Some transmission line transients. Graphical evaluation by Fourier's series     

J.A. Strelzoff 《Journal of The Franklin Institute》1934,217(3):353-372

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Release of formaldehyde during the biofiltration of methanol vapors in a peat biofilter inoculated with Pichia pastoris GS115     

《Electronic Journal of Biotechnology》2019

BackgroundMethanol can be effectively removed from air by biofiltration. However, formaldehyde is one of the first metabolic intermediates in the consumption of methanol in methylotrophic microorganisms, and it can be released out of the cell constituting a secondary emission.ResultsThe total removal of methanol was achieved up to input loads of 263 g m⁻³ h⁻¹ and the maximum elimination capacity of the system was obtained at an empty bed residence times of 90 s and reached 330 g m⁻³ h⁻¹ at an input methanol load of 414 g m⁻³ h⁻¹ and 80% of removal efficiency. Formaldehyde was detected inside the biofilter when the input methanol load was above 212 g m⁻³ h⁻¹. Biomass in the filter bed was able to degrade the formaldehyde generated, but with the increase of the methanol input load, the unconsumed formaldehyde was released outside the biofilter. The maximum concentration registered at the output of the system was 3.98 g m⁻³ when the methanol load was 672 g m⁻³ h⁻¹ in an empty bed residence times of 60 s.ConclusionsFormaldehyde is produced inside a biofilter when methanol is treated in a biofiltration system inoculated with Pichia pastoris. Biomass present in the reactor is capable of degrading the formaldehyde generated as the concentration of methanol decreases. However, high methanol loads can lead to the generation and release of formaldehyde into the environment.How to cite: Guerrero K, Arancibia A, Cáceres M, et al. Release of formaldehyde during the biofiltration of methanol vapors in a peat biofilter inoculated with Pichia pastoris GS115. Electron J Biotechnol 2019;40. https://doi.org/10.1016/j.ejbt.2019.04.003.  相似文献   

Periodic solutions to systems of reaction-diffusion equations     

Gerald Rosen 《Journal of The Franklin Institute》1976,301(3):307-312

In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?c_i/?t = D_i?²c_i+Q_i(c), where the enumerator index i runs 1 to n, c_i = c_i(x, t) denotes the concentration or density of the ith participating molecular or biological species, D_i is the diffusivity constant for the ith species and Q_i(c), an algebraic function of the n-tuple c = (c₁,\3., c_n), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.  相似文献   

Advanced stability criteria for linear systems with time-varying delays     

M.J. Park  O.M. Kwon  J.H. Ryu 《Journal of The Franklin Institute》2018,355(1):520-543

This paper investigates a stability problem for linear systems with time-varying delays. By constructing suitable augmented Lyapunov–Krasovskii functionals, improved stability criteria under various conditions of time-varying delays are derived within the framework of linear matrix inequalities (LMIs). Moreover, to reduce the computational burden caused by the non-convex term including h²(t), how to deal with it is applied by estimating it to the convex term including h(t). Finally, three illustrative examples are given to show the effectiveness of the proposed criteria.  相似文献   

Artificial helical microswimmers with mastigoneme-inspired appendages     

Soichiro Tottori  Bradley J. Nelson 《Biomicrofluidics》2013,7(6)

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Label-free density difference amplification-based cell sorting     

Jihwan Song  Minsun Song  Taewook Kang  Dongchoul Kim  Luke P. Lee 《Biomicrofluidics》2014,8(6)

