The formation and evolution of immersed surface micro- and nanobubbles are essential in various practical applications, such as the usage of superhydrophobic materials, drug delivery, and mineral flotation. In this work, we investigate the entrapment of microbubbles on a hydrophobic surface, structured with microwells, when water flow passes along, and the subsequent microbubble dissolution. At entrapment, the microbubble is initially pinned at the edge of the microwell. At some point, the three-phase contact line detaches from one side of the edge and separates from the wall, after which it further recedes. We systematically investigate the evolution of the footprint diameter and the contact angle of the entrapped microbubbles, which reveals that the dissolution process is in the constant contact angle mode. By varying the gas undersaturation level, we quantify how a high gas undersaturation enhances the dissolution process, and compare with simplified theoretical predictions for dissolving bubbles on a plane surface. We find that geometric partial blockage effects of the diffusive flux out of the microbubble trapped in the microwell lead to reduced dissolution rates.
The formation and evolution of immersed surface micro- and nanobubbles are essential in various practical applications, such as the usage of superhydrophobic materials, drug delivery, and mineral flotation. In this work, we investigate the entrapment of microbubbles on a hydrophobic surface, structured with microwells, when water flow passes along, and the subsequent microbubble dissolution. At entrapment, the microbubble is initially pinned at the edge of the microwell. At some point, the three-phase contact line detaches from one side of the edge and separates from the wall, after which it further recedes. We systematically investigate the evolution of the footprint diameter and the contact angle of the entrapped microbubbles, which reveals that the dissolution process is in the constant contact angle mode. By varying the gas undersaturation level, we quantify how a high gas undersaturation enhances the dissolution process, and compare with simplified theoretical predictions for dissolving bubbles on a plane surface. We find that geometric partial blockage effects of the diffusive flux out of the microbubble trapped in the microwell lead to reduced dissolution rates.
Submicron surface bubbles, namely nanobubbles
at solid–liquid
interfaces with heights between 5 and 100 nm and footprint diameters
between 50 and 800 nm, have extensively been studied over the last
2 decades.[1] The surface bubbles play an
important role in various chemical and physical processes and have
numerous potential applications,[2] such
as mineral flotation and separation,[3] transport
in nanofluidic devices,[4] nanostructured
surface fabrication[5,6] or application in the context
of catalysis and electrolysis.[7,8] So far, various theoretical
and experimental studies have been performed to investigate surface
nanobubbles[9,10] and their intriguing properties,
such as their stability, their small contact angle, and collective
effects.[1,11−14] Surface nanobubbles can be obtained
by several methods,[1] such as solvent exchange,[9] spontaneous generation at immersion,[10] electrochemical or catalytic production,[15] etc. However, it is still challenging to achieve
full control over the formation of surface nanobubbles.To achieve
such controllable generation of nanobubbles, it is essential
to understand the formation mechanism. The so-called crevice model
has been proposed to explain the formation mechanism of nucleating
surface micro and nanobubbles, e.g., under pressure reduction.[16,17] According to this model, gas is entrapped in crevices on surfaces
and forms bubble nuclei. These bubble nuclei can then grow by diffusion
of gas from the surrounding oversaturated liquid or due to expansion
upon the reduction of the liquid pressure. Numerous experimental studies
have been conducted at a microscale to validate this nucleation model.
