Ice Adhesion Measurements of Ice Mitigation Coatings

Pertinent to Aircraft Icing

Prashanth Beeram1, Rye Waldman2, Hui Hu3 ()

Department of Aerospace Engineering, Iowa State University, Ames, Iowa, 50010

Aircraft anti-icing/de-icing is one of the important areas of concern in current aerospace research.

One of the several techniques that are currently identified to address this problem is the use of special

ice mitigation coatings which can be applied to prevent or reduce the adhesion of ice on the essential

control surfaces. Measurement of ice adhesion strength through shear test is a common method to

evaluate the ice phobic performance of such coatings. In the present study, a static ice shear testing

mechanism was developed to investigate the effectiveness of different surfaces and super

hydrophobic coatings. Furthermore, the ice adhesion test model was validated and the measurement

uncertainties related to geometric parameters of the model were identified using finite element

analysis model and subsequently validated with the ice adhesion experiment.

I. Introduction

ircraft operating in cold conditions are at risk of ice accretion over aircraft wings that significantly degrade flight

performance and may pose a danger to safety [1]. To mitigate the detrimental effects of accreted ice, various de-

icing/anti-icing techniques are employed to eliminate, reduce, or prevent ice accretion on the aircraft. Traditional

approaches to de-icing have utilized heating or de-icing fluids to melt ice and mechanical devices to breakup and shed

the accreted ice. The energy requirements of the heating and mechanical anti-icing devices must be minimized to

realize an efficiency benefit from the applications of anti-icing techniques. Passive anti-icing techniques are highly

desirable because they may reduce or eliminate the cost penalty associated with active anti-icing techniques. Future

generation of aircraft will require an effective anti-/de-icing solution to extend their operating capabilities, improve

safety, and reduce operating costs in cold weather.

Heating entire surfaces is an inefficient approach to anti- and de-icing. The ice accretion process is a complex

interaction of mass and heat transfer [2]. The strength of the convective cooling varies across the surface of the body,

such that uniform surface heating leads to hot and cold regions on the airfoil surface. Furthermore, under some

conditions the ice melt may simply run back and re-freeze at a downstream location beyond the region protected by

thermal de-icing device to cause uncontrolled ice accretion [3]. The distribution of the water and ice on the wing is

determined by a coupled mass and energy balance. The amount of added heat required to melt the ice accretion depends

on the local convective heat transfer. In cases where refreezing may occur, fully evaporative heating may be required.

The challenge for constructing an effective anti- and de-icing solution for aircraft is applying only the required power

to active de-icing in the required locations, while utilizing passive coatings to reject the water runback and ice accretion

in regions with the requisite aerodynamic forces.

Recently, functionalized surfaces have been proposed as candidates for anti-icing applications. One type of

functionalized surfaces is the class of superhydrophobic surfaces. Experiments have demonstrated that some

superhydrophobic coatings do have icephobic properties [4], that droplets can bounce off of cold superhydrophobic

surfaces without phase change [5], and some authors assert that superhydrophobicity directly implies anti-icing

functionality [6]. The superhydrophobicity of the surface results from a combination of chemical hydrophobicity with

a micro- or nano-textured surface. The structure of the surface plays an important role both in the wettability of the

surface and in the ability of the surface to resist ice accretion [4]. An alternate surface coating strategy attempts to

1 Graduate Student, Department of Aerospace Engineering. 2 Postdoctoral Research Associate, Department of Aerospace Engineering. 3 Martin C. Jischke Professor, Dept. of Aerospace Engineering, AIAA Associate Fellow, Email: huhui@iastate.edu

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9th AIAA Atmospheric and Space Environments Conference

5-9 June 2017, Denver, Colorado

AIAA 2017-3928

Copyright © 2017 by Prashanth Beeram, Rye Waldman, Hui Hu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA AVIATION Forum

reduce the surface adhesion strength by using a lubricating fluid impregnated in the coating matrix [7,8]. In these

coatings, a lubrication fluid (such as an oil) prevents a strong bond between the ice and the surface. Diffusion

replenishes any lubricant lost from the surface (e.g., lubricant is lost during an ice shedding event), making these

surfaces robust and self-healing.

The choice of surface treatment on an airfoil will determine how impinging water and ice interact with the wing

surface. The adhesion forces between the water or ice and the surface resist the aerodynamic stress that act on surface

water and ice accretions, therefore the surface chemistry of the wing plays a critical role in the dynamics of surface

water runback, the shape of ice accretions, and the strength of the bond between the surface and accreted ice [9–12].