The selective cell separation is a critical step in fundamental life sciences, translational medicine, biotechnology, and energy harvesting. Conventional cell separation methods are fluorescent activated cell sorting and magnetic-activated cell sorting based on fluorescent probes and magnetic particles on cell surfaces. Label-free cell separation methods such as Raman-activated cell sorting, electro-physiologically activated cell sorting, dielectric-activated cell sorting, or inertial microfluidic cell sorting are, however, limited when separating cells of the same kind or cells with similar sizes and dielectric properties, as well as similar electrophysiological phenotypes. Here we report a label-free density difference amplification-based cell sorting (dDACS) without using any external optical, magnetic, electrical forces, or fluidic activations. The conceptual microfluidic design consists of an inlet, hydraulic jump cavity, and multiple outlets. Incoming particles experience gravity, buoyancy, and drag forces in the separation chamber. The height and distance that each particle can reach in the chamber are different and depend on its density, thus allowing for the separation of particles into multiple outlets. The separation behavior of the particles, based on the ratio of the channel heights of the inlet and chamber and Reynolds number has been systematically studied. Numerical simulation reveals that the difference between the heights of only lighter particles with densities close to that of water increases with increasing the ratio of the channel heights, while decreasing Reynolds number can amplify the difference in the heights between the particles considered irrespective of their densities.Separating specific cells from heterogeneous or homogeneous mixtures has been considered as a key step in a wide variety of applications ranging from biomedicine to energy harvesting. For example, the separation and sorting of rare circulating tumor cells (CTCs) from whole blood has gained significant importance in the potential diagnosis and treatment of metastatic cancers.^1,2 Similarly, malaria detection relies on the collection of infected red blood cells (RBCs) from whole blood.^3,4 In addition, the selective separation of lipid-rich microalgae from homogeneous mixtures of microalgae is a promising technique in biomass conversion.⁵To date, conventional cell separation can be done by labelling cells with biomolecules to induce differences in physical properties. For instance, in a fluorescence-activated cell sorter (FACS), cells to be separated are labelled with antibodies or aptamers with fluorescent molecules, and then sorted by applying an electrical potential.^6,7 Similarly, magnetic-activated cell sorter (MACS) uses magnetic.^8,9 Alternatively, label-free cell separation methods have exploited inherent differences in the physical properties (e.g., size and dielectric properties) of different kinds of cells. For example, acoustophoresis forces particles larger than a desired size to move into the center of a fluidic channel by using ultrasonic standing waves.^10–12 Inertial microfluidics takes advantage of curved fluidic channels in order to amplify the size differences between particles.^13,14 Mass-dependent separation of particles based on gravity and hydrodynamic flow was also reported.¹⁵ Particles with different dielectric properties can also be sorted by dielectrophoresis which induces the movement of polarizable particles.^16–18The disadvantage of these methods, however, is that they require external forces and labels that may cause unexpected damage to biological cells.^19–21 More importantly, most methods are limited in separating cells of the same kind or cells with similar sizes and dielectric properties.Here we designed a novel, label-free density difference amplification-based cell sorting (dDACS) that allows the separation of particles with the same size and charge by exploiting subtle differences in density without the use of external forces. Figure 1(a) illustrates the proposed microfluidic model and its underlying mechanism. The conceptual microfluidic system consists of an inlet, a separation chamber (hydraulic jump cavity), and multiple outlets. Particles entering through the inlet experience gravity (F_G), buoyancy (F_B), and drag (F_D) forces in the separation chamber. The net force acting on the particles can be described as F = F_G + F_B + F_D.(1)As particles enter the separation chamber (i.e., hydraulic jump cavity), F_D acting on the particles changes its direction along the streamline. The particles experience additional forces in the y direction due to large tangential angle (Fig. 1(b)). For lighter particles, whose densities are close to that of the surrounding water, F_D becomes comparable to F_G (i.e., in the y direction), while the net force for heavier particles is less affected by this additional contribution of F_D due to a large F_G. As a result, the height (H) and distance (D) that each particle can travel are different depending on its density. The difference in the maximum height (ΔH_max) between two particles with different density (ρ_p1 and ρ_p2) can be further approximated as ΔHmax∝(vyp0)2(vyf−vyp0), (ρp1−ρp2) ,(2)where v_yp0 and v_yf represent the velocity of particle and fluid along the y direction at the entrance of hydraulic jump cavity, respectively.Open in a separate windowFIG. 