For example, techniques such as centrifugation, shock wave, and acoustics
were applied to drastically reduce the liquid pressure to a negative
value to find the cavitation pressure threshold.[18−21] These studies mostly focused
on controlling the liquid condition after gas entrapment. However,
the detailed entrapment process, namely the entrapment dynamics, in
which the surface structures play an important role because they affect
liquid flows and provide pinning sites, was less studied.Several
previous studies have used structured surfaces to explore
the nucleation mechanism and controllable interfacial nanobubble formation.[22−25] With nanopatterned hydrophobic/hydrophilic surfaces, Agrawal et
al.[26] found that interfacial nanobubbles
only nucleate on hydrophobic domains. In our previous work,[24] the in situ entrapment of nanobubbles was observed
with an atomic force microscope (AFM). The size of the nucleated surface
nanobubbles is linearly correlated with that of the surface nanopores
on hydrophobic surfaces, which supports that the nanobubbles form
from gas entrapment on the nanoscopic cavities. Although the entrapped
nanobubbles have been observed in these works, further investigation
on the entrapment dynamics is extremely challenging due to the limited
temporal resolution of the measurement equipment at nanoscale, e.g.,
AFM. Essentially, the entrapments of surface microbubbles and surface
nanobubbles share the same mechanism. Therefore, the investigation
of nucleation dynamics of surface microbubbles, which is experimentally
feasible to be visualized, will lead us to a better understanding
of the nanobubble entrapment dynamics.Recently, Langley et
al.[27] demonstrated
the entrapment-based microbubble formation and observed the dynamical
process in their work. They studied air entrapment by performing drop
impact experiment on nanoparticle-decorated surfaces. As the drops
approach the solid surfaces, a central air disc is entrapped due to
the deformation of the drop by the intervening air layer. After the
drops touch the sample surface, the liquid blocks the escape path
for the gas, leading to the entrapment of microbubbles in surface
structures. The size of the microbubbles depends on the lateral roughness
variation. These results confirm that bubble nucleation is mediated
by gas entrapment and shed light on the dynamics of nucleation.In this study, we aim to reveal entrapment and diffusive dynamics
of surface microbubbles. Our work can provide (i) a better understanding
of the surface bubble nucleation mechanism and (ii) a potential method
of reproducible micro- and nanobubble formation. Here, we investigate
the temporal evolution of the surface microbubbles entrapped by microwells
on hydrophobic surfaces using a confocal microscope. To study the
effect of the microwell diameter on entrapment and dissolution effectively,
we prepared wells with different sizes on one sample. We will show
that the microwells can be used to trap surface microbubbles. After
this, the trapped surface microbubbles will dissolve. The detailed
process of microbubble dissolution, as well as factors such as gas
concentration and lateral size of surface microstructures on the microbubble
dissolution will be investigated in detail.
Experimental
Section
Preparation of the Sample and Its Characterization
Two solutions, polystyrene (PS)–toluene and water–acetone,
were prepared to fabricate the structured polystyrene (PS) surface
on a glass substrate. The PS–toluene solution was prepared
by dissolving PS particles (molecular weigh 350 000, Sigma-Aldrich)
into toluene (Mallinckrodt Chemical) with a concentration of 1.0%
(weight). The water–acetone solution was made by mixing water
and acetone with a water concentration of 5.0%. The two solutions
were first mixed with a ratio of 1:3 (volume, PS–toluene to
water–acetone). About 200 μL of the mixed solution was
then dropped on a piece of glass substrate (20 mm × 20 mm). The
deposited droplet solution will rapidly spread over the glass substrate.
Due to the lower solubility in the acetone–water mixture compared
to that in toluene, PS precipitates from the mixed solution and deposits
on the glass substrate to form a film. Among the three different liquids
(acetone, toluene, and water), acetone has the highest evaporation
rate, followed by toluene. As a result, the water droplets remain
on the PS film after acetone and toluene have evaporated within several
seconds. Eventually, the remaining water droplets will also evaporate
within about 10 min and the PS film with microwells (at the locations
where the droplets were) remains.The morphology of the surface
was measured with an AFM (Resolve, Bruker) in the tapping mode, as
shown in Figure a.
The width of the microwells is in between 10 and 80 μm. We confirm
that the bottom of the microwells is also coated by the PS film by
scratching it with an AFM tip (NSC36/ALBS, MikroMasch). The thickness
of the film at the bottom of the microwell is about 30 nm, whereas
the film itself is in between 0.8 and 1.2 μm. It is noteworthy
to point out that there are other surface preparation techniques available
that are able to produce more monodisperse distributions of microwells.
In this work it is of key importance to have microwells with different
diameters as we want to study the effect of the bubble diameter on
the entrapment and the dissolution dynamics of the bubble.
