Clathrate Adhesion Induced by Quasi-Liquid Layer
The adhesive force of clathrates to surfaces is a century-old problem of pipeline blockage for the energy industry. Here, we provide new physical insight into the origin of this force by accounting for the existence of a quasi-liquid layer (QLL) on clathrate surfaces. To gain this insight, we measure the adhesive force between a tetrahydrofuran clathrate and a solid sphere. We detect a strong adhesion, which originates from a capillary bridge that is formed from a nanometer-thick QLL on the clathrate surface. The curvature of this capillary bridge is nanoscaled, causes a large negative Laplace pressure, and leads to a strong capillary attraction. The microscopic capillary bridge expands and consolidates over time. This dynamic behavior explains the time-dependent increase of measured capillary forces. The adhesive force decreases greatly upon increasing the roughness and the hydrophobicity of the sphere, which founds the fundamental basics for reducing clathrate adhesion by using surface coating.
Introduction<!>Preparation
of Clathrate Surfaces<!><!>Coating of Silica Spheres<!>Measurement of the Adhesive
force<!>Probing the Contact Area<!>Modeling Capillary Forces<!>Experimental Observations<!><!>Experimental Observations<!>Origin of Large Capillary
Forces in Premelting
Region<!><!>Origin of Large Capillary
Forces in Premelting
Region<!>Dynamic Nature of Microscopic Capillary Bridge<!><!>Dynamic Nature of Microscopic Capillary Bridge<!><!>Dynamic Nature of Microscopic Capillary Bridge<!><!>Conclusions
and Remarks<!>
<p>Adhesive forces between clathrates and solid surfaces are a field
of practical importance.1−6 Especially, this force causes a century-old problem of clathrate
agglomeration and the consequence of pipeline blockage in the oil
and gas industry. However, the origin of adhesion forces for clathrate
surfaces is poorly understood. Recently, it was reported that clathrate
surfaces are not rigid solids but covered by an intrinsic nanometer-thick
quasi-liquid layer (QLL) due to surface premelting.7−11 However, to what extent the QLL affects the adhesion
force of clathrate surfaces was not understood. Therefore, we carry
out force measurements and theoretical modeling to find out how the
QLL affects the adhesion of clathrate surfaces to other solid surfaces.</p><p>Fundamentally, clathrates are solid structures composed of water
and guest molecules.12−14 The structures are sustained by the hydrogen bonding
of water molecules that leads to an ice-like framework of water which
acts as a host structure. Guest molecules are incorporated in the
regular cavities of the host structure.15 In this way, clathrate structures encapsulate guest molecules up
to mole fractions of an order of 0.1, although most guest species
are hydrophobic and nearly insoluble in liquid water.15 In nature, the largest part of methane on Earth is encapsulated
in natural clathrates under subsea and permafrost sediments.15,16 Natural clathrates constitute a vast source of low-carbon energy
but also a significant environmental hazard due to potential large-scale
emissions of methane as a potent greenhouse gas.16,17 Meanwhile, synthetic clathrates are considered as the next generation
material for fuel gas storage.18−23 For example, hydrogen can be loaded into a hosting clathrate formed
by tetrahydrofuran (THF) up to a mass fraction of 4.0 wt %.24 High storage capacity and slow liberation of
gas upon dissociation enable efficient and safe storage of fuel gas
based on clathrates.24,25 Nevertheless, clathrates are
a major safety hazard in the oil and gas industry. Residual water
present in crude oil or natural gas tends to form clathrate particles
which then accumulate at the pipe surfaces and plug the flow.26−28</p><p>For all fields mentioned above, the adhesive force between
clathrates
and natural or technical surfaces plays a significant role. This force
drives the adhesion of clathrate particles to pipe surfaces in oil
and gas pipelines and leads to plugging.26−28 Similar problems
happen in the facilities for clathrate productions, e.g., for storage
of fuel gas. Synthetic clathrates tend to attach to equipment walls,
accumulate, and finally block the reactors and circulation systems.
