Roughness optimization for biomimetic superhydrophobic surfaces

For non-wetting liquids the contact angle with a rough surface is greater than with a flat surface and may approach 180°, as reported for leaves of water-repellent plants, such as lotus. Roughness affects the contact angle due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. High roughness may lead to composite solid–liquid–air interface, which may be either stable or unstable. A comprehensive analytical model is proposed to provide a relationship between local roughness and contact angle, which is used to develop roughness distribution and to create biomimetic superhydrophobic surfaces. Various roughness distributions are considered, including periodic and surfaces with rectangular, hemispherically topped cylindrical, conical and pyramidal asperities and the random Gaussian height distribution. Verification of the model is conducted using experimental data for the contact angle of water droplet on a lotus leaf surface. For two solid bodies in contact, for wetting liquids, wetting leads to the meniscus force, which affects friction. Dependence of the meniscus force on roughness, previously ignored, is considered in the paper and it is found that with increasing roughness meniscus force can grow due to scale effect.

多尺度粗糙表面的实时绘制方法

目的 大部分材质表面都具有一定的细微结构,而这些细微结构的存在增加了真实感图形绘制的复杂性.方法 首先将材质表面的细微结构分为3类:宏观结构、介观结构和微观结构,并对每类结构分别建模:宏观结构采用三角面片建模,介观结构则采用法向图表示,而微观结构直接采用单一的粗糙度表达.然后针对每种结构,分别获得它们的法向分布函数(NDF),并用混合vMF分布拟合.最终屏幕空间每个像素内的法向分布用3个尺度NDF的卷积操作近似获得.此外,在处理环境光照时引入抛物面图(PM)和summed-area table(SAT),满足了动态场景的实时绘制需求.结果 实验结果表明本文方法可以在不同视点范围下生成高真实感的反射效果,并获得实时的绘制性能.结论 本文提出的实时绘制方法能够处理表面材质结构复杂的3维模型在环境光下的真实感反射效果,并支持动态光照和形变物体.     

Droplet mixing using electrically tunable superhydrophobic nanostructured surfaces

We demonstrate effective mixing of microliter droplets using electrically tunable superhydrophobic nanostructured surfaces. By applying electrical voltage and current, droplets can be reversibly switched from a wetting to a non-wetting state, which induces fluid motion within the droplet. This mixing concept was verified using a DNA hybridization assay, in which a single droplet reversibility accelerated the hybridization reaction by an order of magnitude as compared to mixing by passive diffusion. This work offers a new method to effectively mix droplets for a variety of microfluidics applications.     

Stochastic model for metastable wetting of roughness-induced superhydrophobic surfaces

A stochastic model for metastable wetting of roughness-induced hydrophobic surfaces is proposed. For a rough surface, increased solid–liquid interface area results in increased interface energy, and increases the contact angle (for non-wetting liquids) or decreases it (for wetting liquids). For a very rough surface, a composite solid–liquid–air interface may form with air pockets trapped in the valleys between asperities, as opposed to the homogeneous solid–liquid interface. Both the homogeneous and composite interface configurations correspond to local energy minima of the system and therefore, there are stable states associated with different energy levels. The system may transform from one stable state to the other due to small perturbations, such as capillary waves. Different probabilities are associated with these different stable states, depending on the energy levels. The contact zone consists of a large number of asperities and valleys, which may be in the homogeneous or composite state. The overall contact angle is calculated based on the statistical model. The model may be used for design of roughness-induced superhydrophobic surfaces.     

Adaptive contouring of three-dimensional surfaces

An adaptive method of contouring a bivariate surface defined over arbitrarily spaced data in two dimensions is introduced. The method has two stages: 1. Produce a Bézier polynomial surface defined over a union of triangles. 2. Use this surface to compute the required contour levels. Using positional data only, this method produces a C¹-continuous surface and contours which can be made arbitrarily close to being C¹-continuous. The contour is represented as a piecewise linear approximation to the C¹-continuous contour.The method computes a linear representation of the surface in the neighborhood of the contour using an adaptive degree reduction algorithm. This algorithm is used to minimize the number of subdivisions necessary to obtain the desired smoothness of the contour. As a result of this adaptive subdivision, no contours are missed due to the coarseness of the original data points.     