1.Schematic illustration of label-free density difference amplification-based cell sorting (dDACS), which exploits differences in the densities (ρ₁ > ρ₂) of particles with similar diameters (d) and charge. (a) The conceptual microfluidic design consists of an inlet, a separation chamber (hydraulic jump cavity), and multiple outlets. Incoming particles experience gravity (F_G), buoyancy (F_B), and drag (F_D) forces in the separation chamber, and depending on their densities, the height (H) and distance (D) that each particle is able to reach will be different, allowing the particles to be separated into multiple outlets. (b) Possible microfluidic channel configurations for density-based separation: Uniform channel height (left), gradual channel expansion (middle), and hydraulic jump cavity with sudden channel expansion (right). The height difference between particles with different densities can be amplified by the sudden channel expansion compared to the other two cases due to the relatively large tangential angle, θ of F_D. (|θ₁|≪ |θ₂|) (see Fig. S1 in the supplementary material²²).In comparison with the other two cases (Fig. 1(b) uniform channel height and gradual channel expansion), the height difference between the particles with different densities can be amplified by the sudden channel expansion in the hydraulic jump cavity due to relatively large tangential angle (see supplementary material²²). Therefore, the particles can be separated through the multiple outlets, depending on their height and distance.In order to analyze the separation behavior of particles in the chamber according to differences in their densities, H and D are systematically investigated. The numerical simulations are performed using a commercial CFD software (CFX 14.0; ANSYS 14.0; ANSYS, Inc.). Particles with the same density may have different trajectories in the separation chamber depending on their inlet positions (Fig. 2(a)). Prior to this investigation, the maximum height (H_max) and distance (D_max) for each particle are compared by examining H and D of 100 identical particles at different inlet positions since the inlet position of particles could be controlled.²⁰ Fig. 2(b) shows H_max and D_max of particles with respect to density at a fixed Reynolds number (Re = 0.1). Note that Reynolds number is defined as Re = ρ_fv_fD_h/μ, where ρ_f, v_f, D_h, μ are density of fluid, velocity of the fluid, hydraulic diameter of a channel, and dynamic viscosity of the fluid, respectively. The hydraulic diameter in the Reynolds number is determined with the inlet channel. Particle densities in the range of 1.1 to 2.0 g/cm³ are chosen with the increase of 0.1 g/cm³. These values are quite reasonable in that the densities of many microorganisms such as microalgae are typically within this range and their densities can be varied by 0.2 g/m³ depending on their cellular context.²³ The lighter particles travel with a higher H_max, and longer D_max. With the separation chamber, the height difference between particles with densities of 1.1 and 1.2 g/cm³ can be amplified by about 10 times as compared to that in a channel without the chamber, judging from the position where the 1.1 g/cm³ particle reaches its H_max.Open in a separate windowFIG. 2.Microfluidic particle separation with respect to Reynolds number (Re). (a) Trajectories in the separation chamber of a hundred particles with the same density starting from inlet positions chosen arbitrarily in order to investigate the effect of the inlet positions on the maxima of the height (H_max) and distance (D_max) prior to further simulation. (b) Representative trajectories of particles having different densities from 1.1 to 2.0 g/cm³. (c) The maximum height (H_max) of each particle with respect to Re. (d) Representative maximum distance (D_max) of each particle at Re = 0.1. (Left) Streamline of fluid and representative trajectories of particles with densities of 1.1 and 2.0 g/cm³ in the separation chamber at Re = 0.1 (right).In Fig. 2(c), the values for H_max of particles with respect to Reynolds number (Re) are presented. Since in our study, the maximum height (H_max) and distance (D_max) for each particle were compared by examining H and D of 100 identical particles that are randomly distributed in the channel (throughout all figures), there is little variation in H_max and D_max between each simulation. However, the standard deviation between each simulation is quite small and can be negligible. The H_max values particles at Re = 0.5 with densities of 1.1 g/cm³ and 1.2 g/cm³ are 2.21 × 10³μm and 2.17 × 10³μm, respectively. The difference between H_max of different particles, ΔH_max, increases with decreasing Re. For example, ΔH_max between particles with densities of 1.1 and 2.0 g/cm³ becomes 0.26 × 10³μm at Re = 1.0, but increases to 1.38 × 10³μm as Re decreases to 0.1. As Re increases (velocity of fluid increases), the relative velocity in the y direction between the fluid and the particle increases resulting in increasing of F_D in the y direction since the velocity of particle in the y direction is very small at the entrance of the separation chamber. Thus, contribution of F_D becomes comparable to the net force in