaller and more irregular cracks, the features are still present, but are convolved with other, as yet unexplained, voltage signals during both shearing and stationary periods. Because the available evidence supports the hypothesis that opening and closing of gaps in powder beds leads to voltage spikes, it is tempting to interpret these additional signals as an indication that powder rearrangements not visible by eye may be occurring. Future, possibly tomographic, investigations will however be necessary to establish precisely what is occurring within the bed that produces to these unexplained voltages.

In summary, our experiments demonstrate that detectable, reproducible, but as yet poorly understood, electrical signals precede slip events in powder beds. We have confirmed these results in two different experimental systems using different materials, different measurement methods, different fill levels, and different rates of stress. We also found in a final experiment that voltage spikes are formed as crack-like defects in powder beds are opened and closed, and we have proposed that the appearance of these signals may be analogous to voltages produced by failures in other materials (19–26).

Several research groups have studied granular stick-slip (32, 35, 36), however an electrical precursor to slip does not appear to have been reported before. The mechanism underlying these precursors remains to be definitively determined: The materials studied are not piezoelectric, the effects persist in the presence of active static elimination as well as at relative humidities up to 70%, and stresses are several orders of magnitude too small to produce chemical changes reported elsewhere (37–39) to lead to measurable voltages. Likewise the effect does not seem to be associated with granular contact electrification: We find in our experiments that large and transient voltages (over 100 V) can be measured outside of the shear zone significantly in advance (approximately 1 s) of slip, whereas studies of contact electrification during granular shear report much smaller and lasting voltages (under 100 mV) in probes that are in contact with shearing surfaces over much shorter precursor times (under 0.1 ms) (40).

It remains to be demonstrated how extensive the implications of our findings may be. On one front, many common materials—ceramics in turbines, chalk in cliffs, and concrete in bridges, to name three—are made from grains or powders, and our results lead us to speculate that failure of these materials may be also preceded by telltale electrical signals. On another front, electrical disturbances have for over 250 years been reported to precede major earthquakes (41, 42) and rockbursts (43). Many of these reports are anecdotal (44) and of uncertain reliability, however the presence of electrical earthquake precursors has been substantiated by a growing body of field measurements (45, 46), and we anticipate that the ability to generate correlated electrical signals and slip events in a controlled setting will enable future research to unveil the mechanisms leading to these curious effects.