Natural clathrates contact and interact with a variety of natural
solid matters through clathrate-solid interfaces.29−31 The interaction
at the interfaces influences the mechanical and physiochemical stability
of the clathrate deposits. Thus, a better understanding of adhesion
forces is required for exploiting natural clathrates.</p><p>Here,
we outline the physics of adhesion forces induced by a nanometer-thick
QLL on clathrate surfaces. Our calculations are in good agreement
with measured adhesion forces acting between a flat clathrate surface
and a solid sphere. Using the configuration of a flat clathrate surface
interacting with a well-defined, spherical solid particle, we are
able to assess the role of the nanoscale QLL for the adhesion. In
applied systems, usually clathrate particles interact with flat surfaces
such as the pipeline wall. However, preparation of clathrate particles
with smooth, well-defined surfaces is hardly achievable.1,2,32,33 The arbitrary shapes of clathrate particles would complicate the
theoretical analysis of the adhesive forces. More importantly, the
adhesive force between a solid sphere and a flat clathrate surface
is comparable to the force between a clathrate sphere and a flat solid
surface (Supporting Information). Furthermore,
we explore the expansion and consolidation of the QLL-formed capillary
bridge between the clathrate surface and the solid sphere, which leads
to solid–solid adhesion and increased adhesive force at prolonged
contact times. On the basis of the capillary nature of the adhesion
mechanism, we develop a simple and efficient coating with defined
roughness and hydrophobicity for reducing the clathrate adhesion.</p><!><p>We used the clathrate
of deuterated tetrahydrofuran (THF-d8,
C4D8O 99.5 atom % D, Carl Roth GmbH) because
we used the same stock solution for nuclear magnetic resonance (NMR)
experiments.34 The independent NMR experiments
were performed in parallel addressing the origin of phase transitions
in clathrates.34 Hereafter, the THF-d8 clathrate may be simply referred to as "clathrate".
Clathrates were prepared in a freezer at atmospheric pressure through
the following steps. A volume (70 Î¼L) of a stoichiometric solution
(mole ratio: ) was deposited on a plastic slide. A glass
slide was imposed in parallel to the plastic one to confine the solution
in the gap (Figure 1). The sample was then cooled down to −15
°C in a freezer. Finally, the plastic surface was removed and
a clathrate slab remained on the glass slide.</p><!><p>Setup for the measurement
of adhesive force and the probe of the
expansion of the contact area. Experiments were carried out in a cold
box (details provided in the Supporting Information).</p><p>Model of the resulting nano capillary bridge
(green domain) which
induces an adhesive force between the sphere and clathrate surface.
Drawing is not to scale.</p><!><p>We tuned the hydrophobicity
of the silica spheres (R = 0.8 mm) via adding a coating
to it. The original silica sphere has a contact angle (θ) around
10° with stoichiometric THF-d8 solution.
Silica spheres were coated in three ways. Gold coating: a 20 nm-thick
layer of gold was coated on the surface of silica spheres using the
sputter method (BAL-TEC, MED 020 Coating System) under argon plasma
at 10–5 at. Teflon coating: Teflon has been identified
as having very low free surface energies and low adhesive properties.35 A silica sphere was dip-coated in a solution
of 4 wt % Teflon AF1600 in FC-43 solvent (Sigma-Aldrich) for 1 min.
After removing the sphere from the solution, it was annealed at 160
°C for 12 h for complete removal of the solvent and consolidation
of the Teflon film. It resulted in a stable Teflon film of 400 nm
thickness covering the silica sphere. Rough hydrophobic coating: Microspheres
(mean diameter 10 Î¼m, Bangs Laboratories Inc.) were dispersed
in the aforementioned Teflon solution to 5 wt % concentration by shaking
and 30 min sonication. Then, the coating was implemented through the
same dip-coating procedure as described for Teflon coating. The surface
of the silica sphere (R = 0.8 mm) was coated by microspheres
who themselves were coated by a Teflon film. These three methods led
to contact angles of 62°, 115°, and 140° with the solution
of dissociated THF clathrate, respectively. Details about coating
and contact angle measurements are discussed in the Supporting Information.</p><!><p>We developed a home-built
setup for measuring the adhesive force between a clathrate surface
and a solid sphere (Figure 1). Hollow microcapillary glass tubes were used as mechanical
force sensors36,37 (Figure S3). Each sphere was glued to the middle of a force sensor using epoxy
glue. Having the sphere positioned in the center of the force sensor
while both sides of the force sensor can move freely in a horizontal
direction avoids any sliding motion of the sphere relative to the
clathrate surface (Figure 1). This improved feature provides a better accuracy of the
force measurements (Figure S5). We used
two different geometries of force sensors, which allowed measuring
the minimum forces of 0.7 Î¼N and 3.5 Î¼N, respectively
(Figure S3). The x,y-translation stages were used to move the sphere laterally
on the clathrate surface for measurements at different locations.
