CN105550476B - A kind of method for designing stable superhydrophobic surface of periodic arrangement micro-column structure - Google Patents
A kind of method for designing stable superhydrophobic surface of periodic arrangement micro-column structure Download PDFInfo
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Abstract
The present invention provides a kind of controllable design method of micro-column structure stable ultra-hydrophobic surface, proposes that droplet formation stablizes the critical altitude criterion of Cassie states from the angle of least-energy principle, can be used as a kind of Theoretical Criterion for preparing stable ultra-hydrophobic micro-structure.Theoretical prediction is carried out to stable Cassie states can be formed by calculating critical altitude, to realize the controllable design of stable ultra-hydrophobic surface.It is lain drop and the Fluent software emulation numerical simulations of dynamic resilience by the static state of the micro-column structure to designing, the micro-column structure surface wettability of design can be verified.The micro-column structure super hydrophobic surface design method of periodic arrangement proposed by the invention considers microtrabeculae height, microtrabeculae spacing, the microtrabeculae bottom surface length of side, influence of the intrinsic contact angle to micro-column structure hydrophobic properties of the surface simultaneously, it is related to super-hydrophobic design, material analogue simulation field, design process is convenient and efficient, and design method is easy to grasp.
Description
Technical field
The invention belongs to super hydrophobic surface design fields, are related to a kind of micro-column structure surface progress by periodic arrangement
The design method of stable ultra-hydrophobic surface is realized in the design of microtrabeculae height, and it is suitable for the micro-column structure stable ultra-hydrophobics of periodic arrangement
The controllable design on surface.
Background technology
Super hydrophobic surface refers to that static contact angle is more than 150 °, and with extremely strong hydrophobic a kind of typical micro-nano knot
Structure surface.Biology, by natural selection, forms the material table that such configuration is unique, has excellent performance during long-term evolution
Face, such as the leg of water skipper, lotus leaf surface.The air layer retained in this kind of micro-structure can effectively reduce contact of the liquid with surface,
To realize multiple functions, such as automatically cleaning, super-buoyancy, surface drag reduction and anti-freeze.Based on bionical thought, by material
Material surface construction micro-nano coarse structure realizes that the super-hydrophobic huge applications that contain are worth.
There are two types of contact situation in surface of solids tool for usual drop：Drop is filled in the pit of rough surface, forms " moistening
Surface ", i.e. Wenzel models；" composite surface " is formed on the top that drop is located at rough surface protrusion, i.e. Cassie models.Its point
Wenzel theories are not corresponded toWith Cassie theoriesWherein, θw *And θc *Point
It is not the apparent contact angle in Wenzel models and Cassie models.θ is the intrinsic contact angle of the surface of solids, even the solid table
The Young contact angle that drop can be formed when face is plane.R is the roughness of the surface of solids, indicates the real contact area between solid-liquid
The area ratio projected in the horizontal plane with it is the numerical value more than 1.It is the Line Integral of solid liquid interface floor projection
Number.Due to relatively easily produced, the micro-column structure surface of periodic arrangement obtains extensive concern.For the microtrabeculae of periodic arrangement
Array surface,WithA, h, l indicate the microtrabeculae bottom surface length of side, microtrabeculae height and microtrabeculae spacing respectively.
In terms of analyzing super-hydrophobic stability, the research table of N.A.Patankar etc. (Langmuir, 2010,26,8941)
It is bright to exist simultaneously Wenzel states and Cassie states in micro-structure surface, when drop is by external interference or its dead weight
Irreversible transformation can occur from Cassie states to Wenzel states when effect, and microtrabeculae height is inquired into from geometric angle
Drop is influenced in micro-structure surface wettability, it is believed that when micro-structure surface is stablized, vertical plane is necessarily less than drop under its freedom
The height of microtrabeculae, otherwise drop will be changed into Wenzel states from Cassie states.