the y direction. As a result, most of the particles even in the case of heavier ones travel quite similarly with the streamline, and ΔH_max subsequently decreases. On the other hand, as Re decreases, the contribution of F_G becomes dominant due to the decrease of F_D in the y direction. Consequently, the particles start to cross downwards streamlines as the density of the particles increases and H_max gradually decreases. In addition, irrespective of their densities, ΔH_max of the particles increases with decreasing Re.Fig. 2(d) shows D_max with respect to the density of the particles (left). Different densities of particles show different trajectories due to the relative contribution of F_D to the net force in the y direction depending on the particle density (right). At Re = 0.1, D_max of particles with densities of 1.1 cm³ and 1.2 g/cm³ are 2.91 × 10⁴μm and 1.43 × 10⁴μm, respectively. As the density of a particle increases, its D_max dramatically decreases. The difference in D_max between particles with densities of 1.1 and 1.2 g/cm³ is 1.48 × 10⁴μm, and 0.0037 × 10⁴μm for particles with densities of 1.9 and 2.0 g/cm³. The effect of F_D is stronger compared to that of F_G on lighter particles. Thus, lighter particles travel quite similarly with the streamline and finally have a large D_max. On the other hand, heavier particles where effect of F_G is stronger compared to that of F_D cross downwards streamlines and finally have a small D_max.Next, in order to investigate the separation behavior of particles with respect to the geometry of the microfluidic device, the effect of the ratio of the height of the separation chamber (h_c) to the inlet (h_i) on H_max is investigated as shown in Fig. ​Fig.3.3. Interestingly, H_max of particles with density of 1.1 g/cm³ increases from 1.93 × 10³μm to 6.48 × 10³μm while that of particles with density of 1.9 g/cm³ slightly changes from 0.70 × 10³μm to 0.73 × 10³μm as h_c/h_i increases from 5 to 20.Open in a separate windowFIG. 3.Microfluidic particle separation with respect to the ratio of the height of the inlet (h_i) to the separation chamber (h_c).This result can be attributed to two effects: (1) the change in the streamline and (2) the relative contribution of drag force to the net force depending on the density. With increasing h_c/h_i, dramatic increase in H_max for lighter particles is because the streamline for the lighter ones experiences more vertical displacement in the separation chamber and the contribution of F_D to the net force acting on the lighter one is more significant (see Fig. S2 in the supplementary material²²).Based on this approach, we propose a microfluidic device for the selective separation of the lightest particle. Fig. 4(a) shows one unit (with three outlets) of the proposed microfluidic device that can be connected in series. The ratio of channel heights (h_c/h_i) is set to 20, and the particle densities are in the range of 1.1 ∼ 1.5 g/m³. Fig. 4(b) shows the representative separation behavior of the particles. A portion of the lightest particles (1.1 g/cm³) is selectively separated into the upper and middle outlets, while remaining light particles together with four other heavier particles with densities in the range of 1.2 to 1.5 g/cm³ leave through the lowest outlet. With a single operation of this unit, 40% of the lightest particles are recovered. In addition, the yield increases with increasing number of cycles (Fig. 4(c)).Open in a separate windowFIG. 4.(a) One unit of the proposed microfluidic device for the selective separation of the lightest particle based on the simulation results. Particles are separated into two outlets based on differences in both the height and distance travelled stemming from differences in density. (b) Representative separation behavior of particles observed in the device. (c) The yield of the lightest particle (1.1 g/cm³) with the proposed microfluidic device according to the number of cycles (i.e., this unit is assumed to be connected in series).In summary, we have demonstrated a label-free microfluidic system for the separation of particles according to subtle differences in their densities without external forces. Our microfluidic design consists simply of an inlet, a separation chamber, and multiple outlets. When entering the separation chamber, the particles experience an additional drag force in the y direction, amplifying the difference in both the height and the distance that the particles with different densities can travel within the chamber. At a fixed Reynolds number, with increasing particle density, H_max decreases monotonously, and D_max decreases dramatically. On the other hand, as Reynolds number increases, the difference between the heights of particles with different densities is attenuated. In addition, the simulation reveals that increasing the ratio of the channel heights increases the difference between the heights of particles only when their densities are close to that of the surrounding water. Based on this approach, a microfluidic device for the separation of the lightest particles has been proposed. We expect that our density-based separation design can be beneficial to the selective separation of specific microorganisms such as lipid-rich microalgae for energy harvesting application.  相似文献   