A motorized z-translation stage engages the clathrate surface toward
the sphere until it gently touches the sphere. After a defined contact
time, the surface is withdrawn at a speed of 0.07 mm/s. The sphere
adheres to the clathrate surface until the restoring force exerted
by the force sensor exceeds the adhesive force. The adhesive force
is determined in accordance to Hooke's law: F = k × Δx. Force sensors
having a spring constant (k) of 0.45 N/m were used
for the original silica spheres and the gold-coated spheres. Force
sensors having k = 0.026 N/m were used for the Teflon-coated
spheres and the rough hydrophobic spheres. Spring constants were measured
by applying reference weights to the center point of the force sensors.
The deflection of the force sensor, Δx, is
defined at the center of the capillary tube and measured using a side-view
camera.</p><p>Experiments on clathrate surfaces were conducted in
a home-built "cold box" having an internal volume of
2 m3. Sample and setup are handled with gastight gloves
fixed to the transparent front side of the cold box (Figure S4). The temperature (T) and relative
humidity (RH) were constantly monitored (KLIMALOGG Pro, TFA, accuracy
of ±0.1 °C and ±1%), respectively. The temperature
is confirmed by a parallel measurement with a thermocouple (±0.1
°C) and a multimeter (EX505, Extech Instruments). Details are
provided in the Supporting Information.</p><!><p>This experimental setup is
similar to the force measurement (Figure 1). A 0.3 mm thin clathrate slab is used for
better transparency. The clathrate surface is driven vertically to
touch the sphere, and the evolution of the contact area is recorded
by a video microscope (Olympus) from below.</p><!><p>We propose
a simple model to describe the physical origin of the adhesive force.
Our model accounts for the premelting nature of clathrate surfaces
by treating the premelting layer as a QLL on a solid clathrate substrate.
As depicted in Figure 2, the approaching sphere displaces a volume of quasi liquid (V1, yellow region) and leads to the formation
of a microscopic meniscus, i.e., nano capillary bridge (V2, green region). This displacement happens as soon as
the sphere touches the surface of the QLL. For a short time after
the attachment, the total volume of quasi liquid is considered constant,
thus V2 = V1. The meniscus induces a capillary force (Fca) acting between the sphere and the clathrate surface.</p><p>Capillary force Fca is the sum of the
integral of the normal component of the interfacial tension around
the neck (FÎ³) and
the contribution of the Laplace pressure acting over the contact area
(FΔP).38,391</p><p>Here, the minus signs
indicates an attractive force. γ, ,
and r are the interfacial
tension of the quasi liquid and the two principal radii of curvature,
respectively (Figure 2). For geometric reasons,  and r can be expressed
as a function of the contact angle θ of the quasi liquid with
the sphere surface (Supporting Information):23</p><p>R, δ, and β are the sphere radius,
thickness of the QLL, and the filling angle, respectively. In the
initial phase, where the sphere has just penetrated the QLL but the
meniscus has not yet grown much, the geometric parameters are constrained
by the condition of V1 ≈ V2. Assuming V1 = V2, the parameters can be expressed by eq 4 (Supporting Information):4</p><p>It is noted that eq 4 only contains β as a variable. Other parameters are constants
for a given physical system (R, θ, and δ).
The QLL thickness (δ) is a temperature-dependent parameter.40−42 However, quantitative data on the QLL on clathrate surfaces are
very rare. Our recent experiments showed δ ≈ 10 nm for
the QLL on the surface of semiclathrate formed by tetrabutyl ammonium
bromide at −4 °C.7 This value
(10 nm) agrees with typical thickness of QLL on pristine ice surfaces
at temperatures of several minus degrees centigrade.41,42 Therefore, we used Î´ = 10 nm as a representative and constant
value for the clathrate in our model, without considering a likely
temperature dependence of the QLL thickness. To estimate the surface
tension of the quasi liquid, we measured the surface tension of a
dissociated THF clathrate at 4 °C and obtained γ = 33.5
mN/m. This value is used in our model.</p><p>Equation 4 can be
solved numerically to obtain β, which is used for calculating , r, and Fca in eq 1–3.