Figure 1
(a) Characterization
of the structured PS surface. Three-dimensional
morphology of the sample surface obtained with AFM. Microwells with
different sizes were obtained on the surface. (b) A side view image
of a sessile drop on the sample surface, indicating a water contact
angle of θ = 109.
(a) Characterization
of the structured PS surface. Three-dimensional
morphology of the sample surface obtained with AFM. Microwells with
different sizes were obtained on the surface. (b) A side view image
of a sessile drop on the sample surface, indicating a water contact
angle of θ = 109.To estimate the surface hydrophobicity, a water drop of 5
μL
was placed on the surface. The static contact angle of about 109°
(on the droplet side) was obtained using a video-based optical contact
angle measuring system (DataPhysics OCA15 Pro), see Figure b. This contact angle is slightly
larger than that of around 95° obtained on continuous PS films.[28] Such surface microwells can be applied in many
applications,[29−31] including serving as cell containers or scaffolds
for cell growth,[32,33] microreactors for chemical reactions,[34] and nucleation sites for photonic crystals.[35,36]
Water Deposition and Gas Concentration Control
During
the experiment, the prepared microstructured PS sample was clamped
in a home designed microfluidic chamber. Then 3 mL of deionized water
(Milli-Q Advantage A10 System, Germany) was deposited on the surface.
This leads to air bubble entrapment in the microwells. The flow rates
were controlled by a motorized syringe pump (Harvard; PHD 2000). The
temporal evolution of the entrapped microsized surface bubbles was
observed using a laser scanning confocal microscope (LSCM, Nikon Confocal
Microscopes A1 system) with a 60× water immersion objective (CFI
Apochromat 60XW NIR, numerical aperture = 1, working distance = 2.8
mm). To obtain the actual morphology of the structured surface, the
sample was first immersed into fully degassed water (the gas concentration
is 0.2 measured by an oxygen meter (Fibox 3 Trace, PreSens)), and
subsequently was scanned with the confocal microscope.To test
the effect of the gas concentration on the microbubble dynamics, the
experiment was conducted in both (nearly) air equilibrated water (AEW)
and in partially degassed water (PDW). In the AEW experiment, a sample
bottle containing water was kept open in air for 10 h. The measured
gas concentration in the nearly air saturated water is 96.0%. For
the PDW, the Milli-Q water was degassed for 3 min in a home-made vacuum
chamber. After partial degassing, the measured air concentration was
63.0%. For visualization, water was labeled in yellow color with fluorescein
isothiocyanate–dextran (Sigma-Aldrich, molecular weight, 70 000).
During experiments, water flow rates from 0.5 to 3.0 mL/min were applied.
All images were captured with the confocal microscope.
Results
and Discussion
Entrapment of Surface Microbubbles
When the flow front
passes over the structured hydrophobic surface, air pockets are entrapped
in the microwells.[37−39] The air entrapment occurs due to the large advancing
contact angle in combination with the surface structure size, as explained
by the crevice model.[37] The entrapped air
then first remains in the microwells, as surface microbubbles are
pinned to the edge of the surface cavities.We subsequently
observed the diffusive evolution of the entrapped surface microbubbles
in the microwells. To obtain the actual topography of the structured
surface before air entrapment, the sample was first immersed into
fully degassed water. The bottom view of the microwell is shown in Figure a. The circular areas
with a green color indicate that no microbubble entrapment occurred
in the fully degassed water (or the entrapped microbubbles dissolved
immediately, see below). After this, the fully degassed water was
removed.
Figure 2
Evolution of the entrapped microbubbles in air equilibrated water.