Estimating aerodynamic resistance of rough surfaces using angular reflectance

Current wind erosion and dust emission models neglect the heterogeneous nature of surface roughness and its geometric anisotropic effect on aerodynamic resistance, and over-estimate the erodible area by assuming it is not covered by roughness elements. We address these shortfalls with a new model which estimates aerodynamic roughness length (z₀) using angular reflectance of a rough surface. The new model is proportional to the frontal area index, directional, and represents the geometric anisotropy of z₀. The model explained most of the variation in two sets of wind tunnel measurements of aerodynamic roughness lengths (z₀). Field estimates of z₀ for varying wind directions were similar to predictions made by the new model. The model was used to estimate the erodible area exposed to abrasion by saltating particles. Vertically integrated horizontal flux (F_h) was calculated using the area not covered by non-erodible hemispheres; the approach embodied in dust emission models. Under the same model conditions, F_h estimated using the new model was up to 85% smaller than that using the conventional area not covered. These F_h simulations imply that wind erosion and dust emission models without geometric anisotropic sheltering of the surface, may considerably over-estimate F_h and hence the amount of dust emission. The new model provides a straightforward method to estimate aerodynamic resistance with the potential to improve the accuracy of wind erosion and dust emission models, a measure that can be retrieved using bi-directional reflectance models from angular satellite sensors, and an alternative to notoriously unreliable field estimates of z₀ and their extrapolations across landform scales.     

Numerical investigation on drag reduction with superhydrophobic surfaces by lattice-Boltzmann method

The mechanism of drag reduction by using superhydrophobic surfaces whose contact angle is greater than 150° is still an open problem that needs to be investigated. The main purpose of this paper is to reveal how the pressure drop can be decreased. The lattice-Boltzmann method (LBM) is employed to investigate fluid flows through channels with different wettability conditions and topographical surfaces. The drag reduction by superhydrophobic surfaces is determined based on numerical experiments. For the smooth-surface flow, a very thin gas film is observed between the fluid and the superhydrophobic wall; hence, the liquid/solid interface is replaced by the gas/liquid interface. For the rough-surface flow, liquid sweeps over the grooves and the contact area is reduced; therefore, the friction is decreased rapidly. Additionally, the effects of surface wettability and surface roughness are analyzed as well. It is found that introducing roughness elements has a positive effect for reducing the pressure drop for the hydrophobic-surface flow, but has a negative effect for the hydrophilic-surface flow.     

Investigation of laminar flow in microtubes with random rough surfaces

A new approach of numerically generating a microtube with three-dimensional random surface roughness is presented. In this approach, we combined a bi-cubic Coons patch with Gaussian distributed roughness heights. Two random roughness generation methods are studied. A computational fluid dynamic solver is used to solve the 3-D N–S equations for the flow through the generated rough microtubes with D = 50 μm and L = 100 μm. The effects of the peak roughness height, H, asperities spacing in the θ direction, S _θ , and Z direction, S _Z , standard deviation of the Gaussian distribution, σ, arithmetical mean roughness, R _a, on the Poiseuille number, Po are investigated. It is found that when H/D < 5% the Po number can still be predicted by the conventional flow theory if the mean diameter of rough microtubes, D _m, is used to be the hydraulic diameter D _h. When H/D = 10%, the main flow is strongly affected by the roughness at Reynolds number Re = 1,500. The Po number increases with Re and deviates from the prediction up to 11.9%. The Po number does not change a lot with S _θ and S _Z because D _m almost keeps constant when the spacing is changed. For the rough microtubes with different R _a values, the Po numbers can be almost the same, which prove that only with the R _a value we can not determine the friction in the rough microtube. The mean value μ, the maximum and minimum values of the random roughness are found to be critical to determine the Po number.     

Real-time rendering of refracting transmissive objects with multi-scale rough surfaces

This paper presents an efficient approach to render refracting transmissive objects with multi-scale surface roughness, under distant illumination. To correctly capture both fine-scale surface details and large-scale appearances, and enable real-time processing at various viewing resolutions, we first divide the surface roughness into three levels, namely, micro-scale, meso-scale and macro-scale. Each scale of roughness is modeled and evaluated using different strategies, and the overall roughness is approximated by their spherical convolution. Then, this representation is incorporated into a microfacet-based BTDF model, and multi-scale rough refractions are simulated on both front and back sides of an object as light enters and exits the object. In particular, non-linear filtering methods are applied to both macro-scale geometries and meso-scale bumps to reduce aliasing when viewed across a range of distances. Finally, experimental results illustrate that our approach produces resolution-dependent refraction effects that match super-sampled ground truth, while achieving a speed up of several orders of magnitude with hardware acceleration.     