In particular, we vary θ in
a range between 10° and 160° to study the effect of the
surface hydrophobicity of the solid on the capillary force.</p><!><p>When measuring
the adhesive force between the clathrate surface and solid spheres
in dependence on temperature, three regions can be distinguished (Figure 3a). The measured
forces were normalized by dividing the value by the radius of the
sphere. For spheres with contact angle ≤ 115°, weak forces
are observed at T < −5 °C. In this
region of low temperatures, the QLL might vanish or become discontinuous
so that the clathrate surface behaves like a typical solid that does
not form a capillary bridge to the sphere. As a result, the adhesive
forces are low. The second region spanning from −5.0 to 2.0
°C corresponds to the "premelting region" since
the temperatures are below the dissociation point of the clathrate.
This premelting region is associated by a 1 order of magnitude increase
of the adhesive force (Figure 3a). We attribute such large adhesive forces to the formation
of a nano capillary bridge between the clathrate surface and the sphere
due to the QLL (section 2.2). Such nano capillary bridges cause capillary forces. For
temperatures > 2.0 °C, named here as "dissociated region",
the capillary forces decrease substantially before staying at constant
values (Figure 3a).
The clathrate softened at 2.0 °C and dissociated gradually. Complete
dissociation observed at 4.0 °C results in a THF-d8 solution interacting with the sphere (inset in Figure 3a). The present observation
of gradual dissociation of THF-d8 clathrate
agrees with our recent nuclear magnetic resonance experiments.34 The THF-d8 clathrate
does not have a fixed dissociation point; instead, it dissociates
gradually in the temperature range from 2 to 4 °C.34</p><!><p>(a) Normalized adhesion force measured between a THF-d8 clathrate surface and a solid sphere (R = 0.8 mm) with different coatings and 0.5 min contact
time. Inset
images visualize the adhesion in the premelting region and the dissociated
region for the experiments using an original silica sphere. Background
colors of the graph indicate three distinct temperature regions disucssed
in the text. (b) SEM image of the surface of a rough hydrophobic sphere
coated by microspheres and a Teflon film on the top. (c) Close look
at a Teflon-coated microsphere on the rough hydrophobic sphere. (d)
Concept of the reduced contact area between a rough hydrophobic sphere
and a clathrate surface (not to scale).</p><!><p>Our experiments reveal that the capillary force between the clathrate
surface and the hydrophilic sphere is largest in the premelting region.
For the original silica sphere, the capillary force is on the order
of 1000 mN/m. In this region, the QLL thickness is on the order of
10 nm.7,41,42 We recorded
optical images close to the maximum force values in both premelting
and dissociated regimes (insets in Figure 3a). For the dissociated clathrate at 4 °C,
the liquid deforms visually over a large vertical range and creates
a macroscopic capillary bridge. Despite that large meniscus deformation,
the capillary force at 4 °C is an order of magnitude smaller
than that at −2.5 °C. This finding is intriguing and is
not reported so far in the literature although an order increase in
adhesive force in the premelting region is of profound importance
as mentioned in the introduction section.</p><p>The measured capillary
forces decrease with increasing contact
angle of the sphere (Figure 3a). In particular, the large capillary forces in the premelting
region vanish for the rough hydrophobic (superhydrophobic-like) sphere.
Only a low normalized force of 4.2 mN/m was observed instead. This
low capillary force is ascribed to the reduced contact area of the
rough hydrophobic sphere with the QLL on the clathrate surface as
discussed below.</p><!><p>In order to understand the force increase in the premelting
region, we plotted the normalized capillary force ()
calculated from eq 1 for
γ = 33.5 mN/m, δ = 10 nm,
and R = 0.8 mm versus contact angle (Figure 4a). The calculated normalized
capillary force decreases with increasing contact angle, i.e., increasing
hydrophobicity of the sphere. For example, the normalized capillary
force is 833 mN/m for a hydrophilic sphere (θ = 10°) but
is reduced to 25 mN/m for a superhydrophobic sphere (θ = 160°).</p><!><p>(a) Normalized
calculated capillary force versus the experimental
force. (b) The Laplace pressure force and the normal surface tension
force. (c) The radii of curvature. These parameters were calculated
using eqs 1–3. The plots of Fγ and  are scaled accordingly to fit the graphs.
Each data point for the experimental force is the averaged force in
the temperature region between −2.5 and 0.0 °C, taken
from Figure 3a, contact
time of 0.5 min.</p><!><p>The decrease of the calculated
capillary force upon increasing
the hydrophobicity of the sphere is in quantitative agreement with
our experimental results (Figure 4a). Both the magnitude and the hydrophobicity-dependence
of modeled forces are reproduced by experiments. For original silica
spheres (10°) and gold-coated spheres (62°), the differences
between experimental and modeled forces fall within the experimental
errors (Figure 4a).