(a) The structured polystyrene surface captured in degassed water,
showing the distribution of microwells on the surface. (b–f)
Confocal microscopy images of the selected surface area at different
times. The dark circular areas marked by yellow circles are the microwells
covered by the initially entrapped microbubbles. The areas marked
by yellow rectangles are the shrinking microbubbles. During shrinkage,
the three-phase contact line keeps receding towards a pinned spot
until the microbubble disappears completely. (g) The sequential images
of an entrapped microbubble on a microwell. Initially, the microwell
was completely filled by the entrapped microbubble. Then part of contact
line detaches from the edge of the microwell and the formed microbubble
gradually shrank and eventually disappeared. (h) Schematic illustration
of the three phases of air entrapment in a microwell, fully entrapped,
shrinking, and fully dissolved.
Evolution of the entrapped microbubbles in air equilibrated water.
(a) The structured polystyrene surface captured in degassed water,
showing the distribution of microwells on the surface. (b–f)
Confocal microscopy images of the selected surface area at different
times. The dark circular areas marked by yellow circles are the microwells
covered by the initially entrapped microbubbles. The areas marked
by yellow rectangles are the shrinking microbubbles. During shrinkage,
the three-phase contact line keeps receding towards a pinned spot
until the microbubble disappears completely. (g) The sequential images
of an entrapped microbubble on a microwell. Initially, the microwell
was completely filled by the entrapped microbubble. Then part of contact
line detaches from the edge of the microwell and the formed microbubble
gradually shrank and eventually disappeared. (h) Schematic illustration
of the three phases of air entrapment in a microwell, fully entrapped,
shrinking, and fully dissolved.The AEW was then injected into the microfluidic chamber.
Subsequently,
the sample was fully immersed in AEW, and we immediately captured
the image of the entrapped microbubbles. At this stage, the microwells
were fully filled with gas. After a certain time, part of the three-phase
contact line detached from the edges of the microwells and the initially
trapped microbubbles rapidly shrank, reducing their lateral sizes. Figure b depicts the area
captured right after the sample was immersed into water. Due to the
limited frame rate of the LSCM (4 fps was applied to achieve optimized
imaging), the initial shrinkage for some of the microbubbles was not
captured. As a result, some of the initially entrapped microbubbles
shrank within the first frame. The areas marked with yellow circles
correspond to the initially entrapped microbubbles, whereas the ones
marked with yellow rectangles are the shrinking microbubbles.Figure c–e
show sequential images of the dissolving surface microbubbles. Noticeably,
in Figure c, the bubbles
appearing at the bottom left quadrant are formed from depinning of
the previous entrapped bubbles, which are marked with yellow circles
in Figure b. In addition,
we observed that a bubble appears between two microwells (top left
quarter). According to the sequential images between Figure b,c, we confirm that it jumps
out of the well from its right side. In Figure f, all entrapped microbubbles have disappeared.In Figure g, the
sequential images of an initially entrapped microbubble and the corresponding
shrinking microbubble in the microwell are presented. Initially, the
three-phase contact line was pinned at the edge of the microwell and
the complete well was covered by the air–water interface, as
illustrated in Figure h (the first). After a certain period, the three-phase contact line
detached from the edge of the well from one side and the microbubble
rapidly shrank in size. The microbubbles right after the initial shrinking
are referred to as initially shrunk microbubbles, as illustrated in Figure h (the second). Subsequently,
the microbubble will gradually further shrink (Figure h (the third)) and eventually disappear (Figure h (the fourth)).
The time required for the transition from the initially entrapped
microbubbles to the initially shrunk microbubbles is much shorter
than the following shrinkage period. Here, the frame which was taken
right after the initial shrinkage is taken as the first frame for
the analysis of the diffusive microbubble shrinkage dynamics.Our results show that the lateral width L0 of the initially shrunk microbubbles are related to the size
of the microwells. Figure a depicts the correlation between L0 and the microwell diameters Lw. One
can see that L0 linearly increases with Lw, with a slope of 0.34. This linear dependence
is independent of the flow rates, at least for the applied flow rates
of 0.5, 1.0, and 3.0 mL/min. This implies that larger microwells are
able to trap more gas. The contact angles always measured on the gas
side of the initially shrunk microbubbles are also size dependent.
As shown in Figure b, the contact angles of the initially shrunk microbubbles changes
from 30 to 80°, and slightly decrease with L0.