A program for perspective views of three-dimensional surfaces

A numerical method is proposed for solving linear differential equations of second order without first derivatives. The new method is superior to de Vogelaere's for this class of equations, and for non-linear equations it becomes an implicit extension of de Vogelaere's method. The global truncation error at a fixed steplength h is bounded by a term of order h⁴, and the interval of absolute stability is [?2.4, 0]. The work of Coleman and Mohamed (1978) is readily adapted to provide truncation error estimates which can be used for automatic error control. It is suggested that the new method should be used in preference to de Vogelaere's for linear equations, and in particular to solve the radial Schrödinger equation. the radial Schrödinger equation.     

Fusion bonding of rough surfaces with polishing technique for silicon micromachining

 Surface roughness is one of the crucial factors in silicon fusion bonding. Due to the enhanced surface roughness, it is almost impossible to bond wafers after KOH etching. This also applies when wafers are heavily doped, have a thick LPCVD silicon nitride layer on top or have a LPCVD polysilicon layer of poor quality. It has been demonstrated that these wafers bond spontaneously after a very brief chemical mechanical polishing step. An adhesion parameter, that comprises of both the mechanical and chemical properties of the surface, is introduced when discussing the influence of surface roughness on the bondability. Fusion bonding, combined with a polishing technique, will broaden the applications of bonding techniques in silicon micromachining. Received 30 October 1996/Accepted: 14 November 1996     

Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves

Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.     

Measuring three-dimensional surfaces with a two-dimensional data tablet

This paper describes a method for measuring the three-dimensional position of points on a surface using only a two-dimensional tablet or digitizer, standard photographic techniques and some computing power. The tablet is used to extract two-dimensional information from photographs of the surface. Data from multiple views of the surface is processed to give the three-dimensional position of points on the surface. This method has been successfully used to obtain point position data for the polygonal representation of several human faces and a human body.     

Light scattering from anisotropic, randomly rough, perfectly conducting surfaces

An approach is introduced for performing rigorous numerical simulations of electromagnetic wave scattering from randomly rough, perfectly conducting surfaces. It is based on a surface integral technique, and consists of determining the unknown electric surface current densities from which the electromagnetic field everywhere can be determined. The method is used to study the scattering of a p-polarized beam from an anisotropic Gaussian, randomly rough, perfectly conducting surface. It is demonstrated that the surface anisotropy gives rise to interesting and pronounced signatures in the angular intensity distribution of the scattered light. The origins of these features are discussed.     

范德华力作用下粗糙表面静态粘附的研究

通过在硅微接触表面上涂覆低表面能的憎水性OTS膜以除去接触面间的表面张力,把两表面均接地以除去接触面间的静电力,研究了仅有范德华力作用时硅微结构接触表面的粘附.根据实际粗糙表面凸峰自相似的高度分布,计算了发生粘附后,微观接触表面产生弹性和塑性变形的两种情况下的范德华粘附能,分析了表面形貌对其影响.     

On Bézier surfaces in three-dimensional Minkowski space

In this paper, we study Bézier surfaces in three-dimensional Minkowski space. In particular, we focus on timelike and spacelike cases for Bézier surfaces. We also deal with the Plateau–Bézier problem in , obtaining conditions over the control net to be extremal of the Dirichlet function for both timelike and spacelike Bézier surfaces. Moreover, we provide interesting examples showing the behavior of the Plateau–Bézier problem in and illustrating the relationship between it and the corresponding Plateau–Bézier problem in the Euclidean space R³.     

A practical method of constructing surfaces in three-dimensional digitized space

We propose a new, practical algorithm for constructing the surface of a three-dimensional object from its planar cross-sections. This algorithm deals with a general case where each cross-section of the object is given as a two-dimensional digital image and no topological information about these two adjacent cross-sections is assumed. In particular, it can handle the case where there are several connected components with some holes in each cross-section. The algorithm's principle is derived from the region growing technique. which is well-known in two-dimensional image processing. By combining this algorithm with existing shading techniques, we can obtain a realistic image of a three-dimensional object.