• 충청수학회지
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• 제34권4호
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• pp.387-395
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• 2021

In this paper, we give a characterization of a Delaunay surface in ℝ³. Let Σ be a CMC-H surface in ℝ³ with H ≠ 0. If Σ meets a plane with constant contact angle along a circle, then it is rotationally symmetric, i.e., Σ is part of a Delaunay surface.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 춘계학술대회논문집
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• pp.662-665
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• 2008

We experimentally investigate the evaporation characteristics of water droplet on surfaces of various wettabilities in the range of contact angle from 30$^{circ}$ to 150$^{circ}$. When a liquid droplet on a solid surface evaporates, the contact angle generally decreases with time and the evaporation rate varies with the droplet geometry such as the contact angle and the radius of curvature. Experimental data on the contact angle as a function of the droplet volume obtained by digital image analysis techniques cannot be explained by the existing theories. By measuring the temporal evolutions of the droplet radius and contact angle, we find the qualitative difference between the evaporation patterns on the hydrophilic surfaces where the contact radius remains constant initially and those on the superhydrophobic surfaces where the contact angle remains constant. Also, the evaporation rate is observed to depend on the surface material although the currently available models assume that the rate is solely determined by the droplet geometry. Despite the fact that the theory to explain this dependence on the surface remains to be pursued by the future work, we give the empirical relations that can be used to predict the droplet volume evolution for each surface. It is expected that the present study will contribute to interpreting the effect of droplet geometry on the evaporation.

• 대한수학회보
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• 제53권1호
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• pp.227-245
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• 2016

A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see [8] for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

• 한국염색가공학회지
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• 제11권2호
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• pp.27-37
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• 1999

Polypropylene(PP) films were treated with plasma glow discharge to produce peroxy radicals on the surfaces. The peroxy radicals formed on the PP film surfaces were subsequently used for the graft polymerization of acrylic acid and acrylamide in an aqueous solution by heating, respectively. Introduction of acrylic acid and acrylamide on the PP film could be confirmed by the observation of carbonyl and primary amine absorptions based on carboxylic acid and amide, respectively. And introduction of functional group could be confirmed by weight analysis and ESCA. The water contact angle(90$^{\circ}$) of PP film was constant, irrespective of elapsed time, while plasma-treated and functional monomer-grafted PP films were slowly increased with elapsed time, showing the rearrangement of surface polar groups in air condition. The water contact angle$(90^\circ)$ of PP film was decreased by the plasma treatment$(56^\circ)$ and further decreased by the grafting of acrylic acid$(34^\circ)$ and acrylamide$(37^\circ)$, indicating increased hydrophilicity of the modified surfaces. The water contact angle of plasma-treated PP film increased a little as time elapsing. The half-life periods of surface voltage on acrylic acid-(31sec) and acrylamide-grafted PP(42sec) were significantly decreased when compared to those on PP(950sec) and plasma-treated PP film(241sec). In the experiments using acid, basic and disperse dyes, absorbance and $\Delta{E}$ values of functional monomer-grafted PP films were significantly increased than that of oxygen plasma-treated one.

• 대한수학회지
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• 제54권4호
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2011년도 제40회 동계학술대회 초록집
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• pp.449-449
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• 2011

We reported the direct effect of intrinsic surface energy of dry adhesive material to the Van der Waals and capillary forces contributions of the total adhesion force in an artificial gecko-inspired adhesion system. To mimic the gecko foot we fabricated tilted nanohairy structures using both lithography and ion beam treatment. The nanohairy structures were replicated from Si wafer mold using UV curable polymeric materials. The control of nanohairs slanting angles was based on the uniform linear argon ion irradiation to the nanohairy polymeric surface. The surface energy was studied utilizing subsequent conventional oxygen ion treatment on the nanohairy structures which resulted in gradient surface energy. Our shear adhesion test results were found in good agreement with the accepted Van der Waals and capillary forces theory in the gecko adhesion system. Surface energy would give a direct impact to the effective Hamaker constant in Van der Waals force and the filling angle (${\varphi}$) of water meniscus in capillary force contributions of gecko inspired adhesion system. With the increasing surface energy, the effective Hamaker constant also increased but the filling angle decreased, resulting in a competition between the two forces. Using a simple mathematical model, we compared our experimental results to show the quantitative contributions of Van der Waals and capillary forces in a single adhesion system on both hydrophobic and hydrophilic surfaces. We found that the Van der Waals force contributes about 82.75% and 89.97% to the total adhesion force on hydrophilic and hydrophobic test surfaces, respectively, while the remaining contribution was occupied by capillary force. We also showed that it is possible to design ultrahigh dry adhesive with adhesion strength of more than 10 times higher than apparent gecko adhesion force by controlling the surface energy and the slanting angle induced-contact line of dry adhesive the materials.

