February 2011 

NASA/TM–2011-217048 

Method and Apparatus for the Quantification of 

Particulate Adhesion Forces on Various 

Substrates 

Christopher J. Wohl 

Langley Research Center, Hampton, Virginia 

Brad M. Atkins 

Rhodes College, Memphis, Tennessee 

John W. Connell 

Langley Research Center, Hampton, Virginia 
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February 2011 

NASA/TM–2011-217048 

Method and Apparatus for the Quantification of 

Particulate Adhesion Forces on Various 

Substrates 

Christopher J. Wohl 

Langley Research Center, Hampton, Virginia 

Brad M. Atkins 

Rhodes College, Memphis, Tennessee 

John W. Connell 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

The authors would like to acknowledge Dr. Brent Hoffmeister from Rhodes College in 

Memphis, Tennessee who contributed significantly to Brad Atkins research at Rhodes 

College and provided a wealth of experience and advice during the construction and 

initial operation of the adhesion device described herein. The authors also acknowledge 

Dr. Michael Mullins from Michigan Technological University. Dr. Mullins was the lead 

author of the literature exemplar from which the adhesion device described in this work 

was generated. He was very forthcoming with information and exhibited a sincere 

interest in the “rebirth” of research he conducted in the past. 

The authors acknowledge the NASA Langley Research Summer Scholars program hosted 

by the National Institute of Aerospace. This program enabled Brad Atkins to conduct 

research at NASA Langley for two summers and also facilitated research he conducted 

during an entire academic year at Rhodes College in Memphis, Tennessee. 

The authors also acknowledge funding from the Creative and Innovative (C&I) research 

program at NASA Langley Research Center directed by Dennis Bushnell. This program 

provided great liberty to pursue the research interests of the authors as they related to 

lunar dust adhesion mitigation and the device described herein was procured, assembled, 

and operated with funding exclusively from the C&I program. 

The authors also acknowledge the patience and assistance of Dr. Jeffrey Hinkley from 

NASA Langley’s Advanced Materials and Processing Branch. Dr. Hinkley contributed 

his time and expertise to analysis of the data and connection with fundamental material 

properties. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
1

 Begin your report below this instruction. Press F1 or Help for more. 

 

Introduction 

The timely and successful completion of lunar surface missions, manned or unmanned, will require 

overcoming several technical challenges. One of several significant challenges identified by NASA that 

could negatively impact mission operations is the presence of lunar dust.1-6 The lunar dust, comprising 

approximately 50% of the lunar regolith, is the fines portion with particulate diameters ≤ 60 m.7

 Due to 

its size, surface topography, and material properties, the lunar dust adheres strongly to exposed 

surfaces.8,9 These attributes are a result of the processes responsible for lunar dust generation. 

Micrometeoroid bombardment causes the fracturing and agglutination of lunar regolith, and has been 

associated with the formation of nanophase iron (Fe0

) deposits.10 This results in the formation of porous 

particles with sharp asperities. Additionally, exposure to UV and other energetic species results in 

electrostatic charging of the lunar dust11-14 which can lead to even greater adhesive forces. Combined, 

these properties introduced several difficulties during the Apollo missions including the abrasion of 

visors, gloves, and boots, degradation of seals and thermal radiator performance, and respiratory 

distress.15,16 Recently, the retro-reflectors deposited on the lunar surface have exhibited a decrease in 

signal intensity of a factor of ten.17 The probable source of this degradation is the accumulation of lunar 

dust on the retro-reflectors’ surface. For these difficulties to be minimized or mitigated, novel materials 

and related technologies will need to be developed to both passively and actively eliminate lunar dust 

adhesion.18-21

As new materials and technologies are developed to minimize the impact of lunar dust on exposed 

surfaces, methods need to be developed that analytically assess and quantitatively evaluate these 

approaches. Since the environmental conditions on the lunar surface and the complex combination of 

properties possessed by lunar dust cannot be reproduced in terrestrial laboratories, correlations need to be 

established between terrestrial properties and measurements, and the predicted performance on the lunar 

surface. For active mitigation strategies, such as electrodynamic dust screens,22 testing the efficacy of the 

technology is an imperative step in the technology development process and will therefore follow a very 

straightforward approach. For passive mitigation strategies (i.e., generation of low surface energy 

materials) the evaluation process is much less obvious. An example of a passive approach to lunar dust 

adhesion mitigation would be the research at NASA Langley Research Center’s Advanced Materials and 

Processing Branch, which has focused on mitigating particulate adhesion through lowering the surface 

energy of materials both chemically and topographically.18 Crude methods, such as surface particulate 

coating and inverting tests or insertion and removal of substrates from particulate filled containers,23 can 

be useful and may even offer insight into the efficacy of the tested material, but these subjective tests 

produce results that are difficult to correlate. 

