Academic literature on the topic 'DIFFERENTIAL MOLECULAR DIFFUSION'

Scalars with different molecular diffusivities can be transported at different rates in a strongly stratified, weakly turbulent flow. Rapid distortion theory (RDT) is used to examine the mechanisms responsible for differential diffusion of scalars in a sheared stratified flow. The theory, which applies when the flow is strongly stratified, predicts upgradient flux and its wavenumber dependence, which previous direct numerical simulations have shown to be important in differential diffusion. The net effect of shear on differential diffusion depends on the Grashof number, or the relative importance of buoyancy and viscous effects. RDT also allows the effects of the density ratio, Schmidt number, Lewis number, scalar activity and mean shear to be examined without the high computational cost of direct numerical simulation. RDT predicts that differential diffusion will increase with increasing density ratio, but only at low Grashof number. When the Lewis number is fixed, the Grashof number below which differential diffusion occurs decreases with increasing Schmidt number, and when one of the Schmidt numbers is fixed, differential diffusion decreases with increasing Lewis number. Also, differential transport of passive scalars increases when the Schmidt number of the scalar stratifying the flow increases.

For the subcutaneous administration of a chemical agent (salubrinal), we constructed a mathematical model of molecule transportation and subsequently evaluated the kinetics of diffusion, convection, and molecular turnover. Salubrinal is a potential therapeutic agent that can reduce cellular damage and death. The understanding of its temporal profiles in local tissue as well as in a whole body is important to develop a proper strategy for its administration. Here, the diffusion and convection kinetics was formulated using partial and ordinary differential equations in one- and three-dimensional (semi-spherical) coordinates. Several key parameters including an injection velocity, a diffusion coefficient, thickness of subcutaneous tissue, and a permeability factor at the tissue-blood boundary were estimated from experimental data in rats. With reference to analytical solutions in a simplified model without convection, numerical solutions revealed that the diffusion coefficient and thickness of subcutaneous tissue determined the timing of the peak concentration in the plasma, and its magnitude was dictated by the permeability factor. Furthermore, the initial velocity, induced by needle injection, elevated an immediate transport of salubrinal at t < 1h. The described analysis with a combination of partial and ordinary differential equations contributes to the prediction of local and systemic effects and the understanding of the transportation mechanism of salubrinal and other agents.

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

In dieser Arbeit betrachten wir das Strömungs-Diffusions-(Reaktions)-Problem für passive Markerteilchen, die in zweidimensionalen laminaren Strömungsmustern mit geringem thermischem Rauschen gelöst sind. Der deterministische Fluss umfasst Zellen in Form von Quadraten oder Katzenaugen. In ihnen tritt Rotationsbewegung auf. Einige der Strömungen bestehen aus wellenförmigen Bereichen mit gerader Vorwärtsbewegung. Alle Systeme sind entweder periodisch oder durch Wände begrenzt. Eine untersuchte Familie von Strömungen interpoliert kontinuierlich zwischen Reihen von Wirbeln und Scherflüssen. Wir analysieren zahlreiche numerische Simulationen, die bisherige theoretische Vorhersagen bestätigen und neue Phänomene offenbaren. Ohne Rauschen sind die Teilchen in einzelnen Bestandteilen des Flusses für immer gefangen. Durch Hinzufügen von schwachem thermischen Rauschen wird die normale Diffusion für lange Zeiten stark verstärkt und führt zu verschiedenen Diffusionsarten für mittlere Zeiten. Mit Continuous-Time-Random-Walk-Modellen leiten wir analytische Ausdrücke in Übereinstimmung mit den numerischen Ergebnissen her, die je nach Parametern, Anfangsbedingungen und Alterungszeiten von subdiffusiver bis superballistischer anomaler Diffusion für mittlere Zeiten reichen. Wir sehen deutlich, dass einige der früheren Vorhersagen nur für Teilchen gelten, die an der Separatrix des Flusses starten - der einzige Fall, der in der Vergangenheit ausführlich betrachtet wurde - und dass das System zu vollkommen anderem Verhalten in anderen Situationen führen kann, einschließlich einem Schwingenden beim Start im Zentrum einesWirbels nach einer gewissen Alterungszeit. Darüber hinaus enthüllen die Simulationen, dass Teilchenreaktionen dort häufiger auftreten, wo sich die Geschwindigkeit der Strömung stark ändert, was dazu führt, dass langsame Teilchen von schnelleren getroffen werden, die ihnen folgen. Die umfangreichen numerischen Simulationen, die für diese Arbeit durchgeführt wurden, mussten jetzt durchgeführt werden, da wir die Rechenleistung dafür besitzen.
In this thesis, we consider the advection-diffusion-(reaction) problem for passive tracer particles suspended in two-dimensional laminar flow patterns with small thermal noise. The deterministic flow comprises cells in the shape of either squares or cat’s eyes. Rotational motion occurs inside them. Some of the flows consist of sinusoidal regions of straight forward motion. All systems are either periodic or are bounded by walls. One examined family of flows continuously interpolates between arrays of eddies and shear flows. We analyse extensive numerical simulations, which confirm previous theoretical predictions as well as reveal new phenomena. Without noise, particles are trapped forever in single building blocks of the flow. Adding small thermal noise, leads to largely enhanced normal diffusion for long times and several kinds of diffusion for intermediate times. Using continuous time random walk models, we derive analytical expressions in accordance with numerical results, ranging from subdiffusive to superballistic anomalous diffusion for intermediate times depending on parameters, initial conditions and aging time. We clearly see, that some of the previous predictions are only true for particles starting at the separatrix of the flow - the only case considered in depth in the past - and that the system might show a vastly different behavior in other situations, including an oscillatory one, when starting in the center of an eddy after a certain aging time. Furthermore, simulations reveal that particle reactions occur more frequently at positions where the velocity of the flow changes the most, resulting in slow particles being hit by faster ones following them. The extensive numerical simulations performed for this thesis had to be done now that we have the computational means to do so. Machines are powerful tools in order to gain a deeper and more detailed insight into the dynamics of many complicated dynamical and stochastic systems.