But it yet there are no the design item for the microtrabeculae height that Cassie states are stably maintained at about micro-column structure surface energy
Part.Why super hydrophobic surface has various excellent performances, is primarily due to the gas-liquid that micro-structure surface forms larger proportion
Interface maintains Cassie states so that material surface has big contact angle and low hysteresis, the stability of gas-liquid interface straight
Connect the sliding for being related to structure and hydrophobic performance.One of the key challenge for preparing super hydrophobic surface is how to consider this wetting shape
How the transformation of state designs microtrabeculae height to ensure that drop can be stable in the presence of Cassie states.
The micro-column structure that this patent inquires into periodic arrangement from the angle of least-energy principle can form stable Cassie states
Critical altitude and geometrical parameters and surface nature relationship, it is proposed that a kind of theory of design stability super hydrophobic surface is sentenced
According to and design method.
Invention content
The present invention provides a kind of controllable design method of micro-column structure stable ultra-hydrophobic surface.It is carried from the angle of least energy
Go out a kind of Theoretical Criterion, so that drop is maintained stable Cassie states on the micro-column structure surface of periodic arrangement, and propose
Microtrabeculae " critical altitude " criterion that can maintain stable Cassie states, to realize the controllable design of stable ultra-hydrophobic surface.
To achieve the goals above, the technical scheme is that：
A kind of controllable design method of micro-column structure stable ultra-hydrophobic surface, design process as shown in Figure 1, specifically include with
Lower step.
The first step establishes the micro-column structure model of periodic arrangement, and the geometric parameter of micro-column structure model is arranged.Described is several
What parameter includes the height h, the bottom edge length of side a of single microtrabeculae, the spacing l of microtrabeculae of single microtrabeculae, micro-column structure surface it is intrinsic
Contact angle θ.
Second step establishes the Theoretical Criterion for maintaining to stablize Cassie states
When analyzing micro-structure surface moisture state from least-energy principle angle, it will maintain to stablize Cassie shapes
The minimum constructive height of state is known as critical altitude, which judges that can the micro-column structure surface of design maintain stable Cassie
State.The formula proving process of critical altitude is：
The knots modification dE of 2.1 gauging surface free energys
As surface spreading dx of the drop in the micro-column structure of periodic arrangement, the knots modification dE of surface free energy, drop exists
It is calculated using formula (1) when micro-structure surface is sprawled, when if forming Wenzel states；Formula is used when if forming Cassie states
(2) it calculates；
DE=r (γSL-γSG)dx+γGLdxcosθ* (1)
Wherein, the area fraction of solid-liquid interfaceRoughnessA indicates each microtrabeculae bottom surface
The length of side, h indicate that each microtrabeculae floor height, l indicate microtrabeculae spacing, γSG,γSL,γGLSolid and gas, solid-liquid and gas-liquid are indicated respectively
Surface tension.
2.2, according to least-energy principle, calculate the critical angle θ on micro-column structure surfacecr
Since the apparent contact angle of drop when system stablizes is smaller, the energy having is smaller, so drop will be stable at
The state of minimum apparent contact angle.By Young's equation γSL=γSG+γGLCos θ substitute into (5) and obtain formula (6)
Wherein, θ is the intrinsic contact angle on micro-column structure surface.
2.3 calculate the critical altitude value on micro-column structure surface
It willIt substitutes into formula (6) and obtains critical altitude hcrCalculation formula (7), critical altitude hcrIt is energy
Maintain the minimum microtrabeculae height of stable Cassie states.Influence in order to eliminate size uses the ratio of height and spacing
At a dimensionless group formula (8).
Third walks, the geometric parameter on pre-designed micro-column structure surface
According toIf calculating table of the drop when micro-column structure surface can maintain Cassie states
Contact angle is seen, judges whether pre-designed micro-column structure surface there may be ultra-hydrophobicity by apparent contact angle.It is connect when apparent
Feeler is not less than 150 °, calculates the critical altitude value on micro-column structure surface；When apparent contact angle be less than 150 °, it is again pre-designed micro-
The geometric parameter on rod structure surface.