Sonic particle detachment offers benefits of both qualitative and quantitative adhesion testing 

techniques. Similar to inversion tests, coating of a material with a large number of particles enables 

determination of surface clearance with many-body interactions. Likewise, adhesion forces can be 

calculated as a function of applied force comparable to that of atomic force microscopy (AFM).25,26 

Sonic particle detachment can also surmount AFM’s constraint to measure forces between a cantilever tip 

and surface rather than actual particulates. Although cantilevers can be modified via chemical 

modification of the surface or affixing objects to the tip itself, the processes can be extremely difficult and 

introduce an array of challenges that need to be overcome to obtain meaningful data.27-30 Sonic 

detachment studies can be correlated to inexpensive and routine screening techniques such as contact 

angle goniometry that permit the assessment of surface engineered materials. 

This report describes the generation and performance of a method and an instrument to evaluate the 

adhesion of particulates to surfaces of interest. An adhesion testing device, based on a literature 

exemplar,24 was used to agitate a surface coated with a monolayer of particles. The surface was 

suspended over an optical particle counter that counted the particles as they were gravitationally fed into 
2

the analytical window. Through precise control of the magnitude of sonic wand tip actuation and 

quantitative determination of the number of particles removed from and remaining on the surface at the 

end of the experimental procedure, adhesion force values were calculated. Materials with minimal 

particle adhesion forces would presumably be preferential for lunar surface applications. 

To ascertain the efficacy of surfaces for lunar dust adhesion mitigation, the forces involved with 

adhesion need to be described. Therefore, what follows is a brief description of the detachment force 

acting on adhered particles as a result of the sonic wand actuation followed by a brief analysis of the 

theory developed for particle substrate interaction forces as they relate to the work of adhesion. Next, the 

materials studied, details of instrument generation, and a description of the processes developed for data 

analysis are explained. Finally, preliminary results are described and additional thoughts are provided 

regarding incorporation of electric field and UV generation devices as an approach better emulate the 

lunar surface environment. 

Particle Detachment via Sonication 

Since the adhesion forces of particulates the size of lunar dust can greatly exceed their earth or in situ 

lunar gravitational forces, detachment techniques using substrate surface vibration necessitate relatively 

large displacement at high accelerations. These acceleration rates may be achieved using ultrasonic 

equipment where controlled oscillation is applied to a sample pre-coated with an approximate monolayer 

of particulates. For the experiments described here, the frequency of oscillation was kept constant, 20 

kHz, while amplitude was adjusted in controlled step-wise intervals from device minimum to maximum. 

This process was designed to result in detachment of particles from the sample substrate when the 

mechanical force arising from sonic wand device vibration overcame the particulate-substrate adhesion 

force. With knowing the particle’s size, the detachment force can be computed directly from Newton’s 

relationship: 

F ma Detach  (1) 

where m is the mass of a particle and a, the surface acceleration is computed from:31

a f A 2 2  4 (2) 

 where f and A denote the frequency and amplitude of oscillation, respectively. This relationship assumes 

that the change in acceleration of the sonic wand follows a sinusoidal pattern. 

Particle Adhesion Theory 

A standard first approximation in the field of particulate adhesion is to model interaction between 

particles and a sample material surface using van der Waals’ equation for adhesion force between a 

sphere and a planar surface: 

( )/(6 )

2

0 F H R d vdW   (3) 

where H’ is: 

1/ 2

1 2 H  (H H ) (4) 

where R is the radius of particulate, and do is the interfacial cut-off distance at which atomic repulsion 

occurs, H’ represents the averaged Hamaker constant, and H1 and H2 are the Hamaker constants for the 

particulate and substrate, respectively. In the studies described here do = 0.165 nm.32 Passive adhesion 

mitigation strategies consist of reducing surface energy and generating surface topographies on materials 

in order to reduce van der Waals interactions. 
3

There are several different approaches and theories that can be used to determine the work of 

adhesion, Wa, from adhesion force values. Hertz theory was developed with the assumption that there 

were no surface forces between the particle and the substrate and the contact geometry was maintained. 

