Effect of pressure gradients on the different stages of roughness induced boundary layer transition

The physical mechanisms of roughness-induced transition (RIT) in pressure gradient boundary layers are studied using direct numerical simulations. Recent investigations have examined RIT processes in zero-pressure-gradient boundary layers (Suryanarayanan et al., 2019). The present study uses a vorticity dynamics point of view to examine how these processes are altered by a locally accelerating or decelerating flow that strains the vorticity field and creates a net vorticity flux at the wall. Flow acceleration is imposed on specific streamwise extents of the flow. This provides an understanding about how the fundamental mechanisms in different stages of RIT are affected by pressure gradients. The present results suggest that both lift-up and subsequent amplification of the unsteady perturbations are mitigated by flow acceleration. The effect on lift-up is explained by the compression (i.e. large negative value of the stretching term) of the wall-normal vorticity by negative dv/dy. Consistent with earlier experimental observations on spots and wedges, favorable pressure gradients reduce turbulent wedge spreading and nearly arrest the spreading when sufficiently strong. This result is also explained in terms of vorticity dynamics.     

An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

Carbon nanotube dielectrophoresis: Theory and applications

Carbon nanotubes (CNTs) are one of the most extensively studied nanomaterials in the 21st century. Since their discovery in 1991, many studies have been reported advancing our knowledge in terms of their structure, properties, synthesis, and applications. CNTs exhibit unique electrothermal and conductive properties which, combined with their mechanical strength, have led to tremendous attention of CNTs as a nanoscale material in the past two decades. To introduce the various types of CNTs, we first provide basic information on their structure followed by some intriguing properties and a brief overview of synthesis methods. Although impressive advances have been demonstrated with CNTs, critical applications require purification, positioning, and separation to yield desired properties and functional elements. Here, we review a versatile technique to manipulate CNTs based on their dielectric properties, namely dielectrophoresis (DEP). A detailed discussion on the DEP aspects of CNTs including the theory and various technical microfluidic realizations is provided. Various advancements in DEP-based manipulations of single-walled and multiwalled CNTs are also discussed with special emphasis on applications involving separation, purification, sensing, and nanofabrication.     

Computation of hydrodynamic mass and damping coefficients for a cavitating marine propeller flow using a panel method

The present paper deals with the numerical calculation of hydrodynamic mass and damping coefficients under consideration of unsteady sheet cavitation on marine propeller flows. In the first part of the paper, the mathematical and numerical background behind the numerical method is introduced. The numerical calculations carried out in this work are based on a low-order panel method. Panel methods belong to the class of collocation techniques and are applied to obtain a numerical solution of a potential flow based system of boundary integral equations. They are suitable for the present application because of their short computation time which makes them applicable in the design process of marine propellers.Additionally, two different approaches for the determination of hydrodynamic masses and damping are introduced in this work. The hydrodynamic masses and damping are important in studies of the ship motion in seaway and in the analysis of vibrations of a vessel and its appendages. The developed approaches are applied on a propeller flow in heave motion. Hereby, the calculations are performed for a non-rotating and rotating propeller under non-cavitating and cavitating conditions. The results obtained from the simulations are discussed in detail and an outlook is given.     

Solvability of the boundary value problem for stationary magnetohydrodynamic equations under mixed boundary conditions for the magnetic field

The global solvability of the boundary value problem for stationary magnetohydrodynamic equations under the Dirichlet boundary condition for the velocity and mixed boundary conditions for the magnetic field is proved.     

High‐performance liquid chromatographic column packings with different particle sizes: Chromatographic behavior for the quality analysis of HuanglianShangqing pill

The chromatographic separation of traditional Chinese medicines is still a highly challenging task in analytical science with respect to its hundreds and thousands of chemical compounds, while increase of separation efficiency can greatly improve the separation power of chromatographic column for traditional Chinese medicine. In this study, 13 bioactive components in HuanglianShangqing pill were selected as an index to optimize the separation conditions and evaluate the system suitability of three commercially available columns packed with 1.8, 3.5, and 5.0 μm particles. The chromatographic separations were obtained by the most appropriate Eclipse Plus C₁₈ column (100 × 2.1 mm, 3.5 μm) within 45 min using gradient elution with aqueous‐ammonium acetate (10 mmol/L, pH 5.0) and acetonitrile, at a flow rate of 0.3 mL/min and an operating temperature of 30°C. The quality of HuanglianShangqing pill was assessed through combining simultaneous quantification of 13 compounds with fingerprint analysis. For the qualitative analysis, mass spectrometry was used to confirm the 13 compounds. All the validation data conformed to the acceptable requirements. For the fingerprint analysis, 32 peaks were selected as the common peaks at 254 nm to evaluate the similarities among HuanglianShangqing pills obtained from ten manufacturers.     

Exact separation theorem for closed sets in Asplund spaces

In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone.