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The effects of electric fields on wind driven particulate detachment
Icarus 220 (2012) 1–5
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The effects of electric fields on wind driven particulate detachment C. von Holstein-Rathlou, J.P. Merrison ⇑, C.F. Brædstrup, P. Nørnberg Mars Simulation Laboratory, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
a r t i c l e
i n f o
Article history: Received 7 February 2012 Revised 6 April 2012 Accepted 11 April 2012 Available online 25 April 2012 Keywords: Geological processes Regoliths Terrestrial planets
a b s t r a c t The effects of external electric fields upon the wind driven detachment of granular material has been investigated experimentally using an environmental wind tunnel facility. It has been shown that for sand sized grains on an electrically conductive surface there is a significant reduction in the threshold shear stress required for detachment at electric fields above 200 kV/m. However, if the surface is insulating then dielectric effects cause an increase in surface adhesion and an increase in the detachment threshold. This would be relevant in arid environments where the surface conductivity is low. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction The generation of intense electric fields close to the surface is a well-documented phenomenon and often associated with wind driven sand/dust transport events (Farrell et al., 2004; Jackson and Farrell, 2006; Schmidt et al., 1998; Kamra, 1972; Brook and Moore, 1974). This is attributed to the electrification of the sand/dust particulates during contact i.e. the processes of contact electrification or tribo-electrifcation (Forward et al., 2009; Baytekin et al., 2011; Horn et al., 1993; Merrison et al., 2006). Empirical measurements have demonstrated that during contact electrification larger grains predominantly electrify positively compared to smaller grains (Kok and Lacks, 2009; Lacks and Levandovsky, 2007; Merrison et al., 2012). Gravitational separation of these particulates, especially the suspension of dust, then leads to the generation of electric fields which are expected to be intense close to a surface. Electric fields associated with dust devil events have been measured in the range of 30–170 kV/m (Jackson and Farrell, 2006). The effects of electric fields on the wind driven detachment and transport of granular material is, however, poorly understood (Kok and Renno, 2006; Merrison, 2012; Zheng et al., 2006; Pahtz et al., 2010). In recent studies the effects of an applied external electric field on the wind driven transport rate of sand was quantified in a wind tunnel simulator in which a natural sand bed was employed. At the highest electric fields (of >250 kV/m) a significant enhancement in the transport rate was observed which agreed well with a simple model assuming a conductive sand bed and an electric field induced surface stress. However, at electric fields in the range of 150–250 kV/m there was observed a suppression ⇑ Corresponding author. Fax: +45 86120740. E-mail address: [email protected] (J.P. Merrison). 0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2012.04.011
of this electric field assisted entrainment which was attributed to poor electrical conductivity of the sand bed and possible dielectric effects of the sand particulates (Rasmussen et al., 2009). The electric field induced levitation of particles from a surface has been studied experimentally for sand sized (63 lm to 2 mm) grains and reduction in the wind driven threshold for sand transport is expected for a conductive surface (Kok and Renno, 2006). However, it is not clear that in nature the surface (for example of a sand bed) is necessarily conductive. In environments of low relative humidity (i.e. arid) it may be expected that the electrical conductivity of the soil/regolith is extremely low and may better be modelled by a (poorly) insulating surface rather than a (poorly) conductive one. Furthermore the structure of a sand bed typically consists of a complex network of physically contacting and electrically conducting chains, such that the electrical conductivity of the surface through to the subsurface is spatially non-uniform (Rasmussen et al., 2009; Merrison, 2012). An example here might be the planets Mars or Venus where the absolute humidity is low. Observations of sharp peaks of material, or razorbacks, on Mars have been suggested as evidence for the presence of chain formation in surface materials within an electric field (Shinbrot et al., 2006). The aim of this study is to investigate the effects of electric fields upon the wind driven detachment threshold for sand sized particulates at a surface. Specifically the effect of the electrical conductivity of the surface is investigated. This is intended to improve the understanding of the interaction of naturally occurring electric fields upon the transport of sand (and dust) within Aeolian events. 2. The application of detachment theory In this section a simple model of wind driven grain detachment will be presented which utilises the application of force balancing
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(Cleaver and Yates, 1973). This model has subsequently been modified with the application of an electric field induced component. The forces here have been expressed in the form of stresses and some discussion will be made of the magnitude of these stress components for these experiments based on previous detachment studies performed in the same environmental wind tunnel (Merrison et al., 2007). The stress applied to a particle at a surface by wind flow can be expressed in terms of two components, a vertical lift stress (sL) and a horizontal torque (sT). However in the experiments performed here attempts have been made to inhibit the horizontal transport of the grains (i.e. rolling) with the use of roughened substrates. As a consequence this simple model does not consider the horizontal torque component. There are two stress components which prevent particulate detachment, one being gravitation (sg) and the other adhesion to the surface (sA). The vertical component of the adhesive stress is of interest here (sA\). The application of a vertical electric field can be assumed to result in an additional vertical stress upon the particulate (sE) which can either aid or hinder detachment. The condition for the detachment of a grain from a surface (at the threshold) is that the combination of wind shear and electric field induced stress is balanced by the gravitational and adhesive stress terms.