Thus only van der Waals forces needed to be surmounted.33 The Johnson-Kendall-Roberts theory (JKR) 

was developed as an extension of Hertz theory. JKR considered the interactions between the particle and 

the surface within the contact area, and allowed modification of the contact geometry as a result of these 

forces. 

According to JKR theory, the adhesion force can be related to the work of adhesion by: 

Fadh RWa 2

3  (5) 

The work of adhesion can then be used to calculate the contact radius, ao, of particles adhered to the 

surface according to: 

3

1

2

0

6















  K

R W

a

 a (6) 

where K is: 

1

2

2

2

1

2 1 1 1

3

4 















    



 



  E

v

E

v K (7) 

Thus, the contact radius and ultimately the work of adhesion depend upon the Poisson’s ratio, vi, and the 

elastic modulus, Ei, of both the substrate and the particle. This value can be compared with the particle 

size to determine an embedding depth of particles on the surface. To determine the embedding depth, a 

right triangle can be envisioned consisting of sides defined as; r (contact radius), R (particle radius), and x 

as illustrated above. Using the Pythagorean theorem, the value of x can be readily determined. Thus the 

embedding depth, h, can be calculated by subtracting x from the particle radius. This assumes that there 

is no significant deformation of the particle upon adhesion. 

Materials and Methods 

Particulates Studied:

The adhesion studies described here have largely focused on using rigid spherical particulates as an 

effort to minimize experimental variables such as differences in particle shape, porosity, and composition. 
4

The particulates used were soda-lime glass particles (diameters from 10 – 70 microns) that have similar 

size domain, chemical composition and electrical conductivity as lunar simulant (NASA/USGS Lunar 

Highlands Simulant), making them excellent candidates for this adhesion study. The relevant mechanical 

properties (obtained from Valley Design Corp.) of the particulates and substrates studied here are detailed 

in Table 1. The Hamaker constants for all of the materials investigated here were obtained from literature 

sources.34

Substrates Studied:

To ascertain the efficacy of the adhesion testing device, substrates with a broad range of material 

properties (Poisson’s ratios and elastic moduli) were investigated (Table 1). A series of substrates were 

selected based on differences in surface energy. The sonic wand tip, fabricated from titanium alloy Ti6Al-4V (Aerospace Specification Metals Inc.), was investigated due to the differences in mechanical 

properties compared with the other substrates investigated here. A commercially available polyimide, 

Kapton® HN (Dupont de Nemours and Corp.) was investigated and the mechanical properties indicated in 

Table 1 were obtained from the manufacturer. A copoly(imide siloxane) (PIS) generated from 4,4’-

oxydiphthalic anhydride (ODPA), 4,4’-oxydianiline (4,4’-ODA), and an amine-terminated siloxane (a 

surface modifying agent, DMS-A21, 6100 g mol-1, Gelest Inc., 1 wt. %) were also studied. The 

copoly(imide siloxane) material was synthesized in a manner similar to that described in ref. 18. 

A two-part silicone material, Silastic T2, (Dow Corning Corporation, mechanical properties obtained 

from literature)35 was also employed to evaluate how changes in surface topography impact adhesion. 

Silicate materials exhibit pronounced adhesive interactions with silicones and as such should strongly 

adhere to Silastic T2 surfaces. To evaluate changes in surface topography, Silastic T2 material was 

molded against a laser ablation patterned aluminum substrate. The aluminum was patterned with a 

frequency-tripled Nd:YAG laser ( = 355 nm) using a 90° cross-hatch pattern resulting in an approximate 

square pillar array with feature width, height, and pitch of 25 m, 15 m, and 25 m respectively. The 

negative of this pattern, which would be an array of 15 m raised rectangular features with depressed 

central regions, was transferred to the Silastic T2 material. 

Table 1. Relevant material properties for the materials and particles studied. 

Material Poisson’s Ratio Young’s 

Modulus (GPa) 

Hamaker 

Constant (J) 

Ti-6Al-4V 0.34 114 4.0x10-19(a)

Kapton® 0.34 2.5 5.0x10-20

PIS 0.34(b) 2.7(c) 4.7x10-20(d)

Silastic® T2 0.45 0.002 4.5x10-20

Soda-lime 

Glass Spheres 0.22 72 3.1x10-20

a

Average value for metallic surfaces.

b

Assumed to be similar to Kapton®. c

Determined in-house. 

d

Taken as the geometric mean of the Kapton® and Silastic® T2 values. 

Adhesion Testing Device: 

The adhesion testing apparatus was assembled from three major components; an environmental 

chamber, a sonication device, and an optical particle counter. The environmental chamber used in this 

study was an aluminum environmental chamber (0.227 m3

 cube, Abbess Instruments and Systems Inc., 

Holliston, MA) capable of maintaining reduced atmospheric pressures down to 10-4 Torr. The chamber 

had several feedthroughs for a variety of instruments and gas inlet valves to introduce inert atmospheres, 
5

control humidity level, etc. The sonication device (Vibracell VCX-750, Sonics and Materials Inc., 

Newtown, CT) operated at 20 kHz and was capable of surface displacements (accelerations) ranging from 

12.2 m (193 km/s) to 124 m (1960 km/s) using 12.7 mm and 19 mm tips. The optical particle counter 

(OPC, Solair 3100, Lighthouse Worldwide Solutions, San Jose, CA) utilized laser scattering for particle 

detection and was capable of measurements as low as 0.1 micron. 

Although there are two possible configurations of the instrumentation within the chamber (a ‘vertical’ 

and ‘horizontal’ configuration) the work described here utilized the horizontal configuration exclusively, 

see Figure 1. In this configuration, the sonic wand tip was positioned approximately 12.7 mm above a 

collection cone that was connected to the optical particle counter with a minimal amount of tubing (the 

major drawback to the vertical configuration was the significant length of requisite tubing connecting the 

collection cone to the optical particle counter within the environmental chamber). 

Figure 1. The adhesion device assembled in a ‘horizontal’ configuration. 

Sample Preparation: 

Samples were prepared by affixing a 6 mm circle of the substrate cut from a hole punch onto the tip 

of the sonication device using a cyano-acrylate adhesive (Hot Stuff, Satellite City Inc., Simi, CA). To 

prevent contamination of the sample surface with the adhesive, a minimal amount of the adhesive was 

applied to a small diameter wooden stick which was translated in a circular motion across the middle of 

the sonic wand tip to apply a thin coating of the adhesive. Next, the sample was placed on the adhesivecoated sonic wand tip using tweezers. (NOTE: for studies involving the sonication device tip itself, 

nothing was affixed to the surface.) The prepared surfaces were allowed to dry for a minimum of 2 h 

prior to their use in the device. In order to yield accurate and reproducible adhesion data, an approximate 

monolayer coating of particulate material was necessary. To achieve an approximate monolayer coating a 

simple aerosolization technique was developed where particulates were lofted into the free space of an 

enclosed container using approximately one burst-per-milligram of particles from a compressed air 

canister (Figure 2A). Optical microscopy was used to verify the extent of particulate coating (Figure 2B). 

Particle coating was restricted to the area comparable to the hole punch size and particulates deposited 

outside this region were carefully removed using dust free laboratory wipes (Kimwipe®, Kimtech 

Sciences). If significant deviation from a monolayer was observed, the sample was carefully cleaned, as 

verified using optical microscopy, and re-coated. Pre-sonication micrographs were taken documenting 

particulates deposited on the substrate, particulate coating, size of particulate, and size of sonic wand tip 

(12.7 mm and 19 mm). These images were compared to post-sonication images to determine the percent 

of surface clearance of the sample surface. 
6

Figure 2. A) The deposition of an approximate monolayer of particles on a substrate. B) A 

12.7 mm sonic wand tip partially coated with 10 μm soda-lime glass particles and 5x and 20x 

magnified images demonstrating a coating approximating a monolayer. 

Adhesion Test Protocol: 

After the sample met the coating requirements (having a sufficient monolayer) it was attached to 

the sonic wand device, which was positioned above the optical particle counter collection cone. The 

sonic wand device and OPC were turned on and data acquisition was initiated for the OPC using a realtime data collection program (LMS Express 2006 RT, Lighthouse Worldwide Solutions, San Jose, CA) 

provided with the instrument. A total of 60 measurements were collected for an individual experiment, 

each over the span of 30 seconds with a halt period of 5 seconds between measurements, partitioned as 

follows: 1) steps 1-4 were recorded to collect information about ambient particles within the testing 

chamber, 2) every following even-numbered step recorded additional ambient background particle data, 

while every following odd-numbered step recorded particle detachment data. The particle detachment 

steps involved an iterative increase in surface acceleration via an increase in percent of maximum sonic 

wand displacement amplitude. These measurement steps are summarized in the sample data log shown 

below (Table 2). The background runs and % amplitude settings are indicated for each step number. The 

10 micron bin particle count column is included to insure that the data downloaded from the instrument 

correlates with real-time observations. 
7

For the particle detachment steps, three brief pulses of the sonic wand, lasting approximately one 

second each were applied at the percentage of maximum sonic wand amplitude displacement. The optical 

particle counter recorded particle counts according to different ‘bin’ sizes which included 1, 3, 5, and 10 

micron partitions that refer to the particle diameter. The bins included particle sizes up to the size of the 

following bin. As an example, the 3 micron bin would contain particle counts for particles ranging from 

3.0 to 4.9 microns; larger particles would be counted in the 5 or 10 micron bin according to their size. 