4th step calculates the critical altitude on micro-column structure surface
The geometric parameter on pre-designed micro-column structure surface is calculated into critical altitude value by formula (7) or formula (8), if in advance
The microtrabeculae height of design is not less than critical altitude value, then hits rebound two from lie drop and dynamic drop of static state by Fluent softwares
A aspect judges that can drop maintain stable Cassie states, if drop maintains stable Cassie states, carries out the 5th
Step, if drop does not maintain stable Cassie states, repeatedly step 3；If pre-designed microtrabeculae height is less than critical altitude
Value, then repeatedly step 3.
5th step prepares micro-column structure surface according to the geometric parameter on pre-designed micro-column structure surface, carries out experimental verification,
Test its super-hydrophobicity and its stability.
The Theoretical Criterion established and maintain to stablize Cassie states is discussed：The dimensionless group formula of derivation considers micro- simultaneously
The influence of pillar height degree, spacing, the bottom edge length of side, intrinsic contact angle to body structure surface hydrophobic performance, and accurately obtained the height
With intrinsic contact angle, solid-liquid interface area fraction and spacing between relationship.It is (public according to the dimensionless height criterion of foundation
Formula 8) make h/l withFunctional arrangement (see Fig. 2) between θ can accurately show that Cassie states institute is stablized in maintenance by image
The condition needed can be used as maintenance and stablize Cassie regime theory criterions.It can for the structure of given surface attribute and microtrabeculae spacing
Make h with the manufacture height by adjusting microtrabeculae>hcrTo realize stable Cassie states, obtain with stable ultra-hydrophobic performance
The micro-column structure surface of periodic arrangement.For the surface of low intrinsic contact angle, can be reached by suitably increasing microtrabeculae height
Stable ultra-hydrophobic state；Since the cost and machining accuracy of finishing are closely related, to reduce economic cost, can suitably increase micro-
Intercolumniation manufactures super hydrophobic surface by adjusting microtrabeculae height and intrinsic contact angle.
The present invention proposes that droplet formation stablizes the critical altitude standard of Cassie states from the angle of least-energy principle
Then, it can be used as a kind of Theoretical Criterion for preparing stable ultra-hydrophobic micro-structure.By calculating critical altitude to stabilization can be formed
Cassie states carry out theoretical prediction, to realize the controllable design of stable ultra-hydrophobic surface.In surface micro-structure geometric parameter
On the basis of pre-designed, while microtrabeculae height, spacing, the bottom surface length of side, intrinsic contact angle are considered to the shadow of structure hydrophobic performance
It rings.Using critical altitude as key parameter, the mentality of designing and Theoretical Criterion of stable Cassie states are given, it is theoretically right
The hydrophobic performance of this class formation is predicted that design process is convenient and efficient, and design method is easy to grasp.In addition, passing through Fluent
VOF methods carry out wettability emulation to such micro-structure surface in software, and the result of emulation confirms theoretical correctness.
Description of the drawings
Fig. 1 is the design flow diagram of super-drainage structure in technic relization scheme；
Fig. 2 be h/l withWith the function relation figure of θ；
Fig. 3 is the microstructure appearance schematic diagram of periodic arrangement；
Fig. 4 is that intrinsic contact angle is 120 ° of quasi-static lower drop wellability analog result figures；
Fig. 5 is that intrinsic contact angle is drop wellability result figure when 120 ° of initial velocity with 1m/s collide micro-structure surface.
Specific implementation mode
Illustrate specific embodiments of the present invention with reference to Fig. 3, Fig. 4 and Fig. 5.Fig. 3 is periodical micro-column structure table
Face, Fig. 4 be radius be 0.25mm water drop in a manner of quasi-static drop of lying 3 surface of hookup be in stablize Cassie states
Situation, Fig. 5 be water drop that radius is 0.25mm with 3 surface deformation of initial velocity Collision diagram of 1m/s, spring back and be ultimately at steady
Determine the situation of Cassie states.Fig. 4 and Fig. 5 is the analogous diagram obtained by Fluent softwares.A, l and h in figure are respectively
The microtrabeculae bottom edge length of side, microtrabeculae height and microtrabeculae spacing.