• 대한수학회보
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• 제58권1호
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• 한국염색가공학회지
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• 제10권3호
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• pp.43-49
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• 1998

Polyvinyl chloride (PVC) sheets were treated with corona discharge to produce peroxy radicals on the surfaces. The peroxy radicals formed on the PVC surfaces were subsequently used as initiators for the graft polymerization of acrylic acid or acrylamide in an aqueous solution. Introduction of acrylic acid and acrylamide on the PVC sheet could be confirmed by the observation of carbonyl and primary amine absorptions based on carboxylic acid and amide, respectively. The water contact angle$(90^\circ)$ of PVC sheet was constant, irrespective of time, while corona-treated and functional monomer-grafted PVCs were slowly increased with time, showing the rearrangement of surface polar groups in air condition. The water contact angle of PVC sheet$(90^\circ)$ was decreased by corona treatment$(78^\circ)$, and further decreased by the grafting of acrylic acid$(55^\circ)$ and acrylamide$(56^\circ)$ , indicating increased hydrophilicity of the modified surfaces. The half-life periods of surface voltage on acrylic acid- (62 sec) and acrylamide-grafted PVC (147sec) were significantly decreased when compared to those on PVC (3,115 sec) and corona-treated PVC (463sec). These results mean that acrylic acid- and acrylamide-grafted PVCs could be used as the antistatic sheets.

• 접착 및 계면
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• 제16권3호
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• pp.116-121
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• 2015

본 연구에서는 발수성 재료로 쓰이고 상대적으로 가격이 비싼 불소계 실란을 대체하기 위해 octadecyltrichlorosilane (OTS)을 사용하였다. 코팅층의 기계적 접착강도를 향상시키기 위해 무기바인더를 산 촉매 하에서 졸-겔 반응에 의해 분산시켜 합성하였다. 합성된 실리카 나노입자는 나노크기의 거칠기를 제공하기 때문에 초소수성을 쉽게 얻기 어려우므로 유기용매에 의한 입자의 응집을 유도하였다. 실리카 나노입자의 적절한 크기 선택에 따라 OTS를 사용해서 표면을 소수화 시킨 후 유기용매의 양이 증가함에 따라 초소수성의 표면을 얻었고 극도의 물 반발 거동이 zero sliding angle과 함께 관찰되었다. 이러한 초소수성은 용매와의 혼합과 상관없이 유전상수가 25보다 작은 값을 가졌으며 용매 내에서 입자의 응집을 통해 유도된 초소수성 표면을 제조하는 것이 저유전상수 값에 대한 지표가 되었다.

• Nuclear Engineering and Technology
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• 제52권10호
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• pp.2353-2360
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• 2020

An anodic electrophoretic deposition (EPD) technique is used to create a uniform TiO₂ thin film coating on boiling thin steel plates (1.1 mm by 90 mm). All of the effective parameters except time of the EPD method are kept constant. To investigate the effect of gamma irradiation on the critical heat flux (CHF), the test specimens were irradiated in a gamma cell to different doses ranging from 100 to 300 kGy, and then SEM and BET analysis were performed. For each coated specimen, the contact angle and capillary length were measured. The specimens were then tested in a boiling pool for CHF and boiling heat transfer coefficient. It was observed that irradiation significantly decreases the maximum pore diameter while it increases the porosity, pore surface area and pore volume. These surface modifications due to gamma irradiation increased the CHF of the nano-coated surfaces compared to that of the unirradiated surfaces. The heat transfer coefficient (HTC) of the nano-coated surfaces irradiated at 300 kGy increased from 83 to 160 kW/(㎡ K) at 885 kW/㎡ wall heat flux by 100%. The CHF of the irradiated (300 kGy) and unirradiated surfaces are 2035 kW/㎡ and 1583 kW/㎡, respectively, an increase of nearly 31%.