Table 2. A typical experimental schedule. 

Sample 

Chamber Temperature: Chamber Humidity: Date: 

Step % of Max. 

Amplitude 

10 m 

Count 

Step % of Max. 

Amplitude 

10 m 

Count 

Step % of Max. 

Amplitude 

10 m 

Count 

Step % of Max. 

Amplitude 

10 m 

Count 

1 Background 16 Background 31 46 Background 

2 Background 17 32 Background 47 

3 Background 18 Background 33 48 Background 

4 Background 19 34 Background 49 

5 20 Background 35 50 Background 

6 Background 21 36 Background 51 

7 22 Background 37 52 Background 

8 Background 23 38 Background 53 

9 24 Background 39 54 Background 

10 Background 25 40 Background 55 

11 26 Background 41 56 Background 

12 Background 27 42 Background 57 

13 28 Background 43 58 Background 

14 Background 29 44 Background 59 

15 30 Background 45 60 Background 

Contact Angle Goniometry:

Sessile drop contact angles were measured for each sample using a 8 L drop of either water or 

ethylene glycol, or a 2.25 L drop of methylene iodide on an FTA 1000 contact angle goniometer (First 

Ten Angstroms, Portsmouth, VA). Interfacial tension measurements of a suspended drop of each liquid 

were made prior to experimentation to verify the purity of the liquid and precision of the focused image. 

Contact angles were determined by drop shape analysis and standard deviations were calculated by 

comparison of the contact angles observed for each frame of a 40 frame movie collected after drop 

deposition on the sample surface. Each sample was measured at least three times.

Results and Discussion 

Data Analysis: 

After completion of the adhesion testing protocol, the sample surface was imaged using optical 

microscopy to determine percent surface clearance. For surfaces that exhibited complete clearance, the 

data from the OPC was used directly. For surfaces that did not completely clear, ImageJ software was 

used to approximate percent clearance by determining the area of the image coated with particulate 

material, Area0 and AreaF from the optical images collected before and after the adhesion testing protocol, 

respectively. To perform the particle analysis, the optical micrograph samples were converted to an 8-bit 

gray scale image and then converted to a threshold image where the lower and upper threshold limits 

were set to separate the particulate material from the substrate. Size and circularity patterns were adjusted 

to capture particle sizes of significance for the particular study. The scaling factor, Clear%, was then 

calculated according to: 
8

 *100%

0

0

% Area

Area Area Clear  F  (8) 

 An example of ImageJ analysis for a Kapton® HN film sample attached to a small sonic wand tip 

is shown below (Figure 3). 

Figure 3. ImageJ analysis of the number of pixels in the optical micrograph image that were 

assigned to adhered particles determined before and after the adhesion testing protocol. 

Before meaningful data could be obtained, background subtraction was necessary to account for 

ambient particles within the chamber. The continuous collection of background information during the 

adhesion testing protocol, as previously described enabled accurate determination of the ambient particle 

contributions. The background data was isolated and found to obey a simple exponential decay 

relationship (Eq. 9): 

where Counts(x) represents the number of particle counts for the particle bin size of interest as a function 

of the adhesion testing protocol step, x. A0 represents the initial amplitude of ambient particles, A is the 

scaling factor of the exponential decay, and B is the decay rate. Eq. 9 was fitted to the background data 

using a Microsoft® Excel® Solver add-in. The parameters determined from this fitting were then used to 

subtract the background contributions to the experimental steps that involved activation of the sonic 

wand. An example of this separation and subtraction process is shown below (Figure 4). 

Bx Counts x A Ae ( )  0  (9) 
9

Figure 4. (A) The background data collected before, after, and between experimental data 

points. (B) The experimental data subtracted from Eq. 9 yielding optical particle counter data. 

