In this study we provide a new proof of C¹,α boundary regularity for finite perimeter sets with flat boundary which are local minimizers of a variational mean curvature formula. Our proof is provided for curvature term H∈LΩ. The proof is a generalization of Cafarelli and C#243;rdoba's method, and combines techniques from geometric measure theory and the theory of viscosity solutions which have been developed in the last 50 years. We rely on the delicate interplay between the global nature of sets which are variational minimizers of a given functional, and the pointwise local nature of comparison surfaces which satisfy certain PDE. As a heuristic, in our proof we can consider the curvature as an error term which is estimated and controlled at each point of the calculation.

The production of alternative transportation fuels is imperative to meet future energy demands without contributing to global climate change. Advances in alternative processing techniques that have emerged due to interest in microalgae as a feedstock have led to a variety of potential processing pathways for the production of bio-based fuels. A major hurdle in the algal production process is maintaining a fast and stable algae culture. Monocultures, developed for their high lipid content, suffer from low productivity, are susceptible to crashes and require a constant supply of carbon dioxide to maintain productivity. In an effort to circumvent these obstacles, algal turf scrubber systems (ATS) are now being targeted not only for water purification, but as a means of producing algae feedstocks for fuel conversion. The resulting algae are capable of being harvested at a much higher density, requiring less energy for dewatering purposes. ATS systems do present other drawbacks that downstream technologies need to account for to make this system a viable means for fuel conversion. While polyculture algae species display great growth characteristics, they contain high percentages of nitrogen containing proteins and low lipid content. If not removed this nitrogen pollutes any resulting biocrude making it unacceptable for diesel fuel blends. This study investigates a processing method which reduces the nitrogen content of the resulting fuel by fermenting both carbohydrates and proteins into intermediate compounds. By tuning the E. coli fermentation stain it is hoped that the process will yield higher value co-products than those investigated in this study. The research contained herein incorporates laboratory experimentation with engineering systems modeling to assess the economic feasibility and environmental impacts of generating biofuels from ATS cultivated algae. Results show a minimum fuel selling price of $5.93 per gasoline gallon equivalent and greenhouse gas emissions of -0.0185 kg CO2eq per MJ fuel. Discussion points include process optimization in terms of minimum fuel selling price and global warming potential.

In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.

<p>The main goal for a packaging is to protect the product inside. Typical packaging nowadays is made of layers of paper and barriers consisting of plastics or aluminum foil. A problem with the barrier used today is the environmental thinking. Xylophane® is an environmental friendly and biodegradable alternative to the current barrier material used in packaging. It consists of the natural carbohydrate xylan and additives. Xylophane® is an efficient barrier to oxygen, grease and aroma and can prolong the shelf life of sensitive food.</p><p>The raw material xylan is water soluble and Xylophane® can be coated on paper, board and plastics without using other solvents. A problem with the drying process is the amount of energy needed and the consumption needs to be decreased. Also, the drying capacity of the equipment to be used is often limited and the amount of water to be dried off is critical for the success of the coating process. By increasing the dry content of Xylophane® without increasing the viscosity too much, the drying process can be more effective. In this thesis, studies were made of using a filler as an additive to increase the dry content without destroying the barrier properties.</p><p>With an experimental design, a suitable relationship between the ingredients xylan (X), plasticizer (P) and filler (F) was found. Xylan is the main component and is needed to get a good oxygen barrier. The plasticizer decreases the oxygen barrier properties but is needed to make the material more flexible. The filler is positive for the barrier properties. The chosen composition was X:P = 7:3 and X:F = 1:1. Some extra experiments were made to find a reasonable value of the dry content. Dry contents around 18 % work well with temperatures at and above 45°C, but to manage to perform coating at room temperature the dry content needs to be lower.</p>

<p>A colloid of magnesium hydroxide is used to stabilize droplets of monomers before suspension polymerisation. The characteristics of precipitated magnesium hydroxide changes significantly during the first hours. The viscosity is high and flucctuating at first but decreases and becomes low and stable after a few hours. When the colloid ages the primary particles agglomerate into larger particles which increases in size by time due to, among other things, Oswald ripening and aggregation. This can cause problems with poor reproducibility in the production. Therefore, the purpose of this study was finding a way to age the colloid without an increase in particle size and without changing any other features. Several experiments were made to optimize the precipitation procedure and to find out what parameters that are most important. The results showed that the stirring rate and colloidal concentration have big influence.</p><p>Small amounts of chemicals that modifies the surface of the colloid was added. This made the particle size near constant over time and the colloid was aged for two months without increasing in size or changing other properties. This was confirmed by making microspheres that had the same characteristics as microspheres made with a fresh colloid.</p>