Figure 3
(a) Correlation of the lateral size L0 of the initially shrunk microbubbles and the width Lw of the microwells. The value L0 approximately linearly increases with Lw. This implies that the larger well contains more entrapped
gas. (b) Contact angle θ of the entrapped microbubbles as a
function of L0. The contact angle decreases
with increasing L0.
(a) Correlation of the lateral size L0 of the initially shrunk microbubbles and the width Lw of the microwells. The value L0 approximately linearly increases with Lw. This implies that the larger well contains more entrapped
gas. (b) Contact angle θ of the entrapped microbubbles as a
function of L0. The contact angle decreases
with increasing L0.
Dissolution of Entrapped Microbubbles
From the above
experimental observations, it is clear that the initially entrapped
microbubbles will shrink and eventually completely disappear. However,
the dynamics of the shrinking microbubbles still remains unknown.
One example of microbubble shrinkage is shown in Figure a, in which the top and bottom
row show the side and bottom view of the confocal microscopy images,
respectively. From the side view images, one can see that both height
and width of the microbubble gradually decrease with time until the
microbubble eventually completely disappears. Moreover, images from
both views indicate that one side of the three-phase contact line
is pinned at the edge of the well and the other side keeps receding
during the shrinking process. As an example, a schematic diagram of
the microbubble shrinkage is shown in Figure b. The phenomenon that one side is pinned
and the other side is detached is due to the heterogeneity of the
pinning site, and thus, the pinning strength. The reason for such
symmetry breaking is that the substrates in the experiments are never
perfectly homogeneous. Slight differences in the surface properties
are sufficient to lead to pinning or depinning on one side only.[40,41]
Figure 4
Shrinkage
process of the entrapped microbubbles, in the CA-mode.
(a) The side and bottom views of a shrinking microbubble. One side
of the three-phase contact line of the microbubbles is pinned to the
edge of the microwell. The other side recedes while the microbubble
dissolves. (b) Cartoon of the microbubbles dissolving. During microbubble
shrinking, it is pinned at one side, and both height and lateral diameter
decrease with time.
Shrinkage
process of the entrapped microbubbles, in the CA-mode.
(a) The side and bottom views of a shrinking microbubble. One side
of the three-phase contact line of the microbubbles is pinned to the
edge of the microwell. The other side recedes while the microbubble
dissolves. (b) Cartoon of the microbubbles dissolving. During microbubble
shrinking, it is pinned at one side, and both height and lateral diameter
decrease with time.To investigate how the
contact angle changes during microbubble
shrinkage, several individually entrapped microbubbles were tracked
in time, using the three-dimensional confocal microscope. As an example,
we consider here three entrapped microbubbles, as shown in Figure . Figure a–c are the side view
images of the shrinking microbubble at different times. All the three
microbubbles exhibit similar dissolving behavior, with one side being
pinned at the edge of the wall and the other side retracting with
time. During the process, one can clearly see that the contact angles
of the individual microbubbles remain almost constant, as shown in Figure d, which implies
that the microbubbles dissolve in the constant contact angle mode.
Figure 5
(a–c)
Side view images of an individual dissolving microbubble
at different times. The three microbubbles behave the same, with one
side of the three-phase contact line pinned at the edge of the wall
while the other side keeps receding with time. (d) Change of the contact
angle of the three microbubbles with time. During shrinkage, the contact
angles remain almost constant.