Developpement d'une approche generale basee sur la formule differentielle de rutherford, avec parametre d'ecran, completee par une formule angulaire parametrique; obtention d'une section efficace differentielle bien adaptee a de nombreuses donnees experimentales et d'une section efficace integree satisfaisante sauf aux tres basses energies de la particule incidente, pour lesquelles on introduit un facteur correctif dependant de deux parametres. Bonne adaptation de ces sections efficaces au code de simulation edifiee au laboratoire pour la modelisation de la structure des traces de particules chargees traversant des tissus vivants

Etude des sections efficaces doublement differentielles des processus elastiques et inelastiques au cours de la collision d'un faisceau d'ions de he avec h ou h::(2), entre 1,5 et 30 kev, pour des angles de diffusion compris entre 5' et 30**(o), par spectrometrie de perte d'energie du projectile. Comparaison des resultats a des valeurs calculees et mesurees anterieurement a d'autres auteurs. Proposition d'un modele permettant d'interpreter les resultats pour la cible h

Self-regulating nonlinear waves in various biological populations are considered as moving attractors in excitable media. Mathematically, waves in populations are solutions of nonstationary parabolic systems of differential diffusion equations with source terms, and the velocity of the wave is an eigenvalue of the problem, and its profile is an eigenvalue function of the problem. There is no general exact method for solving such a problem. An approximate method for its solution is proposed (the semi-infinite reaction zone method), which essentially reduces to solving an algebraic system of equations. The method is used to calculate the waves in various biological populations. It is shown that there are two types of waves: a wave of conquest and a solitary wave. In all cases considered, formulas for calculating the velocity of the wave and its profile were obtained. One of the important examples considered is the analysis of solitary waves in populations of the herd locust.

A practical engineering calculation method has been formulated for commercial multicomponent fuel stagnant droplet evaporation with variable finite mass and thermal diffusivity. Instead of solving the transient liquid phase mass and heat transfer partial differential equation set, a totally different approach is used. With zero or infinite mass diffusion resistance in liquid phase, it is possible to obtain vapor pressure and vapor molecular mass based on the distillation curve of these turbine fuels. It is determined that Peclet number (Pef) is a suitable parameter to represent the mass diffusion resistance in liquid phase. The vapor pressure and vapor molecular mass at constant finite Pef is expressed as a function of finite Pef, vapor pressure, and molecular mass at zero Pef and infinite Pef. At any time step, with variable finite Pef, the above equation is still valid, and PFsPef=∞, PFsPef=0, MfvPef=∞, MfvPef=0 are calculated from PFsPef≡∞, PFsPef≡0, MfvPef≡∞, MfvPef≡0, thus PFs and Mfv can be determined in a global way which eventually is based on the distillation curve of fuel. The explicit solution of transient heat transfer equation is used to have droplet surface temperature and droplet average temperature as a function of surface Nusselt number and non-dimensional time. The effect of varying com position of multi-component fuel evaporation is taken into account by expressing the properties as a function of molecular mass, acentric factor, critical temperature, and critical pressure. A specific calculation method is developed for liquid fuel diffusion coefficient, also special care is taken to calculate the binary diffusion coefficient of fuel vapor-air in gaseous phase. The effect of Stefan flow and natural convection has been included. The predictions from the present evaporation model for different turbine fuels under very wide temperature ranges have been compared with experimental data with good agreement.