Specialized water- and ice-phobic coatings are currently undergoing development for use as viable strategies to

assist mitigating impact ice accretion on aircraft. While most of those coatings have undergone simple and static tests

to demonstrate water- and ice-phobic characteristics, very little work has been done to prove their capabilities extend

to rime and glaze ice in-flight conditions (i.e., with dynamic impingement of super-cooled droplets at very high impact

velocity of 50 m/s or greater). There are various approaches to surface coating design. Superhydrophobic coatings

provide a surface with extremely low wettability and water adhesion forces. The effect of surface wettability on the

glaze ice accretion process over a wing surface is readily apparent in Figure 1, which shows how a superhydrophobic

wing surface reduces the area of the wing covered in ice. Here, the aerodynamic stresses from the airflow over the

wing surface sweeps away super-cooled water droplets from most of the wing's surface. However, ice still forms at

the leading edge in the vicinity of the stagnation line. This highlights one of the major challenges facing water- and

ice-phobic coating strategies. These coatings produce low adhesion forces between the water and/or ice and rely on

aerodynamic stresses acting tangentially to the surface to remove the accretion. This approach breaks down at the

stagnation line because the required shear stress near the stagnation line is very small or completely vanishes. Further

exacerbating the problem is that the collection efficiency is a maximum at the stagnation line. This example illustrates

how coatings that are effectively ice-phobic at nominal conditions may not perform well under in-flight impact icing

conditions.

Figure 1. Ice accretion on an airfoil with and without a superhydrophobic treatment. The superhydrophobic

coated wing (left) shows significantly less ice on top of the wing surface compared to the untreated wing

(right); however, the leading edge ice accretion is thicker on the superhydrophobic wing. Ice adheres at the

leading edge, regardless of treatment [12].

The performance of ice mitigation coatings under in-flight conditions is challenging to study, because the harsh

environment consisting of micron-sized super cooled liquid water droplets carried at high speed by cold air impacting

a surface is difficult to recreate in a benchtop laboratory experiment. Furthermore, the stress state acting on the accreted

ice depends on the location and shape of the ice accretion on the body and in the aerodynamic flow. Our approach to

better understanding the performance ice mitigation coatings is to experimentally investigate the adhesion strength of

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surface coatings in a repeatable benchtop test, and to use a numerical model to understand the stresses created in the

test. This study will provide a point of reference for future studies of ice mitigation coatings under in-flight conditions

in an icing wind tunnel. First, a simple, standalone ice adhesion strength experiment is utilized to characterize the ice

adhesion strength of ice formed in a static, cold environment. The adhesion strength experiment is designed to allow

repeatable stress states to be induced at ice-surface interface, and the delamination force and displacements to be

determined. Then, a finite-element model of the adhesion experiment is constructed to determine the relationship

between the forces and displacements applied during the adhesion experiment to the stress state at the ice-surface

interface; hence, the stress distribution at the delamination surface is known.

II. Methods

A. Static ice adhesion strength test.

The experimental study was performed in a shear force adhesion strength facility available in the Aerospace

Engineering Department of Iowa State University (ISU). The configuration of the experiment is similar to an ice

adhesion strength measurement system utilized to test polymeric anti-icing surfaces [9, 15]. A cylindrical ice sample

is frozen on a temperature controlled substrate, and a probe applies a lateral force to the sample to shear it off of the

surface. Figure 2 shows diagram of the experiment, which identifies the geometry of the ice cylinder diameter, D, the

mold shell thickness, t, the height of the displacement probe, h, and the probe contact face height, δ.

Figure 2. Diagram of the ice adhesion experiment. The probe applies a fixed displacement in the x-direction.

The specimen diameter, mold thickness, probe height, and contact face size D, t, h, and δ, respectively, are

identified. The broken line indicates the only symmetry plane in the experiment. The ice sample is blue, the

3-d printed mold is orange, and the substrate is gray.