(a–c)
Side view images of an individual dissolving microbubble
at different times. The three microbubbles behave the same, with one
side of the three-phase contact line pinned at the edge of the wall
while the other side keeps receding with time. (d) Change of the contact
angle of the three microbubbles with time. During shrinkage, the contact
angles remain almost constant.Under the conditions of constant contact angle shrinkage,
on a
plane surface spherical-cap-shaped microbubbles dissolve through air
diffusion from microbubble to liquid, governed by[40]In the equation, κ is the dissolution
rate and is given bywhere D is the
diffusion
coefficient, cs is the solubility of air
in water, ρ is the gas density in the microbubble, θ again
is the contact angle of microbubble from the gas side, and ζ
is the air undersaturation of water defined as ζ = 1 – c∞/cs, andandFor
an air–water solution with a certain
undersaturation value, the dissolution rate κ only depends on
the contact angle θ. Therefore, a constant contact angle leads
to constant κ. As a result, L2 is
expected to linearly decrease with t, see eq . To verify the linear
dependence, the lateral diameter L(t) of the entrapped microbubbles was first tracked in air equilibrated
water, as shown in Figure a. The value of L2(t) is plotted in Figure b. Indeed, L2(t) linearly
decreases with time, which is consistent with the constant contact
angle mode, and a spherical-cap bubble on a plane surface. Note that
this latter assumption is not given, as the bubbles in our experiments
are not sitting on a plane surface, but in a microwell, where the
diffusive gas flux is partially blocked. Therefore, quantitatively
the dissolution rate should be slightly slower than that for a bubble
on a plane surface.
Figure 6
Change of the microbubble lateral diameter L (a,
c) and its square L2 (b, d) as a function
of time during microbubble shrinkage in air equilibrated water (a,
b) and partially degassed water (c, d), respectively. In both cases, L2 decreases linearly with time.
Change of the microbubble lateral diameter L (a,
c) and its square L2 (b, d) as a function
of time during microbubble shrinkage in air equilibrated water (a,
b) and partially degassed water (c, d), respectively. In both cases, L2 decreases linearly with time.The constant contact angle dissolution mode, as
well as the linear
dependence of L2 on t holds for all gas concentrations. To verify this, we conducted further
experiment in partially degassed water. The results are shown in Figure c,d, showing that L2 still linearly decreases with time.We now become more quantitative: from eq , which holds for the spherical-cap bubble
on a plane surface, one can see how the value of the dissolution rate
κ depends on the undersaturation level ζ of water. This
implies that the dissolution time tdiss (defined by L(t) = 0) of the microbubbles
also depends on ζ. The value of tdiss can be obtained by rewriting eq aswhereWe can see that in this purely diffusive regime and for a
spherical-cap
bubble on a plane surface, the dissolution time tdiss quadratically depends on the initial lateral microbubble
diameter L0, and is inversely proportional
to the undersaturation. The relative gas concentration in AEW and
PDW used in this study is 0.96 and 0.63, respectively. The corresponding
undersaturation ζ is 0.04 and 0.37. Two different flow rates Q were applied in the experiment for both AEW and PDW cases.
In Figure , the dissolution
rate κ and the dissolution time tdiss are compared for microbubbles with various initial lateral diameters
for the two undersaturation levels. The results in Figure a show that κ in PDW
is higher than that in AEW, which is consistent with eq . It means that the microbubbles
dissolve faster in water with a higher ζ. In addition, we observed
that κ varies even for the same lateral diameter and slightly
increases with increasing L0. This is
believed to be due to different contact angle values even for microbubbles
with similar sizes, due to the difference in pinning. In Figure b, we can see that
the measured tdiss in AEW is larger than
that in PDW, which agrees with eq . From the results shown in Figure , we conclude that neither the dissolution
rate nor the lifetime is affected by the flow rates.
Figure 7
Comparison of the dissolution
rate κ and dissolution time tdiss for microbubbles in AEW and PDW for two
different flow rates Q (value given in mL/min). (a)
The value of κ in PDW is higher than that in AEW. (b) The dissolution
time tdiss in AEW is larger than that
in PDW. Clearly, the microbubbles dissolve faster in the water with
a higher undersaturation value, independent of the flow rates. (c)
The experimental dissolution time tdiss is larger than the theoretical one for a spherical-cap-shaped bubble
on a plane surface, both in AEW and PDW. The dissolution of microbubbles
in the experiments is delayed, due to the wall blockage effect of
the gas diffusion out of the entrapped bubble. This was supported
by a quantitative estimation of the dissolution time (eqs and 10)
when the bottom part of the bubbles is blocked (data points correspond
to the upper open triangles). (d) The geometry and notation for the
microbubble with the bottom part blocked by the side wall of the microwell.
