Wenzel determined that when the liquid is in intimate contact with a microstructured surface, θ will change to θW*
cos
θ
W
∗
=
r
cos
θ
{\displaystyle \cos \theta _{W}*=r\cos \theta }
Cassie and Baxter found that if the liquid is suspended on the tops of microstructures, θ will change to θCB*
cos
θ
C
B
∗
=
φ
(
cos
θ
+
1
)
−
1
{\displaystyle \cos \theta _{CB}*=\varphi (\cos \theta +1)-1}
It can be predicted whether the Wenzel or Cassie-Baxter state should exist by calculating the new contact angle with both equations. By a minimization of free energy argument, the relation that predicted the smaller new contact angle is the state most likely to exist. Stated mathematically, for the Cassie-Baxter state to exist, the following inequality must be true.
cos
θ
<
φ
−
1
r
−
φ
{\displaystyle \cos \theta <{\frac {\varphi -1}{r-\varphi }}}
A recent alternative criteria for the Cassie-Baxter state asserts that the Cassie-Baxter state exists when the following 2 criteria are met:
1) Contact line forces overcome body forces of unsupported droplet weight and
2) The microstructures are tall enough to prevent the liquid that bridges microstructures from touching the base of the microstructures.
A simple model can be used to predict the effectiveness of a synthetic micro- or nano-fabricated surface for its conditional state (Wenzel or Cassie-Baxter), contact angle and contact angle hysteresis. The main factor of this model is the contact line density, Λ, which is the total perimeter of asperities over a given unit area.
To calculate updated advancing and receding contact angles in the Cassie-Baxter state, the following equations can be used.
θ
a
=
λ
p
(
θ
a
,
0
+
w
)
+
(
1
−
λ
p
)
θ
a
i
r
{\displaystyle \theta _{a}=\lambda _{p}(\theta _{a,0}+w)+(1-\lambda _{p})\theta _{air}}
θ
r
=
λ
p
θ
r
,
0
+
(
1
−
λ
p
)
θ
a
i
r
{\displaystyle \theta _{r}=\lambda _{p}\theta _{r,0}+(1-\lambda _{p})\theta _{air}}
M. Nosonovsky and B. Bhushan studied the effect of unitary (non-hierarchical) structures of micro and nano roughness, and hierarchical structures (micro roughness covered with nano roughness). They found that hierarchical structure was not only necessary for a high contact angle but essential for the stability of the water-solid and water-air interfaces (the composite interface). Due to an external perturbation, a standing capillary wave can form at the liquid–air interface. If the amplitude of the capillary wave is greater than the height of the asperity, the liquid can touch the valley between the asperities; and if the angle under which the liquid comes in contact with the solid is greater than h0, it is energetically profitable for the liquid to fill the valley. The effect of capillary waves is more pronounced for small asperities with heights comparable to the wave amplitude. An example of this is seen in the case of unitary roughness, where the amplitude of asperity is very low. This is why the likelihood of instability of a unitary interface will be very high. However, in a recent study, Eyal Bittoun and Abraham Marmur found that multiscale roughness is not necessarily essential for superhydrophobicity but beneficial for mechanical stability of the surface.
Research in superhydrophobicity recently accelerated with a letter that reported man-made superhydrophobic samples produced by allowing alkylketene dimer (AKD) to solidify into a nanostructured fractal surface. Many papers have since presented fabrication methods for producing superhydrophobic surfaces including particle deposition, sol-gel techniques, plasma treatments, vapor deposition, and casting techniques. Current opportunity for research impact lies mainly in fundamental research and practical manufacturing. Debates have recently emerged concerning the applicability of the Wenzel and Cassie-Baxter models. In an experiment designed to challenge the surface energy perspective of the Wenzel and Cassie-Baxter model and promote a contact line perspective, water drops were placed on a smooth hydrophobic spot in a rough hydrophobic field, a rough hydrophobic spot in a smooth hydrophobic field, and a hydrophilic spot in a hydrophobic field. Experiments showed that the surface chemistry and geometry at the contact line affected the contact angle and contact angle hysteresis, but the surface area inside the contact line had no effect. An argument that increased jaggedness in the contact line enhances droplet mobility has also been proposed. One method to experimentally measure the jaggedness in the contact line uses low melting temperature metal melted and deposited onto micro/nano structured surfaces. When the metal cools and solidifies, it is removed from the surface, flipped, and inspected for contact line micro geometry.