Release of formaldehyde during the biofiltration of methanol vapors in a peat biofilter inoculated with Pichia pastoris GS115     

《Electronic Journal of Biotechnology》2020

BackgroundMethanol can be effectively removed from air by biofiltration (Shareefdeen et al., 1993; Babbitt et al., 2009 [1,2]). However, formaldehyde is one of the first metabolic intermediates in the consumption of methanol in methylotrophic microorganisms (Negruţa et al., 2010 [3]), and it can be released out of the cell constituting a secondary emission.ResultsThe total removal of methanol was achieved up to input loads of 263 g m⁻³ h⁻¹ and the maximum elimination capacity of the system was obtained at an empty bed residence times of 90 s and reached 330 g m⁻³ h⁻¹ at an input methanol load of 414 g m⁻³ h⁻¹ and 80% of removal efficiency. Formaldehyde was detected inside the biofilter when the input methanol load was above 212 g m⁻³ h⁻¹. Biomass in the filter bed was able to degrade the formaldehyde generated, but with the increase of the methanol input load, the unconsumed formaldehyde was released outside the biofilter. The maximum concentration registered at the output of the system was 3.98 g m⁻³ when the methanol load was 672 g m⁻³ h⁻¹ in an empty bed residence times of 60 s.ConclusionsFormaldehyde is produced inside a biofilter when methanol is treated in a biofiltration system inoculated with Pichia pastoris. Biomass present in the reactor is capable of degrading the formaldehyde generated as the concentration of methanol decreases. However, high methanol loads can lead to the generation and release of formaldehyde into the environment.How to cite: Guerrero K, Arancibia A, Caceres M, et al. Release of formaldehyde during the biofiltration of methanol vapors in a peat biofilter inoculated with Pichia pastoris GS115. Electron J Biotechnol 2019;40. https://doi.org/10.1016/j.ejbt.2019.04.003.  相似文献   

Output feedback stabilization for symmetric control systems     

Carmen Coll  Néstor Thome 《Journal of The Franklin Institute》2005,342(7):814-823

This work is devoted to the study of symmetric control systems. It establishes a relation between internal symmetry and external one for a linear invariant control system having n real simple poles. The symmetric stabilization problem is studied using a symmetric feedback gain such that the output control stabilizes the closed-loop system. A necessary and sufficient condition is given to solve this stabilization problem for a symmetric control system (A,B,C) and a generalized symmetric control system (E,A,B,C).  相似文献   

Increases in alginate production and transcription levels of alginate lyase (alyA1) by control of the oxygen transfer rate in Azotobacter vinelandii cultures under diazotrophic conditions     

《Electronic Journal of Biotechnology》2021

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Enhancement of biosensing performance in a droplet-based bioreactor by in situ microstreaming     

Olivier Ducloux  Elisabeth Galopin  Farzam Zoueshtiagh  Alain Merlen    Vincent Thomy 《Biomicrofluidics》2010,4(1)