The experiment consists of an environmental chamber housing a digitally controlled Peltier cooler (TETech CP-

061 and TC-48-20) and a linear actuator with integrated motion controller (Newport CONEX-LTA-HS) that drives a

40N range force-torque transducer (JR3 30E12A4) supporting an aluminum force probe. The force signals were

recorded by a 16-bit data acquisition card (NI PCI-6052E). A 3D-printed ice mold is used to create a 6 or 8 mm

diameter ice cylinder on the test substrate. Very low adhesion strength materials may require larger sample diameters

of 12, 14, 16, or 18 mm, where the total force required to delaminate the ice sample is expected to scale as D2. In

general, the size of the ice sample must be tuned to the test substrate and the force range of the transducer. The

experiment is depicted in Figure 3.

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Figure 3. Ice adhesion experiment configuration.

The test substrates were a 50 mm square plates over which the control surfaces were created. The testing include

aluminum surfaces with different roughness or surface finish were hand polished using sandpaper grits of P220, 400,

1000, 2000 and a 4um polishing compound (higher sand paper grit indicates lower surface roughness of aluminum).

The aluminum substrate was also used as a base for applying coatings and films which include commercial

superhydrophobic coatings like Hydrobead®, NeverWet® and other hydrophobic surfaces like Teflon, PFA. The

SLIPS (Slippery Liquid Infused Porous Surface) is another super hydrophobic surface [17] used which was prepared

by impregnating a thin, porous cloth in oil and allowed to dry for sufficient time before sticking to the aluminum

substrate. The Hydrobead and NeverWet were spray coated, whereas the Teflon and PFA were thin films adhered to

base plate. In addition, Rustoleum® enamel spray paint was also used as a source of reference to compare the ice

adhesion performance of other surfaces.

The test procedure started with clamping the test plate onto the cooler. Next, the ice mold was placed onto the

surface, and a syringe was used to inject deionized water into the mold, ensuring that no air bubbles were trapped

underneath. The lid to the environmental chamber was closed, and the chamber was allowed to fill with carbon dioxide

released from sublimating dry ice. The CO2 displaced the humid air from the test chamber, preventing condensation

from forming on the test surface. The Peltier cooler was turned on and set to the test temperature of -8°C, and allowed

to stabilize for 15 minutes, allowing the water sample to freeze and the temperature to remain steady during the test.

While the temperature stabilized, the force probe was aligned with the sample and set at 0.5 mm above the test surface.

A custom MATLAB code sampled the voltage signals from the force transducer at 2000 Samples/s. First a 10 second

force tare measurement was recorded prior to bringing the probe into contact with the ice sample. Then forces were

recorded while the linear actuator stage was moved at a rate of about 0.5 mm/s, until the sample was sheared of the

surface. Because the force values for time step are easily discernable in the data, a force vs displacement relationship

can be inferred from the known probe speed and time taken for the interface failure as shown in Figure 8.

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The MATLAB code applied the transducer’s calibration matrix to the voltage signals, and divided by the sample’s

area to compute the average shear force per adhesion area. The adhesion strength was taken as the maximum force-

per-area observed before failure. Each test surface was measured multiple times for a reliable measure of the average

and standard deviation of the measured adhesion strengths.

B. Parametric FE model of ice adhesion experiment

A finite element model of the adhesion strength experiment is used to quantify the stress distribution at the ice-

substrate interface. A linear static model was built and solved using ANSYS. The model geometry was defined based

on the geometry illustrated in Figure 2. The problem size was reduced by a factor of two by using the symmetry

condition transverse to the loading direction. Figure 4 gives the schematic for the geometric model.

Figure 4. Geometric model for the finite element study

The geometry of the ice cylinder diameter, D, the mold shell thickness, t, the height of the displacement probe, h,

and the probe contact face height, δ, are all parameters that were defined in ANSYS. The probe contact area was

approximated as a square region, therefore, in the half-model, is defined as δ/2 wide. In actuality, the probe will contact

increasingly larger regions of the shell as the applied loading increases and the shell deforms; however, the point of

this model is to capture the stresses at the ice-substrate interface rather than the stress details in the plastic mold under

then probe contact face. Therefore, the fixed area approximation with dimension of 0.07 x 0.25 in (where δ = 0.07 in)

was employed to keep the analysis linear, and avoid the substantial modelling complexity and expense associated with

a nonlinear contact problem.

All three material regions were modeled as linear elastic materials with Young’s Modulus Y and Poisson ratio υ.