sL þ sE þ sA? þ sg ¼ 0
ð1Þ
In previous studies the stress terms not related to the electric field have been empirically determined. This was achieved (for spherical glass particles) by measuring the threshold shear stress for wind induced detachment for hollow glass spheres of varying mass density and fitting the data to expected expressions for the adhesive, lift and gravitational terms (Merrison et al., 2007). The Newtonian expression for lift stress is given by
sL C L qU 2
ð2Þ
where q is the fluid density and CL is the coefficient of lift which has been empirically determined (Merrison et al., 2007). The friction wind speed, U⁄, is dependent on the turbulent component (i.e. standard deviation) of the wind speed UT, in this case; U⁄ UT/2.1 (Monin and Yaglom, 1973). At a wind tunnel wind speed of 5.5 m/s the turbulence (UT) was measured to be around 18%, giving a value of U⁄ 0.4 m/s and yielding a value of sL 0.7 N/m2. Note that the stress is negative indicating that it is away from the surface (upward). Particulate adhesion to a surface is linearly dependent on particle diameter via the coefficient of adhesion, Cad, which has also been empirically determined (Merrison et al., 2007). For glass spheres of diameter around 60 lm the stress term is found to be sA 0.6 N/m2. Although the gravitational term should in principle be trivial to determine, requiring knowledge only of the mass density and size of the grains, the use of a gravitational stress (sg) requires knowledge of the packing conditions of the grains i.e. the actual mass density of the granular material (qg). Glass spheres with diameters around 60 lm and mass density of 2.7 g/cm3 yield a stress of sg 1.2 N/m2. The stress applied to the conductive surface of a parallel plate electrode while creating a uniform electric field (E) is given by (Griffiths, 1999);
e sE ¼ 0 E 2 2
ð3Þ
where e0 is the vacuum permittivity and electric field, E, is vertical (perpendicular to the surface). This stress term can also be applied to calculate the stress upon a conducting grain of material in contact with (resting upon) a conducting surface as a result of applying
an electric field. The negative sign in Eq. (3) signifies that the force opposes the field direction i.e. it is vertically upwards away from the conducting plate. However, in the case of a (spherical) dielectric resting upon other identical spherical dielectric particles (i.e. an insulating surface) the application of an electric field would be expected to induce chain formation. This is analogous to chain formation observed by magnetically susceptible particulates in an applied magnetic field. A detailed theoretical treatment of contacting glass spheres in an electric field has led to the relation (Stoy, 1995):
sE ¼ F 1 e0 er E2 r2
ð4Þ
For a dielectric material with a susceptibility of around 3 (typical for glass) the term F1 3, er is the relative permittivity of the medium, which may be assumed to be 1 for ambient air (Stoy, 1995). Note that this force is positive i.e. attractive towards the surface. The assumption in this model calculation is that the glass sphere is resting on top of another sphere. Note that in the case of a conductive particle (e.g. metallic) upon an insulating substrate, since it is unable to exchange charge with the substrate a dielectric model should also be applicable here. At an electric field strength of around 300 kV/m (E2 = 9 104 kV2/m2) Eq. (3) predicts a stress value of sE = 0.8 N/m2 for a conducting surface and Eq. (4) predicts a stress value of sE = +0.4 N/m2 for dielectric (SiO2) particles. These values are inaccurate since they are based upon a simple geometric model and not based on measurement, however the magnitudes of these stress terms are comparable to those of the wind driven stress terms (around 1 N/m2) and are therefore significant. In the case of the conductive surface this electric field would be expected to be close to the levitation threshold in the absence of wind.
3. Experimental procedure The goal of this study is to examine the effect of an electric field upon the wind driven detachment of sand sized particles from surfaces with different electrical conductivities, specifically to compare conductive and insulating surfaces. The technique employed here was similar to that used previously for the study of wind induced detachment in which small circular deposits of granular material were placed upon a surface within an environmental wind tunnel (Merrison et al., 2007, 2008). The deposits were imaged using a camera while the wind speed within the wind tunnel was increased until the deposits were seen to be removed (i.e. the material detached). In the experiments presented here the deposits were placed within a parallel plate electrode system such that an electric field could be applied. Both conducting and insulating surfaces were used as substrates for different types of granular material. The environmental wind tunnel facility consists of an air tight chamber within which a re-circulating wind tunnel is housed. This is capable of generating wind speeds in the range of 1–20 m/s with turbulent velocity (UT) typically around 10–20% of the wind speed. The studies here have been performed at ambient temperature and pressure (i.e. around 20 °C and 1 bar respectively) and relative humidity in the range 60–80%. Wind speed calibration was performed using a commercial one dimensional Laser Doppler Anemometer (LDA) which quantified the wind speed and turbulence (Dantec Flowlite). The granular materials used in this study included soda lime glass spheres, irregular quartz particles and copper particles (see Fig. 1). These materials had been sorted by sieving to diameters in the range of 100–125 lm, however sieving is typically not a precise method for particle size separation and as seen in Fig. 1
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Fig. 1. Microscope images of the three granular materials used in the study. From left to right: glass spheres in the size range 102–124 lm, quartz particles and copper particles of sizes 106–125 lm. All three images are on the same scale.
the average glass sphere diameter appears to be significantly less than 100 lm with a broad distribution. The glass spheres were chosen since they have the benefit of having a well characterised geometry and composition (dominated by silicon dioxide) and were therefore well suited to theoretical treatment both with regard to electrical properties and wind detachment (Stoy, 1995; Jones et al., 2002; Merrison et al., 2007). The quartz particles were chosen in order to examine the effect of morphological differences. The copper particles were chosen to represent conductive granular materials. A uniform electric field was generated using a parallel-plate system (see Fig. 2) with an electrode separation, d, of 55 ± 1 mm. A metal mesh constituting the upper electrode was fastened to a glass plate for stability. This upper metal electrode was also covered by a thin plastic film in order to prevent electrical charge exchange with entrained particles. The use of a mesh was to allow imaging of the lower mounting plate (and granular samples) by the camera. A high voltage generator (Brandenburg Regulated Power Supply, model 905) was used to apply a DC voltage, V, across the upper and lower electrodes which determined the electric field strength, E. The applied voltage was typically varied between 0 and 25 kV resulting in electric field strengths of up to E 500 kV/m. Calibration of the voltage was performed using a high voltage probe (Brandenburg Solid State HV Meter, model 88 M). Note that these electrical fields were close to, but below the electrical breakdown voltage for this system. Two types of surface (substrate) material were used in this study. One was a conducting electrode consisting of a copper plate (around 1 mm thick) and the second was an electrically insulating polycarbonate plate (around 3 mm thick). In the case of an experiment requiring a conductive surface the electric field strength was given by; E = V/(d 4 mm), see Fig. 2. In the case of an experiment requiring an electrically insulating surface the copper electrode was placed under the plastic plate instead of on top of it. Here the electric field strength was given by; E = V/(d + 4.7 mm) due to combined effects of electrode separation and the presence of the dielectric plastic plate (given a dielectric constant of 2.9 for polycarbonate). Both mounting plates had been roughened using sandpaper (corn 60) resulting in a surface with a roughness scale of around 260 lm. This was intended to hinder the particles in rolling or sliding over the surface under the influence of wind. The dimensions of the copper plate electrode were 140 mm 200 mm.