Current commonly use viscosity measurement techniques cannot be used for all types of fluids. For fluids in the under cooled region a new method of measuring the viscosity is required. A process of viscosity measurement, by measuring the speed of droplet coalescence in a microgravity environment, was developed. This paper analyses validation experiments performed on the International Space Station. Four experiments were analyzed. Two of the experiments provided results consistent with the known value for the viscosity. One of the experiments did not provide sufficient data for analysis. The final experiment had possible errors due to the experimental setup. The resulting data from these experiments demonstrated that the method is feasible. However, more experiments are needed to fully verify the process.

Proper selection of drilling fluids plays a major role in determining the efficient completion of any drilling operation. With the increasing number of ultra-deep offshore wells being drilled and ever stringent environmental and safety regulations coming into effect, it becomes necessary to examine and understand the behavior of water based drilling fluids - which are cheaper and less polluting than their oil based counterpart - under extreme temperature and pressure conditions. In most of the existing literature, the testing procedure is simple - increase the temperature of the fluid in steps and record rheological properties at each step. A major drawback of this testing procedure is that it does not represent the continuous temperature change that occurs in a drilling fluid as it is circulated through the well bore. To have a better understanding of fluid behavior under such temperature variation, a continuous test procedure was devised in which the temperature of the drilling fluid was continuously increased to a pre-determined maximum value while monitoring one rheological parameter. The results of such tests may then be used to plan fluid treatment schedules. The experiments were conducted on a Chandler 7600 XHPHT viscometer and they seem to indicate specific temperature ranges above which the properties of the drilling fluid deteriorate. Different fluid compositions and drilling fluids in use in the field were tested and the results are discussed in detail.

A colloid of magnesium hydroxide is used to stabilize droplets of monomers before suspension polymerisation. The characteristics of precipitated magnesium hydroxide changes significantly during the first hours. The viscosity is high and flucctuating at first but decreases and becomes low and stable after a few hours. When the colloid ages the primary particles agglomerate into larger particles which increases in size by time due to, among other things, Oswald ripening and aggregation. This can cause problems with poor reproducibility in the production. Therefore, the purpose of this study was finding a way to age the colloid without an increase in particle size and without changing any other features. Several experiments were made to optimize the precipitation procedure and to find out what parameters that are most important. The results showed that the stirring rate and colloidal concentration have big influence. Small amounts of chemicals that modifies the surface of the colloid was added. This made the particle size near constant over time and the colloid was aged for two months without increasing in size or changing other properties. This was confirmed by making microspheres that had the same characteristics as microspheres made with a fresh colloid.

No description available.

Blood is a dense suspension of flexible red blood cells. In response to a background flow, these cells distribute themselves non-uniformly throughout the vessel. As a result, material properties that are well defined in homogeneous fluids, such as viscosity, are no longer so, and depend upon the flow geometry along with the particle properties. Using a simple model that accounts for the steady-state particle distribution in vessel flow, we derive an expression for the effective viscosity of blood and the suspension flow velocity field in a pressure-driven tube flow. <br /><br /> We derive the steady-state particle distribution from a conservation equation with convective flux arising from particle deformation in the flow. We then relate the particle microstructure to the overall flow through a generalized Newtonian stress-tensor, with the particle volume fraction appearing in the expression for the local viscosity. Comparing with experimental data, we show that the model quantitatively reproduces the observed rheology of blood in tube flow. <br /><br /> We reconsider the problem in an alternate geometry corresponding to the flow between two concentric cylinders. The steady-state particle distribution, suspension velocity field and the measured effective viscosity are all very different from their counterparts in tube flow, casting serious doubt upon the practice of using data from a Couette viscometer to parameterize constitutive models applied to vascular blood flow. <br /><br /> Finally, we calculate the effect of random fluctuations in the particle velocity on the averaged behaviour of the particle conservation equation. Using a smoothing method for linear stochastic differential equations, we derive a correction to the free Einstein-Stokes diffusion coeffcient that is due to the interaction of the particles with their neighbours.