Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Plasmon-enhanced dynamic light scattering of gold nanorods in bulk and near a wall

Transportprozesse von anisotropen metallischen Nanopartikeln wie zum Beispiel Gold-Nanostäbchen in komplexen Flüssigkeiten und/oder begrenzten Geometrien spielen eine bedeutende Rolle in einer Vielzahl von biomedizinischen und industriellen Anwendungen. Ein Weg zu einem tiefen, grundlegenden Verständnis von Transportmechanismen ist die Verwendung zweier leistungsstarker Methoden - dynamischer Lichtstreuung (DLS) und resonanzverstärkter Lichtstreuung (REDLS) in der Nähe einer Grenzfläche. In dieser Arbeit wurden nanomolare Suspensionen von Gold-Nanostäbchen, stabilisiert mit Cetyltrimethylammoniumbromid (CTAB), mit DLS sowie in der Nähe einer Grenzfläche mit REDLS untersucht. Mit DLS wurde eine wellenlängenabhängige Verstärkung der anisotropen Streuung beobachtet, welche sich durch die Anregung von longitudinaler Oberflächenplasmonenresonanz ergibt. Die hohe Streuintensität nahe der longitudinalen Oberflächenplasmonenresonanzfrequenz für Stäbchen, welche parallel zum anregenden optischen Feld liegen, erlaubte die Auflösung der translationalen Anisotropie in einem isotropen Medium. Diese wellenlängenabhängige anisotrope Lichtstreuung ermöglicht neue Anwendungen wie etwa die Untersuchung der Dynamik einzelner Partikel in komplexen Umgebungen mittels depolarisierter dynamischer Lichtstreuung. In der Nähe einer Grenzfläche wurde eine starke Verlangsamung der translationalen Diffusion beobachtet. Hingegen zeigte sich für die Rotation zwar eine ausgeprägte aber weniger starke Verlangsamung. Um den möglichen Einfluss von Ladung auf der festen Grenzfläche zu untersuchen, wurde das Metall mit elektrisch neutralem Polymethylmethacrylat (PMMA) beschichtet. In einem weiteren Ansatz wurde das CTAB in der Gold-Nanostäbchen Lösung durch das kovalent gebundene 16-Mercaptohexadecyltrimethylammoniumbromid (MTAB) ersetzt. Daraus ergab sich eine deutlich geringere Verlangsamung.

Properties of patchy colloidal particles close to a surface: a Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Why are slip lengths so large in carbon nanotubes?

The enhanced flow in carbon nanotubes is explained using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why `slip-lengths' may be greater than the tube radius.

Gravity in the Randall-Sundrum brane world

We discuss the weak gravitational field created by isolated matter sources in the Randall-Sundrum brane world. For the case of a single wall of positive tension, the field stays localized near the wall if the source is stationary. We calculate the leading Kaluza-Klein corrections to the linearized gravitational field of a nonrelativistic spherical object, which is different from the Schwarzschild solution at large distances. In the case of two branes of opposite tension, linearized Brans-Dicke (BD) gravity is recovered on either wall, with different BD parameters. On the wall with positive tension the BD parameter is larger than 3000 provided that the separation between walls is larger than 4 times the AdS radius. The gravitational field due to shadow matter is also considered.

Simulation of Boundary Layers and Heat Transfer in the Entrance Region of Pipes

The study of fluid flow in pipes is one of the main topic of interest for engineers in industries. In this thesis, an effort is made to study the boundary layers formed near the wall of the pipe and how it behaves as a resistance to heat transfer. Before few decades, the scientists used to derive the analytical and empirical results by hand as there were limited means available to solve the complex fluid flow phenomena. Due to the increase in technology, now it has been practically possible to understand and analyze the actual fluid flow in any type of geometry. Several methodologies have been used in the past to analyze the boundary layer equations and to derive the expression for heat transfer. An integral relation approach is used for the analytical solution of the boundary layer equations and is compared with the FLUENT simulations for the laminar case. Law of the wall approach is used to derive the empirical correlation between dimensionless numbers and is then compared with the results from FLUENT for the turbulent case. In this thesis, different approaches like analytical, empirical and numerical are compared for the same set of fluid flow equations.

Lämmönlähteiden aiheuttamien konvektiovirtausten vaikutus vastakkaiseen tuloilmasuihkuun

Huoneen sisäisten lämpölähteiden aiheuttamilla konvektiovirtauksilla eli pluumeilla on huomattava vaikutus ilmastointipalkkijärjestelmäntoimintaan. Tätä vaikutusta ei ole tutkittu kovin paljon. Tässä työssä tutkittiin huoneen päätyseinässä olevan sähkölämmityspatterin vaikutusta aktiivisen ilmastointipalkin toimintaan. Tutkimus kohdistui vastakkaisten suihkujen törmäykseen. Suihkuina olivat pluumit ja tuloilmavirtaus. Tutkimukseen kuului sekä teoreettinen että kokeellinen osio. Teoreettisessa tarkastelussa käytiin läpi ilmastointipalkin teoriaa sekä konvektiovirtausten muodostumisen teoriaa. Lisäksi esitettiin, kuinka suihkuista lasketaan liikemäärävirta. Kokeellisessa osiossa mitattiin huoneen sisäisten lämpölähteiden aiheuttamia pluumeja. Lämpölähteet oli sijoitettuina tutkimushuoneen päätyseinän viereen. Mittauksissa keskityttiin tarkemmin sähkölämmityspatteriin ja sitä mallinnettiin eri tehoilla. Lisäksi mitattiin ilmastointipalkin tuloilmavirtausta eri ilmamäärillä. Pluumien ja tuloilmavirtauksen törmäyskäyttäytymistä selvitettiin savukuvauksella. Analyysiosiossa sähkölämmityspatterin aiheuttaman pluumin ja palkin tuloilmavirtauksen törmäyskäyttäytymiselle kehitettiin malli. Mallissa huomioitiin vastaikkaisten törmäävien suihkujen liikemäärät ja esitettiin kohdat tutkimushuoneen pituussuunnassa, jossa tuloilmavirtaus kääntyy oleskeluvyöhykkeelle. Ilmastointipalkkijärjestelmässä tuloilmavirtauksen tulisi kääntyä oleskeluvyöhykkeelle vasta huoneen seinustalla. Tutkimuksen perusteella näin käy, jos pluumin liikemäärä on noin 10% tai vähemmän tuloilman liikemäärästä. Muulloin palkin tuloilmavirtaus kääntyy oleskeluvyöhykkeelle liian aikaisin ja aiheuttaa mahdollisestivedontunnetta.

Vortices in superconductors with a columnar defect: Finite size effects

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it is considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated. (c) 2005 Elsevier B.V. All rights reserved.

The carreau-yasuda fluids: a skin friction equation for turbulent flow in pipes and kolmogorov dissipative scales

In this work the turbulent flow of the Non-Newtonian Carreau-Yasuda fluid will be studied. A skin friction equation for the turbulent flow of Carreau-Yasuda fluids will be derived assuming a logarithmic behavior of the turbulent mean velocity for the near wall flow out of the viscous sub layer. An alternative near wall characteristic length scale which takes into account the effects of the relaxation time will be introduced. The characteristic length will be obtained through the analysis of viscous region near the wall. The results compared with experimental data obtained with Tylose (methyl hydroxil cellulose) solutions showing good agreement. The relations between scales integral and dissipative obtained for length, time, velocity, kinetic energy, and vorticity will be derived for this type of fluid. When the power law index approach to unity the relations reduces to Newtonian case.