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The preparation for each experiment involved forming four to six uniform circular deposits (spots) of granular material upon the substrate surface each with a diameter of 10 mm and with a separation of 10 mm. A paper mask was used to define the deposits and excess material was removed by scraping to ensure that the spots were of the same height. Due to possible electrification of the particles during deposition the granular material was left undisturbed for at least 2 h before experimentation. An overhead mirror was placed above the electrode system in order to view the sample region. The camera was mounted externally to the wind tunnel and had optical access through a window. Experiments involved installing the electrode system within the wind tunnel and applying a constant electric field. The wind speed was systematically increased every 2 min in steps of 0.6 m/s from a minimum value of around 1.3 m/s until the deposited spots were not visible which was typically between 5 and 10 m/s depending on the combination of substrate and granular material. The setup was observed for an additional 4 min as the wind and electric field were turned off. A Nikon Coolpix 8800 camera was used to document the experimental process by taking pictures of the sample area every 30 s from 1 min before the electric field was turned on and until the additional final 4 min had elapsed. The resulting image series were used in analysis. 4. Analysis Analysis of the images obtained in these studies involved determining the contrast of each individual spot of granular material in the sample area at specific wavelengths (colours) with respect to the grain free substrate. This contrast was used to quantify the degree of grain coverage within each spot. Specifically the coverage of a spot was used as a measure for the percentage of material remaining in the sample area and was calculated as the average colour value of the pixels contained within a tight rectangle around the spot for the red, blue and green filters of the image, respectively. Converting this number into percentage of total coverage is in some cases complicated due to poor contrast either due to lighting conditions or dust contamination which affect absolute colour values. A system of relative colour index calculation was therefore devised. Here the average colour value of the pixels in a rectangle enclosing the spot was calculated and compared to (divided by) similar values taken for regions in front of (or behind) the spot i.e. a background region (Merrison et al., 2007). The wind speed required for aeolian detachment is defined here as the image value (frame) at which the relative colour index has fallen to half way (50%) between its maximum (full coverage) and minimum (removed) value. The colour filter used in this analysis was chosen as the one giving greatest contrast i.e. largest difference in colour index. The final threshold detachment wind speed, U½, has been calculated as the wind speed at which the detachment image frame was observed. This value was averaged over all of the (4–6) spots in an experiment in order to generate a single measured data point. Uncertainties were determined from a combination of the finite wind speed or electric field increments and the spread in measured detachment obtained for the different spots within an experiment (standard deviation). 5. Results
Fig. 2. Schematic drawing of the electrode system used to study the effects of an electric field upon the aeolian detachment of sand sized grains (not to scale). V is the voltage applied to the electrodes. In the case of an insulating surface the copper plate was placed under the plastic plate.
In this study the measured parameter is the threshold at which particle detachment occurs and this has been quantified while varying wind speed and applied electric field. As discussed in Section 2 it would be desirable to perform comparison of the wind
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induced (sL) and electric field induced (sE) stress terms, however absolute determination of these stress components is inaccurate given their empirical nature. From Eqs. (1)–(4) it has been established that these stress components have the following dependence; sE / E2 and sL / U2. In the analysis presented here E2 and U2 have therefore been chosen to represent the stress terms. In Figs. 3 and 4 the detachment threshold wind stress has been plotted for respectively; copper grains and silicon dioxide particles (glass spheres and irregular quartz) as a function of applied electric field stress both for electrically conducting and electrically insulating substrates. Clearly there is a qualitatively different behaviour between these two types of surface. In the case of a conducting surface the effect of the applied electric field is to reduce the wind shear stress necessary to detach the material and at sufficiently high electric field strength particulate levitation is observed even in the absence of wind. When the surface is not conductive then the electric field appears to increase the stress necessary for wind shear to detach the material. These results support the prediction, that the threshold stress for wind driven detachment is increased for an insulating surface and decreased for a conductive surface. The simple vertical force balance model presented in Section 2 (Eq. (1)) implies a linear relation between sL and sE (i.e. U2 and E2). This is in reasonable agreement with the observed behaviour, especially for the copper particles (Fig. 3). However, there is a large spread in the measured data for the glass/quartz particles and possibly evidence for a more complex behaviour involving a low field suppression of these electric field induced effects. 6. Discussion Brief discussion will be made here of experimental factors which may have led to the (non-statistical) deviation from the simple vertical stress model which has been observed in the detachment data for the glass/quartz particles. Probably of most significance is that the deposited granular material typically consisted of a few layers of particulates instead of (ideally) one monolayer. Although this had the benefit that the grains could be assumed to lie upon other grains (making the simple model more realistic), it may have introduced complication to the idealised model of an immobile substrate with a single overlaid particulate especially with respect to electrical conductivity. Multiple grain layers could lead to electric charge conduction between
Fig. 3. The detachment threshold wind stress (square of the wind speed) plotted as a function of applied electric field stress (square of the electrical field) for sand sized copper particles on both conductive and insulating surfaces. Linear trend lines have been included.