The aluminum properties are Y=68.9 GPa and υ=0.33, the ice properties are Y=9.332 GPa and υ=0.3252 (from [13]),

and the VeroWhite 3d-printed plastic properties are Y=2.5 GPa and υ=0.35. The boundary conditions used for the

model were to approximate the clamped edges of the test plate with a fixed displacement at the model edge. The

displacement of the force probe was enforced over the contact patch as a prescribed nodal x-displacement at the contact

patch face (Figure 5a) and symmetry condition was applied along the centerline of the model (Figure 5b)

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(a) Fixed support condition (blue), close up shows the where the probe displacement (yellow) is applied

(b) Symmetry displacement (red)

Figure 5. Model Boundary Conditions

A mesh refinement study was performed with three different meshing pattern; Unstructured meshes with auto-

generated tetrahedral and hexahedral quadratic elements as well as a structured hexahedral mesh (sweep) with a user

defined divisions and spacing. The mesh depicted in Figure 6 is the finest structured mesh, which employed 20

elements through the mold shell, 20 elements between the substrate and the bottom of the applied load, and 40 elements

across the contact patch.

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Figure 6. Structured mesh

The finite element parametric analysis was considered for three cases with the diameter (d), thickness (t), probe

height (h) as defined in Figure 2 as a single variable in each case. Table 1 shows the geometric values for all three

cases.

Table 1. Summary of parametric study cases

Case Diameter

(mm)

Probe Height

(mm)

Shell thickness

(mm)

1 6, 8, 10, 12, 14, 16, 18, 20 0.5 0.5

2 20 0.1, 0.25, 0.5,0.75, 1, 2, 5 0.5

3 20 0.5 0.1-0.9 (0.1 mm interval)

1-8 (1mm interval)

Subsequently, ice adhesion measurements for the three cases were also obtained using to validate the finite element

simulation results. The experimental procedure was followed in a similar fashion as mentioned in the previous section

using multiple sizes of plastic 3-D printed tubes. In order to contain any water leak from the underside of the plastic

molds, water is carefully transferred into the cylinder at sub-zero temperature to speed up the freezing process.

A. Ice adhesion strength experiment results

The ice adhesion strengths measured are summarized in Table 2 below. The adhesion strength of aluminum was

evaluated with specified surface finish obtained using sandpaper of known grit sizes. The ice adhesion results of

aluminum 220 and 400 grit finishes are within the range of previously reported measured adhesion values of ice to

bare aluminum [14] while the results for stainless steel surface were similar to that of the data reported previously [9].

Each coating’s adhesion strength was compared to the Rust-oleum enamel reference by calculating the adhesion

strength reduction factor by dividing the observed adhesion strength of each coating with the adhesion strength of the

enamel coating. Figure 7 shows the table data, comparing the measured adhesion strengths of the different test

surfaces.

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Table 2. Summary of adhesion strength experiment results

Figure 7. Summary of ice adhesion strength experiment results

The ice adhesion strength results in Table 2 shows that the Hydrobead and NeverWet commercial

superhydrophobic surfaces are not significantly effective in reducing the ice adhesion compared to aluminum surfaces.

Interestingly, only SLIP surface indicated ice phobic properties with adhesion strength below 100 KPa. Moreover, the

roughness study on aluminum presented a seemingly linear relationship with ice adhesion strength as reported in

earlier research for hydrophilic surfaces [16].

The experimental results helped to find out the displacement and strain properties of the ice-substrate interface

using the force data recorded by the load sensor connected to the probe. In figure 8(a), the raw data is shown where

the ratio of applied force recorded from the load sensor to the ice sample area is plotted for the time elapsed since the

initiation of the experiment and until after the ice is broken at the aluminum substrate interface. The maximum value

of this ratio or peak stress is considered as the adhesion strength of ice on a surface. From the initial force and time

data, we could obtain the displacement result as shown in the figure 8(b) along with the stress-strain curve. The load-

displacement curves here depict almost linear relationship which suggests the elastic behavior of ice bonding

mechanism. However, a little non-linearity is also visible which could be attributed to the elongation properties of the

plastic shell that holds the ice or perhaps it could also be related to the non-linearity of the adhesion mechanism itself.