There have been a few efforts in fabricating a surface with tunable wettability. For the purpose of spontaneous droplet mobility, a surface can be fabricated with varying tower widths and spacings to gradually increase the free energy of the surface. The trend shows that as tower width increases, the free energy barrier becomes larger and the contact angle drops, lowering the hydrophobicity of the material. Increasing tower spacing will increase the contact angle, but also increase the free energy barrier. Droplets naturally move towards areas of weak hydrophobicity, so to make a droplet spontaneously move from one spot to the next, the ideal surface would consist of small width towers with large spacing to large width towers with small spacing. One caveat to this spontaneous motion is the resistance of stationary droplets to move. Initial droplet motion requires an external stimulus, from something as large as a vibration of the surface or as small as a simple syringe "push" as it is released from the needle.
An example of readily tunable wettability is found with special developed fabrics. By stretching a dip-coated commercial fabric, contact angles were typically allowed to increase. This is largely caused by an increase in tower spacing. However, this trend does not continue towards greater hydrophobicity with higher strain. Eventually, the Cassie-Baxter state reaches an instability and transitions to the Wenzel state, soaking the fabric.
Another example of a biomimetic surface includes micro-flowers on common polymer polycarbonates. The micro/nano binary structures (MNBS) imitate the typical micro/nanostructure of a lotus leaf. These micro-flowers offer nanoscale features which enhance the surface's hydrophobicity, without the use of low surface energy coatings. Creation of the superhydrophobic surface through vapor-induced phase separation at varying surrounding relative humidities caused a likewise change to the contact angle of the surface. Surfaces prepared offer contact angles higher than 160° with typical sliding angles around 10°. A recent study has revealed a honeycomb like micro-structures on the taro leaf, which makes the leaf superhydrophobic. The measured contact angle on the taro leaf in this study is around 148 degrees.
Fabricating superhydrophobic polymer surfaces with controlled geometry can be expensive and time consuming, but a small number of commercial sources provide specimens for research labs.
Active recent research on superhydrophobic materials might eventually lead to industrial applications. Some attempts at fabricating a superhydrophobic surface include mimicking a lotus leaf surface, namely the two-tiered characteristic. This requires micro-scale surfaces with typically nanoscale features on top of them. For example, a simple routine of coating cotton fabric with silica or titania particles by sol-gel technique has been reported, which protects the fabric from UV light and makes it superhydrophobic. Similarly, silica nanoparticles can be deposited on top of already hydrophobic carbon fabric. The carbon fabric by itself is identified as inherently hydrophobic, but not distinguished as superhydrophobic since its contact angle is not higher than 150°. With the adhesion of silica nanoparticles, contact angles as high as 162° are achieved. Using silica nano-particles is also of interest to develop transparent hydrophobic materials for car windshields and self-cleaning windows. By coating an already transparent surface with nano-silica with about 1 wt%, droplet contact angles can be raised up to 168° with a 12° sliding angle.
There has been a recent development of super hydrophobic paper which has unique properties for its application in paper based electronics and medical industry. The paper is synthesized in an organic free medium which makes it environment friendly. The paper has antimicrobial properties as it does not hold moisture so it makes it perfect for surgical applications. This paper can be a huge breakthrough for the paper based electronics industry. The resistance to aqueous and organic solvents makes it an ideal choice in developing electronic sensors and chips. Skin based analyte detection is now possible without damaging and continuous replacing of the electrodes as this paper will be immune to sweat. With its endless applications this field of material science is sure to be more explored.
A recent application of hydrophobic structures and materials is in the development of micro fuel cell chips. Reactions within the fuel cell produce waste gas CO2 which can be vented out through these hydrophobic membranes. The membrane consists of many microcavities which allow the gas to escape, while its hydrophobicity characteristic prevents the liquid fuel from leaking through. More fuel flows in to replace the volume previously kept by the waste gas, and the reaction is allowed to continue.
A well-known application of ultrahydrophobic surfaces is on heat exchangers, where they can improve droplet shedding and even cause jumping-droplet condensation, with potential for powerplants, heating and air conditioning, and desalination. Rare earth oxides, which are found to exhibit intrinsically hydrophobic surfaces, offer an alternative to surface coatings, allowing the development of thermally stable hydrophobic surfaces for heat exchangers operating at high temperature Ultrahydrophobic desalination membranes for membrane distillation have also been fabricated for improved fouling resistance, which can be fabricated effectively with chemical vapor deposition.
It has been also suggested that the superhydrophobic surfaces can also repel ice or prevent ice accumulation leading to the phenomenon of icephobicity. However, not every superhydrophobic surface is icephobic and the approach is still under development. In particular, the frost formation over the entire surface is inevitable as a result of undesired inter-droplet freezing wave propagation initiated by the sample edges. Moreover, the frost formation directly results in an increased frost adhesion, posing severe challenges for the subsequent defrosting process. By creating hierarchical surface, the interdroplet freezing wave propagation can be suppressed whereas the ice/frost removal can be promoted. The enhanced performances are mainly owing to the activation of the microscale edge effect in the hierarchical surface, which increases the energy barrier for ice bridging as well as engendering the liquid lubrication during the deicing/defrosting process.
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