Significant apparent discrepancy is observed only for the rough hydrophobic
sphere (140°) where the modeled force is 97.4 mN/m while the
measured force is only 4.2 mN/m. This discrepancy arises from the
fact that the modeled force (97.4 mN/m) was calculated based on a
smooth hydrophobic sphere of 0.8 mm radius and 140° contact angle.
However, experiments were carried out on a sphere coated by 10 Î¼m
particles to form a rough sphere (Figure 3b,c) with effective contact angle of 140°.
Note that this contact angle could not be achieved for any smooth
surface.43,44 This rough sphere contacts the QLL only
through a number of the microspheres (Figure 3d). Taking this contact configuration into
account, we calculated the expected capillary force by applying our
model to each microsphere contacting the QLL (Figure 3d). The calculated capillary force varies
in a range between 2.8 and 8.6 mN/m (sum of capillary forces acting
on microspheres contacting the QLL divided by the apparent radius
of the big silica sphere), depending on the coverage (i.e., density)
of the microspheres coated on the silica sphere. The calculated force
falls in the same range of the measured force. Hence, the model provides
a universal physical principle for describing the capillary force
between a solid sphere and clathrate surface.</p><p>When comparing
the contributions of the Laplace pressure force
(FΔP) and the surface tension force
(FÎ³) to the total
capillary force (Fca), we find that the FΔP dominates (Figure 4b). Moreover, FΔP is very sensitive to the hydrophobicity of the solid surface. This
force decreases from 831 mN/m at θ = 10° to 23 mN/m at
θ = 160°. In contrast, the surface tension force Fγ only decreases slightly
from 1.5 to 1.4 mN/m for the same contact angle increase. Meanwhile,
the radius of curvature r is 3 orders of magnitude
smaller than the radius  (Figure 4c). For example, r increases strongly
from 5 nm at θ = 10° to 168 nm at θ = 160°,
whereas  only decreases slightly from 5.6 Î¼m
at θ = 10° to 5.5 μm at θ = 160°. The
nanoscaled radius (r) of curvature gives rise to
the dominating Laplace pressure force compared to contribution of
the surface tension force (Figure 4b,c). In other words, the nanoscaled radius of curvature r is the determining factor of the capillary force at clathrate
surfaces.</p><p>Incorporating the modeling results with the experimental
force
in Figure 3a leads
to the following conclusions. First, the capillary force induced by
a nano capillary bridge in the premelting region is large because
of a small respective radius r. Second, the capillary
force induced by macroscopic meniscus in the dissociated region is
weak because of a much larger corresponding radius r. Third, the decrease in the capillary force upon approaching the
temperature of the dissociated region can be explained by the rapid
thickening of the QLL. In general, QLL thickens as the temperature
increases9,42 and leads to an increasing radius r. Finally, low adhesive forces in the low-temperature region
are explained by a vanishing or discontinuous QLL. The latter makes
the clathrate surface behave solid-like, with only van der Waals forces
acting.</p><p>In the experiments described so far, we have used a
short contact
time of 0.5 min. During this initial phase of the sphere-clathrate
attachment, the nano capillary bridge forms and dominates the adhesive
force between the two objects. The measured adhesive force is fully
described by the capillary force in our model (Figure 4a) based on the approximation V1 ≈ V2. For longer
contact times, the measured forces increase (discussed below) and
exceed the forces predicted by our model. This suggests that the initial
meniscus formed by displacement of quasi liquid from the contact zone
is followed by a further growth of the meniscus volume. This will
invalidate the condition V1 ≈ V2 and lead to a change of the meniscus shape.
This dynamic change of the capillary bridge is discussed below.</p><!><p>The normalized measured adhesive forces increase with increasing
contact time (Figure 5). Although the measured forces exhibit different degrees of dependence
on the contact time and the temperature, all curves show a similar
"bell" shape with maximum values in the premelting region.