A droplet-based micro-total-analysis system involving biosensor performance enhancement by integrated surface-acoustic-wave (SAW) microstreaming is shown. The bioreactor consists of an encapsulated droplet with a biosensor on its periphery, with in situ streaming induced by SAW. This paper highlights the characterization by particle image tracking of the speed distribution inside the droplet. The analyte-biosensor interaction is then evaluated by finite element simulation with different streaming conditions. Calculation of the biosensing enhancement shows an optimum in the biosensor response. These results confirm that the evaluation of the Damköhler and Peclet numbers is of primary importance when designing biosensors enhanced by streaming.It has been pointed out that biosensing performances can be limited by the diffusion of the analytes near the sensing surface.¹ In the case of low Peclet number hydrodynamic flows, typical of microfluidic systems, molecule displacements are mainly governed by diffusive effects that affect time scales and sensitivity. To overcome this problem, the enhancement of biosensor performance by electrothermal stirring within microchannels was first reported by Meinhart et al.² Other authors^{3, 4} numerically studied the analyte transport as a function of the position of a nanowire-based sensor inside a microchannel, stressing on the fact that the challenge for nanobiosensors is not the sensor itself but the fluidic system that delivers the sample. Addressing this problem, Squires et al.⁵ developed a simple model applicable to biosensors embedded in microchannels. However, the presented model is limited to the case of a steady flow. The use of surface-acoustic waves (SAWs) for stirring in biomicrofluidic and chemical systems is becoming a popular investigation field,^{6, 7, 8, 9} especially to overcome problems linked to steady flows by enhancing the liquid∕surface interaction.^{1, 10, 11} The main challenges that need to be addressed when using SAW-induced stirring are the complexity of the flow and its poor reproducibility. However, some technical solutions were proposed to yield a simplified microstreaming. Yeo et al. presented a centrifugation system based on SAW that produces the rotation of the liquid in a droplet in a reproducible way by playing on the configuration of the transducers and reflectors,¹² and presented a comprehensive experimental study of the three-dimensional (3D) flow that causes particle concentration in SAW-stirred droplets,¹³ revealing the presence of an azimuthal secondary flow in addition to the main vortexlike circular flow present in acoustically stirred droplets. The efficiency of SAW stirring in microdroplets to favorably cope with mass transport issues was finally shown by Galopin et al.,¹⁴ but the effect of the stirring on the analyte∕biosensor interaction was not studied. It is expected to overcome mass transport limitations by bringing fresh analytes from the bulk solution to the sensing surface.The studied system, described in Fig. ​Fig.1,1, consists of a microliter droplet microchamber squeezed between a hydrophobic piezoelectric substrate and a hydrophobic glass cover. Rayleigh SAWs are generated using interdigitated transducers (interdigital spacing of 50 μm) laid on an X-cut LiNbO₃ substrate.^{1, 15, 16} The hydrophobicity of the substrate and the cover are obtained by grafting octadecyltrichlorosilane (OTS) self-assembled monolayers (contact angle of 108° and hysteresis of 9°). To do so, the surface is first hydroxylized using oxygen plasma (150 W, 100 mT, and 30 sccm³ O₂) during 1 min and then immersed for 3 h into a 1 mM OTS solution with n-hexane as a solvent.Open in a separate windowFigure 1(a) General view of the considered system. (b) Mean value of the measured speeds within the droplet as a function of the inlet power before amplification.When Rayleigh waves are radiated toward one-half of the microchamber, a vortex is created in the liquid around an axis orthogonal to the substrate due to the momentum transfer between the solid and the liquid. This wave is generated under the Rayleigh angle into the liquid.Speed cartographies of the flow induced in the droplet are realized using the particle image tracking technique for different SAW generation powers. To do so, instantaneous images of the flow are taken with a high-speed video camera at 200 frames∕s and an aperture time of 500 μs on a 0.25 μl droplet containing 1 μm diameter fluorescent particles. Figure ​Figure11 shows the mean speed measured in the droplet as a function of the inlet power. The great dependence of the induced mean speed with the SAW power enables a large range of flow speeds in the stirred droplet. Moreover, the flow was visualized with a low depth of field objective. It was found to be circular and two dimensional (2D) in a large thickness range of the droplet.The binding of analytes to immobilized ligands on a biosensor is a two step process, including the mass transport of the analyte to the surface, followed by a complexation step,Abulk↔kmAsurface+B↔ka,kdAB(1)with k_m as the constant rate for mass transport from and to the sensor, and k_a and k_d as the constant rates of association and dissociation of the complex.At the biosensor surface, the reaction kinetics consumes analytes but their transport is limited by diffusive effects. In this case, the Damköhler number brings valuable information by comparing these two effects. Calling the characteristic time of reaction and diffusion, respectively, τ_C and τ_M, the mixing time in diffusion regime can be approximated by τ_M≈h²∕D with D as the diffusion coefficient and h a characteristic length of the microchannel. Calling R_T the ligand concentration on the surface in mole∕m², the Damköhler number (D_a) can be written asDa=τMτC=kaRThD.