Fig. 4. The detachment threshold wind stress (square of the wind speed) plotted as a function of applied electric field stress (square of the electrical field) for sand sized (SiO2) glass spheres and quartz particles on both conductive and insulating surfaces. Linear trend lines have been included.
the layers and therefore cause grain electrification in the case of an insulating substrate. This effect was also suggested in order to explain the results of electric field assisted sand transport (Rasmussen et al., 2009). In the case of a conducting substrate multiple grain layering could lead to poor electrical contact to the electrode. These effects could explain a suppression of electric field effects (see Fig. 4). In the experimental procedure employed in these studies it was unavoidable that some degree of contact electrification of the granular material occurred during deposition (Horn et al., 1993; Baytekin et al., 2011). Although no such electrification was observed in the case of a conducting surface, in the case of the insulating surface it was seen to cause enhanced surface adhesion (in the absence of an electric field) and in some cases the particles remained adhered even during physical inversion (with respect to gravity). Similarly electric field induced levitation was observed at anomalously low applied electric fields, occasionally also for an insulating surface. Although time was given for electrical discharge after grain deposition (over a 2 h time frame) this process may not have ensured complete discharge for all particles. Note also that it is probable that electrification also occurs following the detachment of a grain from the surface and led to electrification of the remaining particulates, though this should not be relevant below threshold. An effect which may have affected the spherical glass particles is that some grain detachment may have occurred as a result of rolling (horizontal torque). Although no evidence for this was observed it remains to be disproved and would complicate the simple vertical stress model presented here. The detachment process may also be made more complex by the non-uniform nature of the surface (on a lm to mm scale) which could lead to non-uniform electric fields (close to the particulates) and distortion of the lift, gravity and adhesive stress vectors. It seems clear that more precision and control is required in the preparation of the particulate samples and substrates and that direct measurement of the stress components would allow improvement in these studies. Some or all of these improvements could be addressed in the future.
7. Conclusion This study has investigated the effect of an electric field on the wind driven detachment of sand sized grains from a surface. It has
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focussed on the role that surface electrical conductivity plays in this process. Previous work has concentrated on conductive surfaces and involved electrostatic levitation and also electric field assisted Aeolian transport. It has been demonstrated here that there is a qualitative difference in the behaviour of an insulating surface. Conductive surfaces were seen to aid in the detachment process i.e. reduce the threshold wind speed for detachment, whereas a dielectric surface was seen to inhibit the detachment. For glass spheres upon an insulating surface the threshold stress for wind driven detachment was increased by more than a factor of two at an electric field of around 340 kV/m, at the same electric field the particles were levitated from a conductive surface. The behaviour of an insulating surface is well described by a simple model in which the substrate and the grains are described as dielectrics. The presence of an electric field induces chain formation leading to an attractive force towards the surface. Crudely, the magnitude of the electric field induced stress has been determined for both conductive and insulating surfaces and at these electric field intensities are seen to be comparable with those of the wind induced lift, gravitation and adhesive stresses. This supports the argument that significant alteration in detachment threshold would be expected here. Accurate determination of these absolute stress terms is, however, experimentally difficult and it has been necessary to make relative rather than absolute comparison here. References Baytekin, H.T., Patashinski, A.Z., Branicki, M., Baytekin, B., Soh, S., Grzybowski, B.A., 2011. The mosaic of surface charge in contact electrification. Science 333 (6040), 308–312. http://dx.doi.org/10.1126/science.1201512. Brook, M., Moore, C.B., 1974. Lightning in volcanic clouds. J. Geophys. Res. 79, 472– 475. Cleaver, J.W., Yates, B., 1973. Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow. J. Colloid Interface Sci. 44, 464–474, http:// dx.doi.org/10.1016/0021-9797(73)90323-8. Farrell, W.M. et al., 2004. Electric and magnetic signatures of dust devils from the 2000–2001 MATADOR desert tests. J. Geophys. Res. 109, E03004. http:// dx.doi.org/10.1029/2003JE002088. Forward, K.M., Lacks, D.J., Sankaran, R.M., 2009. Charge segregation depends on particle size in triboelectrically charged granular materials. Phys. Rev. Lett. 102, 028001. http://dx.doi.org/10.1103/PhysRevLett.102.028001. Griffiths, D.J., 1999. Introduction to Electrodynamics, third ed. Prentice-Hall Inc., New Jersey.
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Horn, R.G., Smith, D.T., Grabbe, A., 1993. Contact electrification induced by monolayer modification of a surface and relation to acid–base interactions. Nature 366, 442–443. http://dx.doi.org/10.1038/366442a0. Jackson, T.L., Farrell, W.M., 2006. Electrostatic fields in dust devils: An analog to Mars. IEEE Trans. Geosci. Remote Sens. 44, 10. http://dx.doi.org/10.1109/ TGRS.2006.875785. Jones, R., Pollock, H.M., Cleaver, J.A.S., Hodges, C.S., 2002. Adhesion forces between glass and silicon surfaces in air studied by AFM: Effects of relative humidity, particle size, roughness and surface treatment. Langmuir 18, 8045–8055. http:// dx.doi.org/10.1021/la0259196. Kamra, A.K., 1972. Visual observation of electric sparks on gypsum dunes. Nature 240, 143–144. Kok, J.F., Lacks, D.J., 2009. Electrification of granular systems of identical insulators. Phys. Rev. E 79, 051304. http://dx.doi.org/10.1103/PhysRevE.79.051304. Kok, J.F., Renno, N.O., 2006. Enhancement of the emission of mineral dust aerosols by electric forces. Geophys. Res. Lett. 33, L19S10. http://dx.doi.org/10.1029/ 2006GL026284. Lacks, D.J., Levandovsky, A., 2007. Effect of particle size distribution on the polarity of triboelectric charging in granular insulator systems. J. Electrostat. 65, 107– 112. http://dx.doi.org/10.1016/j.elstat.2006.07.010. Merrison, J.P., 2012. Sand transport, erosion and granular electrification. Aeolian Res. 4, 1–16. Merrison, J.P. et al., 2006. An integrated laser anemometer and dust accumulator for studying wind-induced dust transport on Mars. Planet. Space Sci. 54, 1065– 1072. http://dx.doi.org/10.1016/j.pss.2006.05.026. Merrison, J.P., Gunnlaugsson, H.P., Nørnberg, P., Jensen, A.E., Rasmussen, K.R., 2007. Determination of the wind induced detachment threshold for granular material on Mars using wind tunnel simulations. Icarus 191, 568–580. http://dx.doi.org/ 10.1016/j.icarus.2007.04.035. Merrison, J.P. et al., 2008. An environmental simulation wind tunnel for studying aeolian transport on Mars. Planet. Space Sci. 56, 426–437. http://dx.doi.org/ 10.1016/j.pss.2007.11.007. Merrison, J.P. et al., 2012. Factors affecting the electrification of wind-driven dust studied with laboratory simulations. Planet. Space Sci. 60, 328–335. Monin, A.S., Yaglom, A.M., 1973. Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. MIT Press, pp. 257–364. Pahtz, T., Herrmann, H.J., Shinbrot, T., 2010. Why do particle clouds generate electric charges? Nature Physics, NPHYS1631. Rasmussen, K.R., Kok, J.F., Merrison, J.P., 2009. Enhancement in wind-driven sand transport by electric fields. Planet. Space Sci. 57, 804–808. http://dx.doi.org/ 10.1016/j.pss.2009.03.001. Schmidt, D.S., Schmidt, R.A., Dent, J.D., 1998. Electrostatic force on saltating sand. J. Geophys. Res. 103 (D8), 8997–9001. http://dx.doi.org/10.1029/98JD00278. Shinbrot, T., LaMarche, K., Glasser, B.J., 2006. Triboelectrification and razorbacks: Geophysical patterns produced in dry grains. Phys. Rev. Lett. 96, 178002. http:// dx.doi.org/10.1103/PhysRevLett.96.178002. Stoy, R.D., 1995. Force on two touching dielectric spheres in parallel field. J. Electrostat. 35, 297–308. http://dx.doi.org/10.1016/0304-3886(95)00003-S. Zheng, X.J., Huang, N., Zhou, Y., 2006. The effect of electrostatic force on the evolution of sand saltation cloud. Eur. Phys. J. E 19 (2), 129–138.