The main aim or the present work is to explore computational fluid dynamics and related turbulence and combustion models for application to the design, understanding and development of gas turbine combustor. Validation studies were conducted using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) scheme to solve the relevant steady, elliptical partial differential equations of the conservation of mass, momentum, energy and chemical species in three-dimensional cylindrical co-ordinate system to simulate the gas turbine combustion chamber configurations. A modified version of k-ε turbulence model was used for characterization of local turbulence in gas turbine combustor. Since, in the present study both diffusion and pre-mixed combustion were considered, in addition to familiar bi-molecular Arhenius relation, influence of turbulence on reaction rates was accounted for based on the eddy break up concept of Spalding and was assumed that the local reaction rate was proportional to the rate of dissipation of turbulent eddies. Firstly, the validity of the present approach with the turbulence and reaction models considered is checked by comparing the computed results with the standard experimental data on recirculation zone, mean axial velocity and temperature profiles, etc. for confined, reacting and non-reacting flows with reasonably well defined boundary conditions. Finally, the results of computation for practical gas turbine combustor using combined diffusion and pre-mixed combustion for different combustion conditions are discussed.

Abstract A high-performance polyamide grade of easy processability which presents excellent thermal and mechanical properties such as resistance to fatigue and creep is studied in this work. An accelerated aging of Polyamide 12 samples was performed in stainless steel autoclaves at 120°C in deoxygenated water at pH 8.7 in order to shorten the aging time and avoid oxidation. The samples were retrieved at distinct aging times which were enough to reach the asymptotic portion of the curve of corrected inherent viscosity (CIV) versus aging time. CIV measurements track modifications of the molecular weight due to hydrolysis. Afterwards, the samples were analyzed through their cross section in the core and edge layer in order to investigate changes due to diffusion effects. Differential scanning calorimetry (DSC) analysis assesses the degree of crystallinity and melting temperature. Thermogravimetric analysis (TGA) was employed in order to investigate changes in the thermal stability and the stage of degradation of the samples. Unlike conventional volumetric analysis techniques, the instrumented indentation tests (IIT) in micro-scale were performed to measure the mechanical properties such as elastic modulus (EIT) and hardness (HIT) along the thickness aiming to detect properties gradient between surface and core. The CIV measurements showed a decrease of 46.3% in the aged sample during the maximum aging time compared to the reference material.

Endothelial cells (ECs) form the inner lining of the blood vasculature and are exposed to shear stress (τ), the tangential component of hemodynamic forces. ECs transduce τ into biochemical signals possibly via EC-membrane perturbations. We have previously used confocal-FRAP on the DiI-stained plasma membranes of confluent cultured bovine aortic ECs (BAECs) to show that τ induces a rapid, spatially heterogeneous, and time-dependent increase in the lateral diffusion of the fluorescent lipoid probe in the BAEC membrane [1]. We now present evidence at the single molecule level that shear stress differentially perturbs membrane domains that are defined by their selective staining by lipoid dyes (DiI) of differing alkyl chain lengths. This study is the first to directly measure perturbation by shear stress of endothelial cell membrane microdomains.

