Search results for: reaction diffusion equation

Authors: L. Ereku, R. E. Mackay, A. Naveenathayalan, K. Ajayi, W. Balachandran

Abstract:

Over the past decade the increase of sexually transmitted infections (STIs) especially in the developing world due to high cost and lack of sufficient medical testing have given rise to the need for a rapid, low cost point of care medical diagnostic that is disposable and most significantly reproduces equivocal results achieved within centralised laboratories. This paper present the development of a disposable PDMS microfluidic cartridge incorporating blisters filled with reagents required for isothermal DNA amplification in clinical diagnostics and point-of-care testing. In view of circumventing the necessity for external complex microfluidic pumps, designing on-chip pressurised fluid reservoirs is embraced using finger actuation and blister storage. The fabrication of the blisters takes into consideration three proponents that include: material characteristics, fluid volume and structural design. Silicone rubber is the chosen material due to its good chemical stability, considerable tear resistance and moderate tension/compression strength. The case of fluid capacity and structural form go hand in hand as the reagent need for the experimental analysis determines the volume size of the blisters, whereas the structural form has to be designed to provide low compression stress when deformed for fluid expulsion. Furthermore, the top and bottom section of the blisters are embedded with miniature polar opposite magnets at a defined parallel distance. These magnets are needed to lock or restrain the blisters when fully compressed so as to prevent unneeded backflow as a result of elasticity. The integrated chip is bonded onto a large microscope glass slide (50mm x 75mm). Each part is manufactured using a 3D printed mould designed using Solidworks software. Die-casting is employed, using 3D printed moulds, to form the deformable blisters by forcing a proprietary liquid silicone rubber through the positive mould cavity. The set silicone rubber is removed from the cast and prefilled with liquid reagent and then sealed with a thin (0.3mm) burstable layer of recast silicone rubber. The main microfluidic cartridge is fabricated using classical soft lithographic techniques. The cartridge incorporates microchannel circuitry, mixing chamber, inlet port, outlet port, reaction chamber and waste chamber. Polydimethylsiloxane (PDMS, QSil 216) is mixed and degassed using a centrifuge (ratio 10:1) is then poured after the prefilled blisters are correctly positioned on the negative mould. Heat treatment of about 50C to 60C in the oven for about 3hours is needed to achieve curing. The latter chip production stage involves bonding the cured PDMS to the glass slide. A plasma coroner treater device BD20-AC (Electro-Technic Products Inc., US) is used to activate the PDMS and glass slide before they are both joined and adequately compressed together, then left in the oven over the night to ensure bonding. There are two blisters in total needed for experimentation; the first will be used as a wash buffer to remove any remaining cell debris and unbound DNA while the second will contain 100uL amplification reagents. This paper will present results of chemical cell lysis, extraction using a biopolymer paper membrane and isothermal amplification on a low-cost platform using the finger actuated blisters for reagent storage. The platform has been shown to detect 1x105 copies of Chlamydia trachomatis using Recombinase Polymerase Amplification (RPA).

Keywords: finger actuation, point of care, reagent storage, silicone blisters

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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