This universal "bell" shape provides further evidence
of the crucial role of the QLL in governing the adhesive forces of
clathrate surfaces.</p><!><p>Time-dependent normalized adhesion force between a THF-d8 clathrate surface and an original silica sphere
(a) or a Teflon-coated silica sphere (b). Both systems show a significant
increase of adhesive force in the premelting region.</p><!><p>Our model can explain the time-dependent increase of the
measured
adhesive forces in Figure 5. A large negative Laplace pressure in the capillary bridge
(FΔP in Figure 4b) would drive a flow of quasi liquid into
the neck and lead to the expansion of contact area and volume of the
capillary bridge (Figure 6a). Assuming that the equilibrium thickness (Î´) of the
QLL has a fixed value for a given temperature, the increased volume
of quasi-liquid at the neck would induce the formation of additional
solid clathrate in the contact region (Figure 6b). This drives the formation of a molecular
solid–solid (clathrate-sphere) contact that will lead to an
additional adhesion. We ascribe the time-dependent increase of the
measured adhesive force to the growing contribution of this solid–solid
adhesion.</p><!><p>Proposed dynamic nature of the microscopic capillary bridge. Red
dashed arrows indicate the flow of quasi liquid driven by negative
Laplace pressure. Blue arrows indicate the expansion of the contact
area by maintaining equilibrium thickness of QLL. Black arrows indicate
the consolidation of the neck upon formation of additional clathrate.
We assume that the QLL is in equilibrum with its bulk, and its thickness
therefore remains constant.</p><!><p>We confirm the growth of the contact area with time using optical
microscopy (Figure 7). The rate of contact area expansion increases with temperature.
At −3 °C, the initial diameter (within time scale of seconds
after the attachment) of the contact area is ≈20 μm which
falls in the same order with the modeled diameter, i.e., 2 ×  =
11 Î¼m in Figure 4c. At a given contact time, for example 30
s, the contact area increases with the temperature (Figure 7), possibly due to the growth
of QLL thickness. At 1 °C, the expansion of the contact area
and the formation of additional clathrate happens at a significant
rate that can be viewed by the side-view optical camera (Figure S8).</p><!><p>Expansion of the contact area between
THF-d8 clathrate surface and original
silica sphere as imaged on
an inverted microscope. The thickness of the clathrate slab was 0.3
mm. Patterns in the images possibly arise from the boundaries between
crystal domains.</p><!><p>Conventional understanding attributes the adhesion
between a clathrate
surface and a solid surface to macroscopic water droplets sitting
on either the clathrate surface or the solid surface. Such macroscopic
water droplets, termed "free water", form macroscopic
capillary bridges and create capillary forces. This common mechanism
of clathrate adhesion discussed in the literature is similar to the
"dissociated region" in Figure 3a where a macroscopic capillary bridge is
observed at, for example, 4 °C. However, the increase of the
adhesive force in the premelting region and the role of the QLL-induced
nano capillary bridge as the origin of such strong adhesion have never
been reported before. We proved that the QLL-induced capillary attraction
is the origin of the large adhesive force between clathrates and solid
substrates.</p><p>The additional formation of clathrates at a capillary
bridge has
been discussed in the literature using the term of "sintering"
effect.45 The "sintering"
effect was considered to take place only upon addition of fresh water
droplets. Again, those macroscopic water droplets could have created
apparent capillary bridges between a clathrate and a counter surface.45 However, the consolidation effect explored in
our study is induced by quasi-liquid flow and is governed by the interfacial
premelting of the clathrate. No newly added "free water"
is required nor involved in this consolidation effect discussed. Therefore,
the present consolidation effect differs in nature from the "sintering"
effect discussed in the literature.</p><p>The concept of surface coating
for reducing clathrate adhesion
have been considered by previous studies.5,46−49 We further proved this concept based on our theoretical and experimental
evidence. The ultralow adhesion of the clathrate to rough hydrophobic
(superhydrophobic-like) surfaces enables the removal of the attached
clathrate particles by the viscous shear forces that are always present
in hydrocarbon flow. For practical applications, however, the coating
must have sufficient durability and robustness to withstand physical
and chemical attritions (e.g., sand erosion) caused by actual conditions
in pipelines.</p><!><p>Sphere coatings, contact
angle measurement; force sensors;
control of temperature and elimination of mechanical vibration; improved
feature of our experimental design; equations for calculating the
angle β; expansion and consolidation of contact area at 1 °C;
solid sphere-clathrate surface and clathrate sphere-solid surface
(PDF)</p><p>jp1c06997_si_001.pdf</p><p>Open access funded by Max
Planck Society.</p><p>The authors
declare no competing financial interest.</p>