Once the cumulative count was scaled according to the Clear% value (0 at start to 100 for complete 

clearance) and the background particulate contributions were subtracted, the surface acceleration 

corresponding to Clear50% was recorded. For surface clearance at the end of the adhesion experimental 

protocol determined to be less than 100% according to Eq. 8, the surface acceleration would be adjusted 

appropriately. Thus, if a surface clearance was determined to be Clear84%, the surface acceleration would 

correlate to the value of Clear50%, not 0.5* Clear84%, which would correlate to Clear42%. An example of 

this is shown below for microspheres attached to the PIS surface (Figure 5) indicated that larger particles 

were removed from the surface at lower surface accelerations as a result of their larger mass generating 

greater detachment forces at a given acceleration. For surfaces that did not clear at least 50%, detachment 

data was classified as a minimal detachment force (indicating that the force required to remove the 

particulates from the surface was at least as large as the maximal force exerted during the adhesion testing 

protocol) and was computed using the maximum surface acceleration of the sonic wand tip. 

Figure 5. Surface accelerations correlating to Clear50% values for 3 particle sizes. 

Comparison of Detachment Force and Surface Energy: 

Low surface energy materials should exhibit decreased particle adhesive interactions relative to 

materials with greater surface energies. Thus, it should be conceivable to correlate a material’s decreased 
10

liquid wetting (increased contact angle value) to its propensity to minimize particulate adhesion. 

Unfortunately, there have been few examples in the literature linking these two properties. Thus, one of 

the objectives in this work was to determine if such a relationship was discernable. 

To compare how differences in surface energy impacted particle adhesion forces, soda-lime glass 

particles of discrete sizes were deposited on three different surfaces, the bare titanium alloy sonic wand 

tip, a commercially available polyimide (Kapton® HN), and a copoly(imide siloxane) PIS sample. The 

particle-coated surfaces were subjected to the adhesion testing protocol, and detachment force values 

were calculated from the collected particle count data (i.e., using the acceleration at Clear50%) and surface 

clearance analysis. The titanium alloy surface required the greatest detachment force for each particle 

size relative to the other two surfaces investigated in this study (Figure 6). For each material, a linear 

regression analysis was performed to determine the relationship between particle diameter and 

detachment force. The slope of the regression line was used to calculate Wa values according to the JKR 

adhesion force equation, Eq. 5. The PIS data resulted in the greatest slope (lowest Wa) indicating that this 

surface required significantly lower detachment forces for each of the particle sizes investigated and 

interpolation/extrapolation would suggest for this relationship to be maintained for other soda-lime glass 

particle sizes not investigated in this work. 

 

Figure 6. Detachment force values for soda-lime glass particles on copoly(imide siloxane) 

(triangle), Kapton® HN (diamond), and titanium (square) surfaces. 

The experimentally determined Wa values were next compared to calculated Wa values derived from 

contact angle measurements. The work of adhesion between two dissimilar surfaces can be 

thermodynamically defined as: 

where 1 and 2 are the surface energies of the two distinct surfaces, particle and substrate respectively, 

and 12 is the interfacial interaction energy.34(a) Since the interfacial interaction energy term cannot be 

determined using contact angle measurements, one approach to calculate the work of adhesion between 

surfaces is to partition the surface energy of a material into dispersive and polar contributions, 

d

 and 

p

respectively, where the total surface energy, 

tot , is simply the sum. Then, the work of adhesion between 

these surfaces is approximated as the geometric mean of these components.36 

1 2 12     Wa (10) 

1/ 2

1 2

1/ 2

1 2 2( ) 2( ) d d p p Wa       (11) 
11

To calculate Wa using surface energy contributions, contact angle goniometry experiments were 

performed on each of the investigated surfaces with a microscope slide as a representative of the sodalime glass particles. Contact angle values were determined on each surface using water, ethylene glycol, 

and methylene iodide which were used to calculate total, dispersive, and polar surface energies using the 

Kaelble plot according to Eq. 12.36 The results are shown in Table 3. 

Table 3. Contact angle values and surface energy parameters. 

Surface Contact Angle (°) Surface Energy (mN m-1) 

 Water 

Ethylene 

glycol 

Methylene 

Iodide 

tot d p

Glass Slide 45 31 47 53 30 23 

Titanium 63 63 54 39 25 14 

Kapton® HN 85 60 49 36 33 3 

Copoly(imide siloxane) 101 86 74 20 18 2 

Using Eq. 11, Wa values were calculated from the surface energy parameters from Table 3. These 

values were then compared to the Wa values obtained from the adhesion testing device according the JKR 

analysis (Eq. 5). There is a clear linear relationship between the Wa values determined experimentally, 

using the adhesion testing device, and those derived thermodynamically, using contact angle 

measurements (Figure 7). To the authors’ knowledge, a similar relationship has only been directly 

investigated in one other instance.37 One caveat to this analysis is that although a linear trend was 

observed, additional electrostatic interactions resulting from highly polarized or ionic functionalities 

present on high surface energy material surfaces would likely result in deviation from this observed 

relationship. 