Embodiment 1
A. the micro-column structure model of periodic arrangement is established, as shown in Figure 3；
B. the Theoretical Criterion for maintaining to stablize Cassie states is established, that is, derives the micro-column structure surface of periodic arrangement
Critical altitude formula (7) or (8)；
C. a=50 μm of the geometric parameter on pre-designed micro-column structure surface, l=100 μm, h=100 μm, θ=120 °.According to
FormulaIt is 151 ° of more than 150 ° progress next step to calculate apparent contact angle.
D. 37.5 μm of critical altitude is calculated according to formula (7).Pre-designed micro-column structure height is more than critical altitude, carries out
Fluent softwares are simulated in terms of static state lies drop and dynamic resilience two, can maintain stable Cassie states, such as Figure 4 and 5
It is shown.It carries out in next step.
E. experiment preparation, its stability of experiment test are carried out according to pre-designed micro-column structure surface parameter.
The above example that this patent proposes only illustrates technical solution, and is not limited.
Claims (1)
1. a kind of controllable design method of the stable ultra-hydrophobic surface of micro-column structure, which is characterized in that include the following steps：
The first step establishes the micro-column structure model of periodic arrangement, and the geometric parameter of micro-column structure model is arranged；The geometry
Parameter includes the height h of single microtrabeculae, the bottom edge length of side a of single microtrabeculae, the spacing l of microtrabeculae, and the intrinsic of micro-column structure surface connects
Feeler θ；
Second step establishes the Theoretical Criterion for maintaining to stablize Cassie states
The minimum constructive height for maintaining to stablize Cassie states is critical altitude, which judges the micro-column structure surface energy of design
It is no to maintain stable Cassie states；The formula proving process of critical altitude is：
The knots modification dE of 2.1 gauging surface free energys
Drop calculates dE if forming Wenzel states when stable ultra-hydrophobic surface sprawls dx using formula (1)；If being formed
Cassie states then use formula (2) to calculate dE；
DE=r (γSL-γSG)dx+γGLdxcosθ* (1)
Wherein, the area fraction of solid-liquid interfaceRoughnessA indicates each microtrabeculae bottom surface length of side,
H indicates that each microtrabeculae floor height, l indicate microtrabeculae spacing, γSG,γSL,γGLThe surface of solid and gas, solid-liquid and gas-liquid is indicated respectively
Tension；
2.2 calculate the critical angle θ on micro-column structure surfacecr
By Young's equation γSL=γSG+γGLCos θ substitute into (5) and obtain formula (6)
Wherein, θ is the intrinsic contact angle on micro-column structure surface；
2.3 calculate the critical altitude value h on micro-column structure surfacecr
Critical altitude value hcrIt is the minimum microtrabeculae height for maintaining to stablize Cassie states, it willFormula (6) is substituted into obtain
To critical altitude value hcrCalculation formula (7)；Formula (8), which eliminates size influence, to be made formula (7) being melted into a dimensionless group
Formula；
Third walks, the geometric parameter on pre-designed micro-column structure surface
According toCalculate drop micro-column structure surface apparent contact angle, according to apparent contact angle
Judge whether pre-designed micro-column structure surface has ultra-hydrophobicity；When apparent contact angle be not less than 150 °, calculate micro-column structure
The critical altitude value on surface；When apparent contact angle is less than 150 °, the geometric parameter on pre-designed micro-column structure surface again；
4th step calculates the critical altitude on micro-column structure surface
The critical altitude value on pre-designed micro-column structure surface is calculated, if pre-designed microtrabeculae height is more than critical altitude value,
Judge that can drop maintain stabilization in terms of static state lies drop and dynamic drop shock rebound two by Fluent softwares
Cassie states carry out the 5th step, if drop does not maintain stable Cassie if drop maintains stable Cassie states
State, then repeatedly step 3；If pre-designed microtrabeculae height is less than critical altitude value, repeatedly step 3；
5th step prepares micro-column structure surface according to the geometric parameter on pre-designed micro-column structure surface, carries out experimental verification, test
Its super-hydrophobicity and stability.