Test

surface

Surface label Number of

trials

Average adhesion

strength[MPa]

Std. deviation

[MPa]

Adhesion strength

reduction

1 Al, 220 Grit 10 0.45 0.07 3.1

2 Al, 400 Grit 10 0.39 0.06 3.6

3 Al, 1000 Grit 10 0.34 0.04 4.2

4 Al, 2000 Grit 10 0.30 0.06 4.7

5 Al, mirror finish 10 0.13 0.06 10.6

6 Enamel 10 1.40 0.13 1.0

7 Teflon 10 0.42 0.06 3.4

8 Hydrobead SHP 10 0.37 0.09 3.8

9 SLIPS 10 0.06 0.01 25.7

10 PFE 10 0.57 0.06 2.5

11 Stainless steel 10 0.55 0.13 2.5

12 NeverWet 10 0.42 0.04 3.3

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(a). Aluminum control surface force-per-area vs time

(b). Applied force vs Displacement (c).Shear stress vs strain

Figure 8. Force-per-area measurement results

B. Parametric study results.

The mesh refinement study was performed by computing the results from a 1um probe displacement on the various

meshes, using quadratic element orders. The models ranged in size from around 30,000 nodes in the very coarsest

mesh, all the way up to 2 million nodes in the most refined quadratic hexahedral mesh. The total reaction force at the

probe prescribed displacement face and the total force transmitted through the ice-substrate interface were computed

by integrated the surface tractions over the respective surfaces. The results were computed by sampling the derived

stresses at the nodes. When the mesh is sufficiently refined, it is expected that both of these methods should yield

similar results. Additionally, the ratio of ice-substrate interface force to the reaction force at the probe was computed

and plotted as a function of the mesh refinement. The mesh refinement study results are summarized by the results

shown in Figure 9. The results in Figure 9(a) and 9(b) show that the magnitude of the forces in the model converge

when given sufficient mesh refinement. Here, the fully refined meshes with quadratic order elements were required to

achieve convergence.

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(a). The probe reaction force per 1µm displacement as a function of the number of nodes in mesh model

(b). The force supported by the ice-substrate interface.

(c). The ratio of the force supported at the ice-substrate interface to the applied load.

Figure 9. Mesh refinement study results. The results from the tetrahedral element meshes are shown in

yellow, while the hexahedral mesh results are shown in red and structured mesh (sweep) shown in blue.

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The relationship between the stress distributions and the experiment parameters such as the sample size, D, the

mold shell thickness, t, and the height of the probe above the substrate, h, were investigated, to allow the comparison

of the adhesion strength results.

Figure 10(a) and 11(a) indicates the normal stress distribution contours for 6mm and 20mm diameter ice cross

section. The effect of moment is seen in both cases where there is tension (in red) on the probe side and compression

on the other side (in blue). It also shows a localized downward stress near the probe contact region which could

contribute to the failure initiation with bi-directional stress distribution concentrated in that region. In plane

comparison for both cases shows that smaller cross section could result in prominent shear stress distribution as seen

in Figure 10(b) and 11(b).

The effect of this stress distribution, however, can be better understood from the Figure 12 which compares the

results for both experimental and finite element studies. The blue line shows the change in adhesion strength with

different sample diameters. Based on this graph, we can identify that the adhesion stress decreases with increasing

diameter where the 6mm and 20mm have values around 0.35 MPa and 0.2 MPa respectively. In addition, the finite

element study shows that there is an increase of transmitted force fraction with larger diameter or sample areas. These

results could support the argument that stress distribution can influence the peak forces recorded when breaking an

ice sample over the substrate. It can be explained that the smaller diameter shell requires higher adhesion stress to

break the sample than the larger diameter one because the bi-directional normal stress created due to effect of moment

and probe contact (Figure 10(a)) will tend to increase the stresses within the ice rather than the interface which

contributes more toward cohesive failure mechanism than adhesive failure.

(a). z-stress distribution (b) zx-shear stress distribution

Figure 10. Stress distributions at the ice-substrate and mold-substrate interface for 6mm ice diameter with

the probe being applied a fixed displacement from the left side.

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(a). z-stress distribution (b) zx-shear stress distribution

Figure 11. Stress distributions at the ice-substrate and mold-substrate interface for 20mm ice diameter with

the probe being applied a fixed displacement from the left side.

Figure 12. Parametric study results for diameter (a) Experimental shear strength results plotted in blue vs

diameter of ice sample (b Finite element result showing force fraction vs. diameter of ice sample.