Figure 7. Comparison of Wa values determined experimentally (y-axis) and calculated using 

contact angle goniometry (x-axis). 

   

1/ 2

1/ 2 1/ 2

1/ 2 ( ) ( )

2

1 cos 















   d

L

p

p L

S

d

S d

L

L



  



  (12) 
12

Variation of Surface Topography: 

 The impact of surface topography on adhesive interactions was investigated by measuring the 

required detachment force and Clear% of soda-lime glass particles on Silastic® T2 surfaces that were 

cured on either flat or patterned surfaces from a laser ablation patterned aluminum template. The 

Silastic® T2 was determined to sufficiently wet the patterned aluminum surface as indicated by optical 

microscopy, and exhibited topographies that were the negative of the aluminum template. Effectively, the 

pattern could be described as a roughened surface, on the micron and sub-micron scale, with 

approximately 25 m holes arranged in a rectangular array. The generated surfaces were then coated with 

particulates and subjected to the adhesion test protocol to determine the detachment force and Clear%. As 

indicated in Table 4, the detachment forces required to remove the soda-lime particles from the patterned 

Silastic® T2 surface were dramatically reduced relative to those required on a flat surface. Similarly, the 

Clear% values improved significantly for the patterned surfaces. Both of these results indicated that the 

surface topography reduced the available surface area for particle adhesion thereby reducing the required 

detachment force for adhered particles. 

Table 4. Adhesion testing experimental results for patterned and un-patterned Silastic® T2 surfaces. 

Surface 

Particle 

Radius 

(m) 

Adhesion 

Force (N) Clear%

Contact 

Radius (m)a

Silastic® T2 12.5 40 < 50 8.4 

20 150 < 50 15.3 

Silastic® T2, 

patterned 

12.5 6.4 75 4.6 

20 86 100 12.7 

a

Calculated according to Eq. 6 

JKR Analysis and van der Waals Forces: 

The contact radius of the adhered particles was calculated for each surface studied according to Eq. 6. 

Using previously described geometric relationships, the embedding depth of the adhered particles was 

also determined and found to be on the nanometer scale for all surfaces except the Silastic T2 surfaces, 

which were determined to have embedding depths as large as 35% of the particle radius. Particles 

adhered to the patterned Silastic T2 surface were calculated to have significant reductions in contact radii 

(Table 4). Molecular level origins of the adhesive interactions between particles and substrates can be 

investigated by calculating the contribution to the adhesion force from van der Waals interactions 

according to Eq. 3 (Table 5). To fully account for the adhesive interactions present in the systems 

investigated here, Eq. 3 would require additional scaling terms to account for surface roughness and 

electrostatic adhesion affects such as contact charging of particles which can increase adhesion.38-40 

However, for the purposes of this work, these additional contributions were not considered. The van der 

Waals contributions were calculated for adhered 25 micron soda-lime glass particles and were found to be 

significant for each surface studied (Table 5). Discrepancies between the calculated and experimental 

adhesion force values (last column in table 5) may arise from other interactions (capillary force, 

electrostatic interactions, etc). The magnitudes of capillary forces and electrostatic interactions are 

currently being investigated. 
13

Table 5. Determination of van der Waals contribution to adhesion force values for adhered 25 m 

soda-lime glass particles. 

Material H’ (J) FvdW (N) Fadh (N) Fadh ‐ FvdW (N)

Ti-6Al-4V 1.6x10-19 1.3x10-6 12.0x10-6 -6.7x10-7

Kapton® 5.9x10-20 4.5x10-6 9.9x10-6 5.4x10-6

PIS 5.7x10-20 4.3x10-6 4.0x10-6 -3.4x10-7

Silastic® T2 5.6x10-20 4.3x10-6 40.0x10-6 3.6x10-5

Conclusions 

An adhesion testing device was assembled and initial results were collected to quantitatively evaluate 

adhesive interactions between surfaces and micron-sized particles with an emphasis towards lunar surface 

applications. The experimental design was organized to evaluate adhesive interactions enabling 

assessment of the efficacy of low surface energy materials developed for lunar dust adhesion mitigation. 