Contents lists available at SciVerse ScienceDirect
Icarus journal homepage: www.elsevier.com/locate/icarus
The effects of electric fields on wind driven particulate detachment C. von Holstein-Rathlou, J.P. Merrison ⇑, C.F. Brædstrup, P. Nørnberg Mars Simulation Laboratory, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
a r t i c l e
i n f o
Article history: Received 7 February 2012 Revised 6 April 2012 Accepted 11 April 2012 Available online 25 April 2012 Keywords: Geological processes Regoliths Terrestrial planets
a b s t r a c t The effects of external electric fields upon the wind driven detachment of granular material has been investigated experimentally using an environmental wind tunnel facility. It has been shown that for sand sized grains on an electrically conductive surface there is a significant reduction in the threshold shear stress required for detachment at electric fields above 200 kV/m. However, if the surface is insulating then dielectric effects cause an increase in surface adhesion and an increase in the detachment threshold. This would be relevant in arid environments where the surface conductivity is low. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction The generation of intense electric fields close to the surface is a well-documented phenomenon and often associated with wind driven sand/dust transport events (Farrell et al., 2004; Jackson and Farrell, 2006; Schmidt et al., 1998; Kamra, 1972; Brook and Moore, 1974). This is attributed to the electrification of the sand/dust particulates during contact i.e. the processes of contact electrification or tribo-electrifcation (Forward et al., 2009; Baytekin et al., 2011; Horn et al., 1993; Merrison et al., 2006). Empirical measurements have demonstrated that during contact electrification larger grains predominantly electrify positively compared to smaller grains (Kok and Lacks, 2009; Lacks and Levandovsky, 2007; Merrison et al., 2012). Gravitational separation of these particulates, especially the suspension of dust, then leads to the generation of electric fields which are expected to be intense close to a surface. Electric fields associated with dust devil events have been measured in the range of 30–170 kV/m (Jackson and Farrell, 2006). The effects of electric fields on the wind driven detachment and transport of granular material is, however, poorly understood (Kok and Renno, 2006; Merrison, 2012; Zheng et al., 2006; Pahtz et al., 2010). In recent studies the effects of an applied external electric field on the wind driven transport rate of sand was quantified in a wind tunnel simulator in which a natural sand bed was employed. At the highest electric fields (of >250 kV/m) a significant enhancement in the transport rate was observed which agreed well with a simple model assuming a conductive sand bed and an electric field induced surface stress. However, at electric fields in the range of 150–250 kV/m there was observed a suppression ⇑ Corresponding author. Fax: +45 86120740. E-mail address: [email protected] (J.P. Merrison). 0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2012.04.011
of this electric field assisted entrainment which was attributed to poor electrical conductivity of the sand bed and possible dielectric effects of the sand particulates (Rasmussen et al., 2009). The electric field induced levitation of particles from a surface has been studied experimentally for sand sized (63 lm to 2 mm) grains and reduction in the wind driven threshold for sand transport is expected for a conductive surface (Kok and Renno, 2006). However, it is not clear that in nature the surface (for example of a sand bed) is necessarily conductive. In environments of low relative humidity (i.e. arid) it may be expected that the electrical conductivity of the soil/regolith is extremely low and may better be modelled by a (poorly) insulating surface rather than a (poorly) conductive one. Furthermore the structure of a sand bed typically consists of a complex network of physically contacting and electrically conducting chains, such that the electrical conductivity of the surface through to the subsurface is spatially non-uniform (Rasmussen et al., 2009; Merrison, 2012). An example here might be the planets Mars or Venus where the absolute humidity is low. Observations of sharp peaks of material, or razorbacks, on Mars have been suggested as evidence for the presence of chain formation in surface materials within an electric field (Shinbrot et al., 2006). The aim of this study is to investigate the effects of electric fields upon the wind driven detachment threshold for sand sized particulates at a surface. Specifically the effect of the electrical conductivity of the surface is investigated. This is intended to improve the understanding of the interaction of naturally occurring electric fields upon the transport of sand (and dust) within Aeolian events. 2. The application of detachment theory In this section a simple model of wind driven grain detachment will be presented which utilises the application of force balancing
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(Cleaver and Yates, 1973). This model has subsequently been modified with the application of an electric field induced component. The forces here have been expressed in the form of stresses and some discussion will be made of the magnitude of these stress components for these experiments based on previous detachment studies performed in the same environmental wind tunnel (Merrison et al., 2007). The stress applied to a particle at a surface by wind flow can be expressed in terms of two components, a vertical lift stress (sL) and a horizontal torque (sT). However in the experiments performed here attempts have been made to inhibit the horizontal transport of the grains (i.e. rolling) with the use of roughened substrates. As a consequence this simple model does not consider the horizontal torque component. There are two stress components which prevent particulate detachment, one being gravitation (sg) and the other adhesion to the surface (sA). The vertical component of the adhesive stress is of interest here (sA\). The application of a vertical electric field can be assumed to result in an additional vertical stress upon the particulate (sE) which can either aid or hinder detachment. The condition for the detachment of a grain from a surface (at the threshold) is that the combination of wind shear and electric field induced stress is balanced by the gravitational and adhesive stress terms.
