The dynamics of liquid slugs forced by a syringe pump

Microfluidic processes for chemical synthesis have become popular in recent years. The small scale of the chemical reactions promise greater control over reaction conditions and more timely creation of products. The small scale of microfluidics poses its own set of problems, however. At the microscale, the dominant fluid forces are viscous resistance and surface tension. The effects of viscosity and scale reduce the Reynolds number and make mixing difficult. Much work has been done to control mixing at the microscale. This problem is concerned with a different microfluidic problem: delivering reactants to the site of reaction. A common setup is to attach syringes full of reactant to a reaction chamber by narrow hydrophobic tubing. Using a stepper motor, a controlled dose of liquid may be injected into the tube. The hydrophobosity causes the dose to curve outward on the sides, becoming a "slug" of reactant with air in front and behind. The syringe at the rear is then switched for one full of air, and air pressure is used to drive the slug to the reaction site. If too much pressure is applied, the slug will arrive with a significant back pressure that will be relieved through bubbling in the reaction site. This causes the formation of a foam and is highly undesirable. We present a simple model based on Boyle’s law for the motion of a slug through a tube. We then extend this model for trains of slugs separated by air bubbles. Last, we consider the case of a flooded reaction site, where the forward air bubble must be pushed through the flooding liquid. In conclusion, we have determined the dynamics of a single slug moving towards an empty reaction chamber giving the final equilibrium position of the slug. A phase-plane analysis then determined a condition on the size of the slug needed to ensure that it comes to rest without oscillating about the equilibrium position. The effect of a flooded reaction chamber was then considered. In this case it is impossible to avoid bubbling due to the design of the device. We found that it is possible, however, to reduce the bubbling by minimising the back pressure behind the slug. Finally, the dynamics of multiple slugs with or without a flooded reaction chamber has been investigated

Homogenization of the Equations Governing the Flow Between a Slider and a Rough Spinning Disk

We have analyzed the behavior of the flow between a slider bearing and a hard-drive magnetic disk under two types of surface roughness. For both cases the length scale of the roughness along the surface is small as compared to the scale of the slider, so that a homogenization of the governing equations was performed. For the case of longitudinal roughness, we derived a one-dimensional lubrication-type equation for the leading behavior of the pressure in the direction parallel to the velocity of the disk. The coefficients of the equation are determined by solving linear elliptic equations on a domain bounded by the gap height in the vertical direction and the period of the roughness in the span-wise direction. For the case of transverse roughness the unsteady lubrication equations were reduced, following a multiple scale homogenization analysis, to a steady equation for the leading behavior of the pressure in the gap. The reduced equation involves certain averages of the gap height, but retains the same form of the usual steady, compressible lubrication equations. Numerical calculations were performed for both cases, and the solution for the case of transverse roughness was shown be in excellent agreement with a corresponding numerical calculation of the original unsteady equations

Automated mobile virtual reality cognitive behavior therapy for aviophobia in a natural setting: a randomized controlled trial

Background: Access to evidence-based psychological treatment is a challenge worldwide. We assessed the effectiveness of a fully automated aviophobia smartphone app treatment delivered in combination with a $5 virtual reality (VR) viewer.Methods: In total, 153 participants from the Dutch general population with aviophobia symptoms and smartphone access were randomized in a single-blind randomized controlled trial to either an automated VR cognitive behavior therapy (VR-CBT) app treatment condition (n = 77) or a wait-list control condition (n = 76). The VR-CBT app was delivered over a 6-week period in the participants' natural environment. Online self-report assessments were completed at baseline, post-treatment, at 3-month and at 12-month follow-up. The primary outcome measure was the Flight Anxiety Situations Questionnaire (FAS). Analyses were based on intent-to-treat.Results: A significant reduction of aviophobia symptoms at post-test for the VR-CBT app compared with the control condition [p Conclusions: This study is the first to show that fully automated mobile VR-CBT therapy delivered in a natural setting can maintain long-term effectiveness in reducing aviophobia symptoms. In doing so, it offers an accessible and scalable evidence-based treatment solution that can be applied globally at a fraction of the cost of current treatment alternatives

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries

AN X-Y CORIOLIS PERTURBATION IN ν4\nu_{4} OF CD3BrCD_{3}Br

Author Institution:The 2242-2273 \mbox{cm}^{-1} region of the $\nu_{4}$ band in $CD_{3}Br$ has been remeasured at a resolution limit of 0.025 \mbox{cm}^{-1}. Line assignments have been extended up to $J = 50$ in some sub-bands. Transitions in the $KAK = -8$ sub-band have been assigned, and the perturbation apparent in this region has been analyzed by considering the Coriolis x-y interaction with $\nu_{3}+\nu_{5}^{\pm 1}+\nu_{6}^{\pm 1}$. The Coriolis x-y coupling parameter $W_{xy}$ and the $\nu_{3}+\nu_{5}^{\pm 1}+\nu_{6}^{\pm 1}$ band center (in \ \mbox{cm}^{-1}) are 0.1960 and 2339.17 for $CD_{3}^{79}Br$, while the corresponding values for $CD_{3}^{81}Br$ are 0.01956 ad 2337.95