While cancers have no known cure, some of them can be successfully treated with the combination of surgery and systematic therapy. In general, systemic/widespread chemotherapy is usually injected into the bloodstream to attempt to target cancer cells. Such procedure often imparts devastating side effects because cancer drugs are nonspecific in activity, and transporting them throughout the bloodstream further reduces their ability to target the right region. This means that they kill both healthy and unhealthy cells. It has been observed that the physiological conditions of the fluids around living cells can be characterized by pH, and the magnitude of pH around a living cell is different from cancerous cells. Moreover, a multiscale anatomy of carcinoma will reveal that the microstructure of cancer cells contains some characteristic elements such as specific biomarker receptors and DNA molecules that exclusively differentiate them from healthy cells. If these cancer specific ligands can be intercalated by some functional molecules supplied from an implantable patch, then the patch can be envisioned to serve as a complementary technology with current systemic therapy to enhance localized treatment efficiency, minimize excess injections/surgeries, and prevent tumor recurrence. The broader objective of our current research is to capture some fundamental insights of such drug delivery patch system. It is envisioned that the essential components of the device is nanodiamonds (ND), parylene buffer layer and doxorubicin (DOX) drugs. In its simplest form, self-assembled nanodiamonds - functionalized or pristine, and DOX molecules are contained inside parylene capsule. The efficient functioning of the device is characterized by its ability to precisely detect targets (cancer cells) and then to release drugs at a controlled manner. The fundamental science issues concerning the development of the ND-based device include: 1. A precise identification of the equilibrium structure and self assembled morphology of nanodiamonds, 2. Fundamental understanding of the drug adsorption and desorption process to and from NDs, and 3. The rate of drug release through the parylene buffers. The structure of the nanodiamond (ND) is crucial to the adsorption and desorption of drug molecules because it not only changes the self-assembly configuration but also alters the surface electrostatics. To date, the structure and electrostatics of NDs are not yet well understood. A density functional tight binding theory (DFTB) study on smaller [2] NDs suggests a facet dependent charge distributions on ND surfaces. These charges are estimated by Mulliken Analysis [1]. Using the charges for smaller NDs (∼valid for 1–3.3 nm dia ND) we first projected surface charges for larger (4–10 nm) truncated octahedral nanodiamonds (TOND), and it has been found that the [100] face and the [111] face contain positively and negatively charged atoms, respectively. These projected charges are then utilized to obtain the self assembled structure of pristine TONDs from Molecular Dynamics (MD) simulations [4] as shown in Fig. 1. The opposite charges on the [100] and [111] face invoked electrostatic attractions among the initially isolated NDs and a network of nanodiamond agglutinates are formed as evidenced in Fig. 1(b). This study confirms why as manufactured NDs are found in agglomerated form. The study also suggests that a large fraction of ND surfaces become unavailable for drug absorption as many of the [100] faces are coherently connected to [111] faces. As a result, it can be perceived that effective area for drug adsorption on ND surfaces will be less compared to theoretical prediction which suggests that a 4nm TOND may contain as high 360 drug molecules on its surface [5]. It has been observed that as manufactured NDs may contain a variety of functional groups, and currently, we are studying the mechanism of self-assembly for functionalized nanodiamonds so that we understand the role of functional groups. The next phase of calculation involves binding of the DOX to the NDs. Essentially, the understanding of drug absorption and desorption profile at a controlled rate to and from NDs is the most critical part of the device design. Some recent quantum calculation suggests that part of NDs and drug molecules contain opposite charges at their surfaces; it has been a natural interpretation that interactions between ND and drug molecules should be straight-forward — NDs should attract to drugs as soon as they come closure. Recent experiments [6], however, suggest that NDs usually do not interact with drug molecules in the presence of neutral solutions. Addition of NaCl in the solution improves the interaction dramatically. In the first part of the study, we [3–5] have studied the interaction of single DOX molecules with TOND surfaces via MD simulation. As shown in Fig. 2, this study suggests that DOX molecules first arrange them around the preferential sites on nanodiamonds (e.g. around the [111] face) and then spontaneously attach on the surface. It is also observed that only DOX molecule is attached per facets of TONDs. It can be noted that each TOND has 6 [100] face and 8 [111] faces. Figure 3 shows the energy minimization process during the DOX-ND interaction. It can be noted that these simulations have been performed in vacuum environment. In order to see how DOX interacts in solution media, another set of simulations have been conducted where “vacuum” environment have been replaced with solution media of different pH. Moreover, functionalization on the ND surfaces will create a different environment for the DOX molecules. Research is underway to capture the fundamental physics on the DOX loading and release to and from functionalized nanodiamonds. Once we understand the essential physics of drug loading and unloading, in the future we plan to model diffusion controlled drug release through ND coated film device by incorporating the multiscale science learned from the current study. Results from this study will provide fundamental insight on the definitive targeting of infected cells and high resolution controlling of drug molecules.

Abstract Wax deposition is an intrinsic problem existing in the production and transportation of waxy crude oil. In the oilfield, non-metallic pipe especially high-density polyethylene pipe (HDPE) has been widely used to solve corrosion problems due to its excellent performance in intensity and corrosion. However, the wax deposition problem in polyethylene (PE) pipe has never been evaluated using dynamic and systemic apparatus. Only a few studies focus on the wax deposition on the coated polyethylene surface by using the cold finger apparatus in recent decades. In this study, the wax deposition experiments were performed using an in-door flow-loop with detachable PE and stainless steel (SS) test sections under the laminar flow regime at the same time to investigate the difference in wax deposition aging rate between the PE and SS pipes. The wax deposits under different operating conditions in both PE and SS pipes were sampled by three layers to study the aging rate at different radial locations during the wax deposition. The wax precipitation characteristics of the wax deposits were determined by using the differential scanning calorimetry (DSC) method. It was found that the wax contents of the wax deposits in PE pipe were lower than that in the SS pipe. And the difference of the wax content between PE pipe and SS pipe decreases with the depositing duration. Eventually, the wax contents of the wax deposits in PE pipe were almost the same as that in the SS pipe. The heat conduction and heat transfer processes in PE pipe and SS pipe were analyzed. The thermal gradient and the concentration gradient at wall were calculated and combined with the heat and mass transfer of wax during the wax deposition to illustrate the difference in wax content. It was found that the variations of the thermal and concentration gradients have significant effects on the diffusion process of wax molecules within the wax deposit layer and thus changing the aging rate. The comparisons and findings of wax deposition between the two kinds of pipes have provided a significant reference for the application of non-metallic pipe in the oilfield.