Comparison of the dissolution
rate κ and dissolution time tdiss for microbubbles in AEW and PDW for two
different flow rates Q (value given in mL/min). (a)
The value of κ in PDW is higher than that in AEW. (b) The dissolution
time tdiss in AEW is larger than that
in PDW. Clearly, the microbubbles dissolve faster in the water with
a higher undersaturation value, independent of the flow rates. (c)
The experimental dissolution time tdiss is larger than the theoretical one for a spherical-cap-shaped bubble
on a plane surface, both in AEW and PDW. The dissolution of microbubbles
in the experiments is delayed, due to the wall blockage effect of
the gas diffusion out of the entrapped bubble. This was supported
by a quantitative estimation of the dissolution time (eqs and 10)
when the bottom part of the bubbles is blocked (data points correspond
to the upper open triangles). (d) The geometry and notation for the
microbubble with the bottom part blocked by the side wall of the microwell.Moreover, according to eq , the theoretical dissolution
time for a spherical-cap-shaped
bubble on a plane surface tdiss can be
obtained with the measured contact angles by taking D = 2 × 10–9 m2/s, cs = 0.023 kg/m3, and ρ = 1.169 kg/m3.[42][42] A comparison of the experimental and theoretical results of tdiss is shown in Figure c. One can see that the experimental value
of tdiss in both AEW and PDW is obviously
larger than that calculated with eq . This means that the actual lifetime of microbubbles
is longer than that expected from the diffusion theory for a bubble
on a plane surface.There are three possible factors which can
be responsible for the
discrepancy: the partial blockage of the gas outflux by the well walls,
collective effects of neighboring microbubbles, and addition partial
blockage of diffusion by absorbing dye.[41−44] Since the bubble is not spherical-cap-shaped,
sitting on a plane surface, but trapped in a microwell, the presence
of the microwell side wall will lead to a partial blockage of the
diffusive gas outflux. On the one hand, the edge of the microwell serves as anchors where the contact
line is pinned. At this pinned portion of the microbubble, the side
wall of the microwell blocks the diffusive outflux. Compared to microbubbles
at flat sample surfaces, the gas cannot escape from the side wall
of the microwell. This helps to slow down the bubble dissolution.
On the other hand, even for the portion of the detached three-phase
contact line from the opening of the microwell, the gas still cannot
escape freely because the side wall of the microwell and the deepening
partially block the gas diffusion. Both geometric effects of the microwell
on the diffusive flux contribute to the increased tdiss.We now roughly estimate how large this diffusive
blockage effect
can be. We assume that the bubble is partially blocked with the well
wall of h = 1 μm (the well depth on our sample
is 0.8–1.2 μm), as depicted in Figure d, where the lower part of the bubble is
completely blocked by the side wall. The initial lateral diameter L0, the height H (with the bottom
side of the well as a reference), and the contact angle θ of
the partially blocked bubble are obtained from experiment. The corresponding
parameters L0′ and θ′
for the unblocked part of the bubble are given as (see Figure d)The mass loss dM/dt of the partially blocked bubble then is[40,45]The mass M of the
bubble
isAccording
to eqs and 10, and the geometric relationship
in eqs and 8, we can numerically determine the time when M(L, θ) = 0 for the constant contact
angle θ. In this way, the theoretical dissolution time tdiss in the partially blocked case is acquired,
as shown in Figure c (open triangles). It is clear from the comparison that the effect
of partial blocking is substantial. Note that theoretical dissolution
time tdiss in the blocked case is slightly
larger than the experimentally measured ones. We expect that the real
blockage effect should be smaller than what we have estimated here,
because the bubbles are only partially pinned at the wall. In addition,
the specific pinning portion along the three-phase contact line varies
for different bubbles and changes during the dynamic process. As a
result, it is difficult to get a completely quantitative evaluation
of the partial blockage effects.Regarding the effect of the
neighboring microbubbles on the dissolution
process, the distance between neighboring microbubbles is crucial.