sL þ sE þ sA? þ sg ¼ 0
ð1Þ
In previous studies the stress terms not related to the electric field have been empirically determined. This was achieved (for spherical glass particles) by measuring the threshold shear stress for wind induced detachment for hollow glass spheres of varying mass density and fitting the data to expected expressions for the adhesive, lift and gravitational terms (Merrison et al., 2007). The Newtonian expression for lift stress is given by
sL C L qU 2
ð2Þ
where q is the fluid density and CL is the coefficient of lift which has been empirically determined (Merrison et al., 2007). The friction wind speed, U⁄, is dependent on the turbulent component (i.e. standard deviation) of the wind speed UT, in this case; U⁄ UT/2.1 (Monin and Yaglom, 1973). At a wind tunnel wind speed of 5.5 m/s the turbulence (UT) was measured to be around 18%, giving a value of U⁄ 0.4 m/s and yielding a value of sL 0.7 N/m2. Note that the stress is negative indicating that it is away from the surface (upward). Particulate adhesion to a surface is linearly dependent on particle diameter via the coefficient of adhesion, Cad, which has also been empirically determined (Merrison et al., 2007). For glass spheres of diameter around 60 lm the stress term is found to be sA 0.6 N/m2. Although the gravitational term should in principle be trivial to determine, requiring knowledge only of the mass density and size of the grains, the use of a gravitational stress (sg) requires knowledge of the packing conditions of the grains i.e. the actual mass density of the granular material (qg). Glass spheres with diameters around 60 lm and mass density of 2.7 g/cm3 yield a stress of sg 1.2 N/m2. The stress applied to the conductive surface of a parallel plate electrode while creating a uniform electric field (E) is given by (Griffiths, 1999);
e sE ¼ 0 E 2 2
ð3Þ
where e0 is the vacuum permittivity and electric field, E, is vertical (perpendicular to the surface). This stress term can also be applied to calculate the stress upon a conducting grain of material in contact with (resting upon) a conducting surface as a result of applying
an electric field. The negative sign in Eq. (3) signifies that the force opposes the field direction i.e. it is vertically upwards away from the conducting plate. However, in the case of a (spherical) dielectric resting upon other identical spherical dielectric particles (i.e. an insulating surface) the application of an electric field would be expected to induce chain formation. This is analogous to chain formation observed by magnetically susceptible particulates in an applied magnetic field. A detailed theoretical treatment of contacting glass spheres in an electric field has led to the relation (Stoy, 1995):
sE ¼ F 1 e0 er E2 r2
ð4Þ
For a dielectric material with a susceptibility of around 3 (typical for glass) the term F1 3, er is the relative permittivity of the medium, which may be assumed to be 1 for ambient air (Stoy, 1995). Note that this force is positive i.e. attractive towards the surface. The assumption in this model calculation is that the glass sphere is resting on top of another sphere. Note that in the case of a conductive particle (e.g. metallic) upon an insulating substrate, since it is unable to exchange charge with the substrate a dielectric model should also be applicable here. At an electric field strength of around 300 kV/m (E2 = 9 104 kV2/m2) Eq. (3) predicts a stress value of sE = 0.8 N/m2 for a conducting surface and Eq. (4) predicts a stress value of sE = +0.4 N/m2 for dielectric (SiO2) particles. These values are inaccurate since they are based upon a simple geometric model and not based on measurement, however the magnitudes of these stress terms are comparable to those of the wind driven stress terms (around 1 N/m2) and are therefore significant. In the case of the conductive surface this electric field would be expected to be close to the levitation threshold in the absence of wind.
3. Experimental procedure The goal of this study is to examine the effect of an electric field upon the wind driven detachment of sand sized particles from surfaces with different electrical conductivities, specifically to compare conductive and insulating surfaces. The technique employed here was similar to that used previously for the study of wind induced detachment in which small circular deposits of granular material were placed upon a surface within an environmental wind tunnel (Merrison et al., 2007, 2008). The deposits were imaged using a camera while the wind speed within the wind tunnel was increased until the deposits were seen to be removed (i.e. the material detached). In the experiments presented here the deposits were placed within a parallel plate electrode system such that an electric field could be applied. Both conducting and insulating surfaces were used as substrates for different types of granular material. The environmental wind tunnel facility consists of an air tight chamber within which a re-circulating wind tunnel is housed. This is capable of generating wind speeds in the range of 1–20 m/s with turbulent velocity (UT) typically around 10–20% of the wind speed. The studies here have been performed at ambient temperature and pressure (i.e. around 20 °C and 1 bar respectively) and relative humidity in the range 60–80%. Wind speed calibration was performed using a commercial one dimensional Laser Doppler Anemometer (LDA) which quantified the wind speed and turbulence (Dantec Flowlite). The granular materials used in this study included soda lime glass spheres, irregular quartz particles and copper particles (see Fig. 1). These materials had been sorted by sieving to diameters in the range of 100–125 lm, however sieving is typically not a precise method for particle size separation and as seen in Fig. 1
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Fig. 1. Microscope images of the three granular materials used in the study. From left to right: glass spheres in the size range 102–124 lm, quartz particles and copper particles of sizes 106–125 lm. All three images are on the same scale.
