An intermediate wavelength, weakly nonlinear theory for the evolution of capillary gravity waves

A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity.     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

Thermomechanics of the interface between a body and its environment

We formulate integral statements of force balance, energy balance, and entropy imbalance for an interface between a body and its environment. These statements account for interfacial energy, entropy, and stress but neglect the inertia of the interface. Our final results consist of boundary conditions describing thermomechanical interactions between the body and its environment. In their most general forms, these results are partial differential equations that account for dissipation and encompass as special cases Navier’s slip law, Newton’s law of cooling, and Kirchhoff’s law of radiation. When dissipation is neglected, our results reduce to the well-known zero-slip, free-surface, zero-shear, prescribed temperature, and flux-free conditions. Dedicated to James K. Knowles: teacher, colleague, friend     

The effect of temperature gradients on the sharkskin surface instability in polymer extrusion through a slit die

The sharkskin surface instability is commonly observed in the extrusion of polymer melts. We present a series of experiments in which a specifically designed rectangular slit die with insulated and independently heated sides and is used to induce precise temperature gradients across a flowing polyethylene melt. Our previous experiments demonstrated that the character of the surface distortions produced by the sharkskin instability was a function of the die wall temperature and therefore the extrudate had viscoelastic properties at the surface. In this paper, we explore the role of temperature and viscoelastic property gradients near the capillary wall. The amplitude of the sharkskin instability is quantified and plotted against apparent shear and extension rates. Analysis of the data demonstrates that the amplitude and frequency of the instability is independent of bulk temperature and temperature gradient and is dependent only on wall temperature. The data are normalized using a dimensionless Weissenberg number based on the extension rate to collapse the data collected over all temperatures and gradients onto a single master curve. We conclude with an example of a rectangular extrudate exhibiting varying surface roughness due to differential die heating and discuss the implications of our observations on the sharkskin surface instability mechanism and on commercial applications.     

Evolution of material voids for highly anisotropic surface energy

In this paper we consider the evolution by surface diffusion of material voids in a linearly elastic solid, focusing on the evolution of voids with large surface energy anisotropy. It is well known that models for the time evolution of similar material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface. Here the ill-posedness is removed through a regularization which incorporates higher order terms in the surface energy. Spectrally accurate numerical simulations are performed to calculate the steady-state solution branches and time-dependent evolution of voids, with a particular emphasis on inferring trends in the zero regularization (c→0) limit. For steady voids with large anisotropy we find that apparent corners form as c→0. In the presence of elastic stresses σ the limiting corner angles are most often found to differ from angles found on the (σ=0) Wulff shape. For large elastic stresses we find that steady solutions no longer exist; instead the void steadily lengthens via a filamenting instability referred to as tip streaming.     

Dilational rheology of an air–water interface functionalized by biomolecules: the role of surface diffusion

As an attempt to develop a sensitive device for biomolecule detection, a micromechanical methodology based on the rheological change of an air–water interface is put forward (Berthier and Davoust, CEA/CNRS patent, PCT International Application WO 2003/080209 A3, 2003). Capillary waves induced from the vertical electrodynamic vibration of a brimful cylindrical tank filled with water stand as a good way to identify dilational elasticity and viscosity of an aging interface. Before, we were interested of the fact that complex wave number and the frequency of waves are obtained through an optical technique, which allows us to accurately recognize the whole interface geometry. These two parameters, a modeling based on a dispersion relation (Lucassen-Reynders and Lucassen, Adv Colloid Interface Sci, 2:347, 1969) and the surface mass transport equation, are jointly used to identify the surface diffusivity and the dilational rheology of the interface for a nonsoluble biochemical surfactant. Preliminary results obtained from a water surface functionalized by DNA, thanks to a lipidic monolayer, demonstrate the capabilities of the proposed methodology. The sensitivity of dilational rheology and the surface diffusivity on DNA adsorption on lipids is made evident.This paper was presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

十二烷基硫酸钠水溶液的动态表面吸附性质

利用MPTC型气泡压力张仪研究了十二烷基硫酸钠(SDS)溶液在不同NaCl 浓度下的动态表面吸附性质, 分析了离子型表面活性剂在表面吸附层和胶束中形成双电层结构产生表面电荷对动态表面扩散过程和胶束性质的影响. 结果表明, SDS在表面吸附过程中, 表面电荷的存在会产生5.5 kJ·mol^-1的吸附势垒(E_a), 显著降低十二烷基硫酸根离子(DS^-)的有效扩散系数(D_eff). 十二烷基硫酸根离子的有效扩散系数与自扩散系数(D)的比值(D_eff/D)仅为0.013, 这表明SDS与非离子型表面活性剂不同, 在吸附初期为混合动力控制吸附机制. 加入NaCl可以降低吸附势垒. 当加入不小于80 mmol·L^-1 NaCl后, E_a小于0.3 kJ·mol^-1, D_eff/D在0.8-1.2之间, 表现出与非离子型表面活性剂相同的扩散控制吸附机制. 同时, 通过分析SDS胶束溶液的动态表面张力获得了表征胶束解体速度的常数(k₂). 发现随着NaCl 浓度的增大, k₂减小, 表明SDS胶束表面电荷的存在会增加十二烷基硫酸根离子间的排斥力, 促进胶束解体.     

MnOx/Al-SBA-15的结构性质及低温NH3选择性催化还原NOx

采用后合成法制备MnO_x/Al-SBA-15催化剂, 考察了催化剂的低温NH₃选择性催化还原(SCR)NO_x的性能. 利用傅里叶透射红外变换(FTIR)光谱、N₂吸附-脱附、X射线衍射(XRD)、扫描电镜(SEM)、拉曼光谱(Raman)、X射线光电子能谱(XPS)及NH₃程序升温脱附(NH₃-TPD)的表征手段, 对催化剂的结构性质和SCR性能进行了系统分析. 结果表明, 适量Al的掺杂能提高MnO_x/SBA-15催化剂的SCR活性, 当硅铝摩尔比为50时, 催化剂活性最佳. 表征结果显示, Al掺杂后, 催化剂仍保持良好的骨架结构, 较大比表面、孔容和孔径, 并且Mn在催化剂表面富集, 由低价态转化为高价态, MnO₂为催化剂的主要活性相. 此外, Al的掺杂使MnO_x在催化剂表面高度分散, 表面酸性增强, 从而提高了催化剂的SCR活性.     

APplication of Continuous Thermodynamics to the Stability of Polymer Systems. II

A determinant criterion for the critical state in solutions and mixtures of polydisperse polymers is established within the general framework of Gibbs theory. The treatment continues an earlier paper by considering more general Gibbs free energy relations: The function replacing the x-term in the classic Flory-Huggins equation is permitted to depend on a finite number of moments of the polymer distribution(s) so as to embrace most Gibbs free energy relations of practical use. The new criterion leads to a very large reduction of computer time and of needed storage capacity compared to the traditional Gibbs determinant criterion. Some relations known from the literature are shown to be special cases of the established new criterion.