On our sample, the shortest distance between the neighboring bubbles
is about 16 μm, which for most bubbles is larger than their
diameter, see Figure . In one of our recent works,[41] we have
calculated the effect of neighboring droplets (which have the same
diffusive dynamics) on the dissolution time. For the closest packaging
of droplets there is with a distance of 5 μm, on a footprint
diameter of 10 μm. This is much closer than what we have here.
Nonetheless, the dissolution time only increases by 60% when increasing
the microwell distance from 5 μm (where there are collective
effects) to 20 μm (hardly any collective effects). This is much
less than the above blockage effect.Finally, we discuss the
effect of the addition of dye, which indeed
will result in a slight increase of the dissolution time. The reasons
are 2-fold: (i) the dye as a surfactant will slightly lower the surface
tension and (ii) more importantly, the dye attachment to the interface
will lead to a partial blockage of diffusion through the interface.
These two effects in principle would contribute to the larger measured
dissolution time, compared to the theoretical prediction. However,
to minimize these dye effects, we used a relatively low dye concentration
of 2 mg/mL. For such low concentrations, the dye effect on the surface
tension is minimal: it decreases from 72.1 to 71.3 mJ/m2 with the concentration of the dye from 0.1 to 20 mg/mL.[46] In summary, it is clear that the partial blockage
of the gas outflux through the air–water interface is the main
reason for delayed dissolution, due to geometric constrains by the
walls of the well and to some degree also due to the partial coverage
of the interface by the dye.
Conclusions
In
this study, the temporal evolution of microbubbles at solid–liquid
interfaces of immersed structured PS surfaces was systematically investigated.
The results clearly show that the microwells on hydrophobic surfaces
are able to trap gas and form microbubbles. The microwells were initially
fully covered by the entrapped microbubbles that are pinned at the
edges of microwells. Then part of three-phase contact line detaches
from the microwell edges and the microbubbles rapidly shrink to a
smaller size. Subsequently, the microbubbles undergo shrinkage in
a constant contact angle mode due to gas diffusion into the liquid.
Experimental results show that the square of footprint area of the
microbubbles decreases linearly with time, which further confirms
the constant contact angle dissolution mode. In addition, our results
show that a higher undersaturation enhances microbubble dissolution,
while the flow rates remarkably have no influence on the dynamics
of microbubble entrapment and dissolution. We also see that geometric
blockage effects due to the microwell lead to reduced dissolution
rates compared to free bubbles on plane surfaces.In general,
we have shown that the position and size of interfacial
microbubbles can be controlled. It is clear that the surface microstructures
lead to gas entrapment. The amount of the entrapped gas directly depends
on the size of the surface structures. In addition, the quantitative
studies under various undersaturation and flow rate conditions give
a rough estimation on the microbubbles lifetime and stability. We
believe that this work will lead to a better understanding of the
mechanism of interfacial nanobubble formation and provide an effective
way to more stable and reproducible interfacial micro- and nanobubble
formation.
Authors: Abhinandan Agrawal; Juhyun Park; Du Yeol Ryu; Paula T Hammond; Thomas P Russell; Gareth H McKinley Journal: Nano Lett Date: 2005-09 Impact factor: 11.189
Authors: Danelle Beattie; Kok Hou Wong; Charles Williams; Laura A Poole-Warren; Thomas P Davis; Christopher Barner-Kowollik; Martina H Stenzel Journal: Biomacromolecules Date: 2006-04 Impact factor: 6.988
Authors: Xiaolai Li; Yuliang Wang; Mikhail E Zaytsev; Guillaume Lajoinie; Hai Le The; Johan G Bomer; Jan C T Eijkel; Harold J W Zandvliet; Xuehua Zhang; Detlef Lohse Journal: J Phys Chem C Nanomater Interfaces Date: 2019-08-28 Impact factor: 4.126