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| CN106096258B (en) * | 2016-06-07 | 2018-06-29 | 上海理工大学 | A kind of analysis method of fluorochemical urethane surface hydrophobic |
| CN106570300B (en) * | 2016-11-17 | 2019-09-20 | 中南大学 | A kind of acquisition methods of rule second order structure surface liquid-drop contact angle |
| CN108052729B (en) * | 2017-12-11 | 2021-06-15 | 中国科学院长春光学精密机械与物理研究所 | Reverse design method of super-hydrophobic surface microstructure |
| CN108107918B (en) * | 2018-01-11 | 2023-11-17 | 广州航海学院 | Device and method for controlling movement direction of liquid drop |
| CN111595273A (en) * | 2020-05-27 | 2020-08-28 | 河北科技大学 | Method for designing isotropic super-hydrophobic surface simulating nepenthes sliding region |
| CN111597728B (en) * | 2020-05-27 | 2022-09-13 | 河北科技大学 | Method for designing anisotropic super-hydrophobic surface simulating nepenthes sliding region |
| CN111537398B (en) * | 2020-05-29 | 2021-10-15 | 河南农业大学 | Method for controlling liquid drop impact form, contact time and controllable liquid drop division |
| CN112284979B (en) * | 2020-09-22 | 2023-02-03 | 上海梭伦信息科技有限公司 | Method for measuring dynamic contact angle of droplet boundary |
| CN112487635B (en) * | 2020-11-26 | 2022-03-08 | 吉林大学 | Method for designing bionic gradient super-hydrophobic structure based on Marangoni effect |
| CN115101134B (en) * | 2022-07-06 | 2024-04-19 | 四川大学 | Evaluation method for anti-wetting performance of material surface |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101256132A (en) * | 2008-01-17 | 2008-09-03 | 江苏大学 | Steady ultra-hydrophobic surface controllable design method based on geometric analysis |
| CN101819125A (en) * | 2010-03-24 | 2010-09-01 | 江苏大学 | Method for designing stable superhydrophobic surface of grating structure |
| CN101817500A (en) * | 2010-03-24 | 2010-09-01 | 江苏大学 | Hydrophilic material surface super hydrophobic functional shift micro structure design method |
| CN101830428A (en) * | 2010-01-18 | 2010-09-15 | 大连理工大学 | Method for manufacturing super hydrophobic surface by microneedle array |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6923216B2 (en) * | 2003-04-15 | 2005-08-02 | Entegris, Inc. | Microfluidic device with ultraphobic surfaces |
-
2016
- 2016-01-25 CN CN201610049180.1A patent/CN105550476B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101256132A (en) * | 2008-01-17 | 2008-09-03 | 江苏大学 | Steady ultra-hydrophobic surface controllable design method based on geometric analysis |
| CN101830428A (en) * | 2010-01-18 | 2010-09-15 | 大连理工大学 | Method for manufacturing super hydrophobic surface by microneedle array |
| CN101819125A (en) * | 2010-03-24 | 2010-09-01 | 江苏大学 | Method for designing stable superhydrophobic surface of grating structure |
| CN101817500A (en) * | 2010-03-24 | 2010-09-01 | 江苏大学 | Hydrophilic material surface super hydrophobic functional shift micro structure design method |
Non-Patent Citations (3)
| Title |
|---|
| Effect of pillar height on the wettability of micro-textured surface:Volume-of-fluid simulations;Wei Zhang 等;《International Journal of Adhesion and Adhesives》;20170430;第74卷;64-69 * |
| 表面微细结构制备超疏水表面;郑黎俊 等;《科学通报》;20040930;第49卷(第17期);1691-1699 * |
| 超疏水表面材料的制备与应用;陈俊 等;《中国材料进展》;20130731;第32卷(第7期);399-405 * |
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