The stress contours in Figure 13 (a) and 13(b) describes normal and shear stress for probe height location of 2mm

from the test surface. It is quite evident that the stress magnitudes are quite less when compared to the 0.5mm probe

height case shown in Figure 11(b) and 11(b). The possible reason is because the probe location reduces the propagation

of contact stresses to the substrate interface which result in mild stress distribution at the interface. This phenomenon

can be better explained from the Figure 14. The finite element study shows that the transmitted force fraction steadily

increases from 0 mm to 0.8 mm probe height and steadies out beyond 1 mm probe height cases. It is also interesting

to see that the experimental results for adhesion strength as indicated by blue line shows a similar effect of probe

height compared to the finite element results. The adhesion strength slightly decreases from 0 to 1 mm and stays

almost constant up to 5mm height. Then the line goes up for 8mm probe height case which is due to the influence

cohesive failure of ice created by the moment resulted as force application moves away from the interface. This was

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evident from the ice residue on the substrate after the experiment for 8mm probe height case. However, the overall

effect of probe height on ice adhesion results is not as significant as the influence of ice sample area.

The results of the last parametric study case are shown in Figure 15 and Figure 16 for 5mm thick plastic shell.

The stress contours in Figure 15 (a) and 15 (b) show that the increase in mold thickness reduces the stress distribution

due to the slightly lower transmitted force fraction as seen in Figure 16. The experimental results show that a linear

increase of adhesion strength with the increase of plastic shell/mold thickness. This could be due to higher force

requirement for a thicker shell model when an equal displacement is applied compared to a thinner model. However,

the effect of thickness can be neglected based on the results obtained here which are not significant enough to influence

the overall adhesion strength and are also within the measurement uncertainties of the experiment.

(a). z-stress distribution (b) zx-shear stress distribution

Figure 13. Stress distributions at the ice-substrate and mold-substrate interface for 2 mm probe height case

with the probe being applied a fixed displacement from the left side.

Figure 14. Parametric study results for probe height ‘h’ (a) Experimental shear strength results plotted in

blue vs diameter of ice sample (b Finite element result showing force fraction vs probe height.

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(a). z-stress distribution (b) zx-shear stress distribution

Figure 15. Stress distributions at the ice-substrate and mold-substrate interface for 5 mm mold thickness with

the probe being applied a fixed displacement from the left side.

Figure 16. Parametric study results for thickness (a) Experimental shear strength results plotted in blue vs

diameter of ice sample (b) Finite element result showing force fraction vs mold thickness.

III. Conclusion

An ice adhesion strength measuring test rig was designed and operated to assess the ice adhesion characteristics

over different surfaces. In addition, effect of surface roughness on ice adhesion is analyzed over a bare aluminum

surface with different surface finishes which indicated a linear relationship where the roughness increased the adhesion

force required to break off the ice. Furthermore, the superhydrophobic coatings like Hydrobead, NeverWet and SLIPS

were tested out and noticed sizable difference between their ice adhesion strengths which could point out that not all

superhydrophobic coatings are effective anti-icing coatings. Therefore, suggesting the requirement for more in depth

understanding of factors affecting such a

Perhaps the most import feature of this study is the numerical model of the ice adhesion experiment which evaluated

the stress state at the ice-substrate interface and validated with the experimental data. Although, the design and

working mechanism of this experiment were already employed in other experiments, the stress distribution of ice

specimen model was not thoroughly studied for this kind of shear testing experiment. This was performed to identify

some of the uncertainties related to the ice adhesion model parameters such as the mold thickness, diameter and probe

location. Subsequently, it was identified that geometric aspects of the model could indeed influence the average

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adhesion strength for a given surface. The diameter study showed that smaller ice sample areas might overestimate

the results due to the stress distribution effects. The probe height study also indicated a suitable distance between the

force probe and the test surface that could reduce the propagation of contact stress on the ice sample.

Based on the capability of the current model of the ice adhesion experiment, it is possible to further investigate the

effectiveness of other coatings and surfaces for anti-icing surfaces. In addition, the ability to obtain the force-

displacement properties of the ice bonding over a surface can be used to develop an analytical model for obtaining

ice-substrate interface characteristics.

IV. Acknowledgments

The research work is partially supported by NASA grant number NNX16AN21A, with Mr. Richard Kreeger as

the technical officer, and the Iowa Space Grant Consortium Base Program for Aircraft Icing Studies, with Dr. Richard

Wlezien as the director. The authors also gratefully acknowledge the support of the National Science Foundation under

award numbers CBET-1064196 and CBET- 1435590.

V. References

[1] Bragg, M. B., Broeren, A. P., and Blumenthal, L. A., “Iced-airfoil aerodynamics,” Progress in Aerospace Sciences, vol. 41,

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