the average glass sphere diameter appears to be significantly less than 100 lm with a broad distribution. The glass spheres were chosen since they have the benefit of having a well characterised geometry and composition (dominated by silicon dioxide) and were therefore well suited to theoretical treatment both with regard to electrical properties and wind detachment (Stoy, 1995; Jones et al., 2002; Merrison et al., 2007). The quartz particles were chosen in order to examine the effect of morphological differences. The copper particles were chosen to represent conductive granular materials. A uniform electric field was generated using a parallel-plate system (see Fig. 2) with an electrode separation, d, of 55 ± 1 mm. A metal mesh constituting the upper electrode was fastened to a glass plate for stability. This upper metal electrode was also covered by a thin plastic film in order to prevent electrical charge exchange with entrained particles. The use of a mesh was to allow imaging of the lower mounting plate (and granular samples) by the camera. A high voltage generator (Brandenburg Regulated Power Supply, model 905) was used to apply a DC voltage, V, across the upper and lower electrodes which determined the electric field strength, E. The applied voltage was typically varied between 0 and 25 kV resulting in electric field strengths of up to E 500 kV/m. Calibration of the voltage was performed using a high voltage probe (Brandenburg Solid State HV Meter, model 88 M). Note that these electrical fields were close to, but below the electrical breakdown voltage for this system. Two types of surface (substrate) material were used in this study. One was a conducting electrode consisting of a copper plate (around 1 mm thick) and the second was an electrically insulating polycarbonate plate (around 3 mm thick). In the case of an experiment requiring a conductive surface the electric field strength was given by; E = V/(d 4 mm), see Fig. 2. In the case of an experiment requiring an electrically insulating surface the copper electrode was placed under the plastic plate instead of on top of it. Here the electric field strength was given by; E = V/(d + 4.7 mm) due to combined effects of electrode separation and the presence of the dielectric plastic plate (given a dielectric constant of 2.9 for polycarbonate). Both mounting plates had been roughened using sandpaper (corn 60) resulting in a surface with a roughness scale of around 260 lm. This was intended to hinder the particles in rolling or sliding over the surface under the influence of wind. The dimensions of the copper plate electrode were 140 mm 200 mm.
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The preparation for each experiment involved forming four to six uniform circular deposits (spots) of granular material upon the substrate surface each with a diameter of 10 mm and with a separation of 10 mm. A paper mask was used to define the deposits and excess material was removed by scraping to ensure that the spots were of the same height. Due to possible electrification of the particles during deposition the granular material was left undisturbed for at least 2 h before experimentation. An overhead mirror was placed above the electrode system in order to view the sample region. The camera was mounted externally to the wind tunnel and had optical access through a window. Experiments involved installing the electrode system within the wind tunnel and applying a constant electric field. The wind speed was systematically increased every 2 min in steps of 0.6 m/s from a minimum value of around 1.3 m/s until the deposited spots were not visible which was typically between 5 and 10 m/s depending on the combination of substrate and granular material. The setup was observed for an additional 4 min as the wind and electric field were turned off. A Nikon Coolpix 8800 camera was used to document the experimental process by taking pictures of the sample area every 30 s from 1 min before the electric field was turned on and until the additional final 4 min had elapsed. The resulting image series were used in analysis. 4. Analysis Analysis of the images obtained in these studies involved determining the contrast of each individual spot of granular material in the sample area at specific wavelengths (colours) with respect to the grain free substrate. This contrast was used to quantify the degree of grain coverage within each spot. Specifically the coverage of a spot was used as a measure for the percentage of material remaining in the sample area and was calculated as the average colour value of the pixels contained within a tight rectangle around the spot for the red, blue and green filters of the image, respectively. Converting this number into percentage of total coverage is in some cases complicated due to poor contrast either due to lighting conditions or dust contamination which affect absolute colour values. A system of relative colour index calculation was therefore devised. Here the average colour value of the pixels in a rectangle enclosing the spot was calculated and compared to (divided by) similar values taken for regions in front of (or behind) the spot i.e. a background region (Merrison et al., 2007). The wind speed required for aeolian detachment is defined here as the image value (frame) at which the relative colour index has fallen to half way (50%) between its maximum (full coverage) and minimum (removed) value. The colour filter used in this analysis was chosen as the one giving greatest contrast i.e. largest difference in colour index. The final threshold detachment wind speed, U½, has been calculated as the wind speed at which the detachment image frame was observed. This value was averaged over all of the (4–6) spots in an experiment in order to generate a single measured data point. Uncertainties were determined from a combination of the finite wind speed or electric field increments and the spread in measured detachment obtained for the different spots within an experiment (standard deviation). 5. Results
Fig. 2. Schematic drawing of the electrode system used to study the effects of an electric field upon the aeolian detachment of sand sized grains (not to scale). V is the voltage applied to the electrodes. In the case of an insulating surface the copper plate was placed under the plastic plate.