Optical particle counter data was collected and data processing practices implemented to obtain 

meaningful data relative to the sonic wand activity. Sonic wand acceleration values were determined for 

Clear50% particle counts which were used to calculate adhesion forces. Preliminary results indicated that 

the adhesion force can be quantitatively determined for particulates on an array of substrates using this 

device. These adhesion force values were then used to calculated work of adhesion using JKR theory. A 

relationship between this work of adhesion values and those determined by contact angle goniometry 

measurements was revealed indicating that surface energy can be used as a predictive tool for adhesive 

interactions. Topographical modification of surfaces was also found to play a significant role in adhesive 

interactions with a reduction in available surface area resulting in a significant reduction in adhesion 

forces. Van der Waals contributions to adhesion forces were calculated and found to be less than those 

determined experimentally, likely due to other contributions not considered, i.e., capillary forces, 

electrostatic interactions, etc. 

Summary and Outlook 

There are a number of modifications that would engender this device with greater analytical 

capabilities. Implementation of a sonication device allowing both variation of the sonication amplitude 

and frequency would facilitate a broader variation of the investigated detachment forces. Utilization of an 

optical particle counter with true real-time detection capabilities would dramatically reduce the duration 

of a single experiment. Research is currently underway to develop integrated software systems capable of 

such measurements. Similarly, the use of an optical particle counter with broader, partitioned, particle 

size detection capabilities more closely aligned with the investigated particle sizes would lend greater 

confidence to the collected data. Another modification would be to house this assembly of instruments in 

a slightly larger environmental chamber which would allow for the sonic wand to be oriented in a vertical 

position relative to the optical particle counter while maintaining a position over the collection cone. This 

would result in all of the forces acting on adhered particles to be oriented normal to the sample plane. 

The array of possible interactions between a lunar dust particle and a surface necessitates the 

development of different instruments oriented to investigate the impact of each interaction on adhesion 

strength. Although the instrument described here does not address all of the plausible contributions to 

adhesion, it is possible to make modifications to incorporate additional components. For example, the 

environmental chamber can be flushed with dry nitrogen and, with the aid of a humidity sensor, the 

impact of capillary forces can be addressed. Different particulate media can be utilized that better 

simulates lunar dust. There are several different types of lunar simulant and for the purposes of 

addressing particulate adhesion and contamination issues, the NASA/USGS Lunar Highlands Simulant 

with particle diameters less than 30 microns will be utilized. 
14

Similarly, research is currently underway to incorporate an electric field generating device to evaluate 

how the presence of electric fields may impact lunar dust adhesion. Motivation to include charging 

affects arises from the particulate coating technique described here which may lead to contact charging of 

particles. In addition, the complex dynamically charged lunar environment not only contributes to the 

charging and transport of lunar dust, but may also influence adhesion through charge polarization 

interactions for sufficiently large electric fields.41 Electric fields of magnitude ~ 1 kV/m have been 

predicted in lunar terminator regions and areas of sharp contrast between illuminated and shaded surfaces 

such as lunar craters.42 Such regions may be preferential exploration sites because prolonged shaded 

regions of lunar craters may contain ice deposits43 and therefore it is critical to generate adhesion 

mitigation materials that can perform effectively in such an environment. An electric field generation 

module has been developed and its implementation into the adhesion testing device and preliminary 

results are currently being evaluated.44

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Space Administration, manuscript in preparation. 
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Method and Apparatus for the Quantification of Particulate Adhesion 

Forces on Various Substrates

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Wohl, Christopher J.; Atkins, Brad M.; Connell, John W.

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14. ABSTRACT

Mitigation strategies for lunar dust adhesion have typically been limited to qualitative analysis. This technical memorandum 

describes the generation and operation of an adhesion testing device capable of quantitative assessment of adhesion forces 

between particulates and substrates. An aerosolization technique is described to coat a surface with a monolayer of 

particulates. Agitation of this surface, via sonication, causes particles to dislodge and be gravitationally fed into an optical 

particle counter. Experimentally determined adhesion force values are compared to forces calculated from van der Waals 

interactions and are used to calculate the work of adhesion using Johnson-Kendall-Roberts (JKR) theory. Preliminary results 

indicate that a reduction in surface energy and available surface area, through topographical modification, improve mitigation 

of particulate adhesion.

15. SUBJECT TERMS

Lunar dust; Particle adhesion; Sonication; Surface engineering

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