In this study the measured parameter is the threshold at which particle detachment occurs and this has been quantified while varying wind speed and applied electric field. As discussed in Section 2 it would be desirable to perform comparison of the wind
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induced (sL) and electric field induced (sE) stress terms, however absolute determination of these stress components is inaccurate given their empirical nature. From Eqs. (1)–(4) it has been established that these stress components have the following dependence; sE / E2 and sL / U2. In the analysis presented here E2 and U2 have therefore been chosen to represent the stress terms. In Figs. 3 and 4 the detachment threshold wind stress has been plotted for respectively; copper grains and silicon dioxide particles (glass spheres and irregular quartz) as a function of applied electric field stress both for electrically conducting and electrically insulating substrates. Clearly there is a qualitatively different behaviour between these two types of surface. In the case of a conducting surface the effect of the applied electric field is to reduce the wind shear stress necessary to detach the material and at sufficiently high electric field strength particulate levitation is observed even in the absence of wind. When the surface is not conductive then the electric field appears to increase the stress necessary for wind shear to detach the material. These results support the prediction, that the threshold stress for wind driven detachment is increased for an insulating surface and decreased for a conductive surface. The simple vertical force balance model presented in Section 2 (Eq. (1)) implies a linear relation between sL and sE (i.e. U2 and E2). This is in reasonable agreement with the observed behaviour, especially for the copper particles (Fig. 3). However, there is a large spread in the measured data for the glass/quartz particles and possibly evidence for a more complex behaviour involving a low field suppression of these electric field induced effects. 6. Discussion Brief discussion will be made here of experimental factors which may have led to the (non-statistical) deviation from the simple vertical stress model which has been observed in the detachment data for the glass/quartz particles. Probably of most significance is that the deposited granular material typically consisted of a few layers of particulates instead of (ideally) one monolayer. Although this had the benefit that the grains could be assumed to lie upon other grains (making the simple model more realistic), it may have introduced complication to the idealised model of an immobile substrate with a single overlaid particulate especially with respect to electrical conductivity. Multiple grain layers could lead to electric charge conduction between
Fig. 3. The detachment threshold wind stress (square of the wind speed) plotted as a function of applied electric field stress (square of the electrical field) for sand sized copper particles on both conductive and insulating surfaces. Linear trend lines have been included.
Fig. 4. The detachment threshold wind stress (square of the wind speed) plotted as a function of applied electric field stress (square of the electrical field) for sand sized (SiO2) glass spheres and quartz particles on both conductive and insulating surfaces. Linear trend lines have been included.
the layers and therefore cause grain electrification in the case of an insulating substrate. This effect was also suggested in order to explain the results of electric field assisted sand transport (Rasmussen et al., 2009). In the case of a conducting substrate multiple grain layering could lead to poor electrical contact to the electrode. These effects could explain a suppression of electric field effects (see Fig. 4). In the experimental procedure employed in these studies it was unavoidable that some degree of contact electrification of the granular material occurred during deposition (Horn et al., 1993; Baytekin et al., 2011). Although no such electrification was observed in the case of a conducting surface, in the case of the insulating surface it was seen to cause enhanced surface adhesion (in the absence of an electric field) and in some cases the particles remained adhered even during physical inversion (with respect to gravity). Similarly electric field induced levitation was observed at anomalously low applied electric fields, occasionally also for an insulating surface. Although time was given for electrical discharge after grain deposition (over a 2 h time frame) this process may not have ensured complete discharge for all particles. Note also that it is probable that electrification also occurs following the detachment of a grain from the surface and led to electrification of the remaining particulates, though this should not be relevant below threshold. An effect which may have affected the spherical glass particles is that some grain detachment may have occurred as a result of rolling (horizontal torque). Although no evidence for this was observed it remains to be disproved and would complicate the simple vertical stress model presented here. The detachment process may also be made more complex by the non-uniform nature of the surface (on a lm to mm scale) which could lead to non-uniform electric fields (close to the particulates) and distortion of the lift, gravity and adhesive stress vectors. It seems clear that more precision and control is required in the preparation of the particulate samples and substrates and that direct measurement of the stress components would allow improvement in these studies. Some or all of these improvements could be addressed in the future.
7. Conclusion This study has investigated the effect of an electric field on the wind driven detachment of sand sized grains from a surface. It has
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focussed on the role that surface electrical conductivity plays in this process. Previous work has concentrated on conductive surfaces and involved electrostatic levitation and also electric field assisted Aeolian transport. It has been demonstrated here that there is a qualitative difference in the behaviour of an insulating surface. Conductive surfaces were seen to aid in the detachment process i.e. reduce the threshold wind speed for detachment, whereas a dielectric surface was seen to inhibit the detachment. For glass spheres upon an insulating surface the threshold stress for wind driven detachment was increased by more than a factor of two at an electric field of around 340 kV/m, at the same electric field the particles were levitated from a conductive surface. The behaviour of an insulating surface is well described by a simple model in which the substrate and the grains are described as dielectrics. The presence of an electric field induces chain formation leading to an attractive force towards the surface. Crudely, the magnitude of the electric field induced stress has been determined for both conductive and insulating surfaces and at these electric field intensities are seen to be comparable with those of the wind induced lift, gravitation and adhesive stresses. This supports the argument that significant alteration in detachment threshold would be expected here. Accurate determination of these absolute stress terms is, however, experimentally difficult and it has been necessary to make relative rather than absolute comparison here. References Baytekin, H.T., Patashinski, A.Z., Branicki, M., Baytekin, B., Soh, S., Grzybowski, B.A., 2011. The mosaic of surface charge in contact electrification. Science 333 (6040), 308–312. http://dx.doi.org/10.1126/science.1201512. Brook, M., Moore, C.B., 1974. Lightning in volcanic clouds. J. Geophys. Res. 79, 472– 475. Cleaver, J.W., Yates, B., 1973. Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow. J. Colloid Interface Sci. 44, 464–474, http:// dx.doi.org/10.1016/0021-9797(73)90323-8. Farrell, W.M. et al., 2004. Electric and magnetic signatures of dust devils from the 2000–2001 MATADOR desert tests. J. Geophys. Res. 109, E03004. http:// dx.doi.org/10.1029/2003JE002088. Forward, K.M., Lacks, D.J., Sankaran, R.M., 2009. Charge segregation depends on particle size in triboelectrically charged granular materials. Phys. Rev. Lett. 102, 028001. http://dx.doi.org/10.1103/PhysRevLett.102.028001. Griffiths, D.J., 1999. Introduction to Electrodynamics, third ed. Prentice-Hall Inc., New Jersey.
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