(2)Depending on the type of reaction, the calculation of D_a helps determine if a specific biointeraction will benefit from a mass SAW-based microstreaming. If the Damköhler number is low, the reaction is slow compared to mass transport and the reaction will not significantly benefit from microstirring. For example, the hybridization of 19 base single stranded DNA in a microfluidic system with a characteristic length of 500 μm is characterized by a Damköhler number of 0.07 and is therefore not significantly influenced by mass transport. On the contrary, the binding of biotin to immobilized streptavidin is characterized by a D_a number of approximately 10⁴. In this case, the stirring solution will significantly improve the reaction rate.COMSOL numerical simulations were carried out to study the efficiency of the SAW stirring in the case of a droplet-based microbioreactor with a diameter of 1 mm. Assuming a 2D flow, the simulated model takes into account the convective and diffusive effects in the analyte-carrying fluid and the binding kinetics on the biosensor surface. This approach was thoroughly developed by Meinhart et al.²On the biosensor surface, the following equations are solved:∂B∂t=kacs(RT−B)−kdB,(3)∂B∂t=D|∂c∂y|y=0(4)with c as the local concentration of analytes in the droplet and B as the surface concentration of bound analytes on the biosensor surface. Simulation results show that a depleted zone is formed near the biosensor in the case of an interaction without stirring. This zone is characterized by a low concentration of analytes and results from the trapping of analytes on the biosensor surface, thus creating a concentration gradient on the vicinity of the biosensor. When stirring is applied, the geometry of the depleted zone is modified, as it is pushed in the direction of the flow. The geometry of the depleted zone then depends on many parameters, among which the diffusion coefficient D, the speed distribution of the flow (not only near the biosensor but also in the whole microfluidic system), and the reaction kinetics on the biosensor. In our case, which is assimilated to a simple circular flow, the depleted zone reaches a permanent state consisting of an analyte-poor layer situated in the exterior perimeter of the stirred droplet. The diffusion of analytes is then limited again by diffusion from the inner part of the droplet toward its exterior perimeter (see Fig. ​Fig.22).Open in a separate windowFigure 2(a) Mean concentration of bound analytes vs time for different mean flow speeds. (b) The obtained concentration profiles with and without circular stirring, t=10 000 s.The initial analyte and receptor concentrations are, respectively, 0.1 nM in the solution and 3.3×10⁻³ nM m on the biosensor surface, the diffusion coefficient is D=10⁻¹¹ m² s⁻¹, and the reaction constants are k_a=10⁶ M⁻¹ s⁻¹ and k_d=10⁻³ s⁻¹. Simulations show that the mean concentration of bound analytes highly increases with the flow speed, improving the efficiency of the biosensing device. To evaluate the benefits of in situ microstreaming with SAW, the same simulations were conducted for D_a numbers ranging from 10⁴ to 10⁸ M⁻¹∕s, by ranging the diffusion coefficient from 4×10⁻¹² to 4×10⁻⁹ m²∕s, and the association coefficient k_a from 10⁴ to 10⁸ M⁻¹∕s. The enhancement factor of analyte capture, defined as the ratio of the binding rate with streaming B and the binding rate without streaming B0, is plotted in Fig. ​Fig.33 for different values of D_a. Calculations are done in the case of a mean flow speed of 0.5 mm∕s.Open in a separate windowFigure 3(a) Enhancement factor (defined as the ratio between binding rate with streaming B and binding rate without streaming B0) for different Damkhöler numbers and (b) normalized enhancement factor for different Peclet numbers.One can notice the saturation of the enhancement factor curve for large value of D_a to the value of 3.5 for high D_a. This can be explained by the fact that for large k_a∕D_a ratios, the analytes, which normally require penetration in the depleted zone by diffusion, do not have time to interact with the biosensor when they pass in the vicinity of its surface. The efficiency of the streaming is then reduced for large values of D_a. In the case of our specific flow configuration, the enhancement factor reaches 3.2 for the interaction of streptavidin on immobilized biotin (D_a=10³).The reported simulation results can be compared to an experimental value obtained using the droplet-based surface plasmon resonance sensor streamed in situ using SAW reported by Yeo et al.¹² By monitoring the streptavidin∕biotin binding interaction on an activated gold slide, they showed that SAW stirring brings an improvement factor of more than 2. This difference can be accounted to the high complexity of the induced 3D flow, which was modeled in a simple manner in our calculations.Other factors must be taken into account when optimizing the improvement factor, such as the flow velocity and the characteristic length of the mixing. To do so, the Peclet number allows the comparison of the convective and diffusive effects.¹⁷ For δC a typical variation in concentration on the distance h, the Peclet number is given byPe=UhD.(5)A significantly high Peclet number causes a decrease in biosensing efficiency as the analytes do not have enough time to interact with the biosensing surface by diffusion through the analyte-poor layer. On the contrary, the case of a low Peclet number corresponds to the diffusion-limited problem. Therefore, for each Damköhler number, there is a Peclet number optimizing this factor. To illustrate this fact, Fig. ​Fig.3b3b shows the calculation of the enhancement factor as a function of the Peclet number for a given D_a.In this paper, we showed that surface loading of typical analytes on a droplet-based biosensor can be highly increased by SAW microstirring. The system permits the enhancement of the biosensing performances by the continuous renewal of the analyte-carrying fluid near the sensing surface. Thanks to mean flow speeds measured up to 1800 μm∕s, the SAW microstreaming can be beneficial to the biosensing of a large range of analyte∕ligand interactions. In addition to the biosensing performance improvement, such a method can be easily integrated in micro-micro-total-analysis systems, which makes it a convenient tool for liquid handling in future biochips.  相似文献   

The search for charmed states of matter     

Philip Ball 《国家科学评论(英文版)》2021,8(11)

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The metallography of aluminum     

Robert J. Anderson 《Journal of The Franklin Institute》1919,187(1):1-47

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Nuclear Resonance Flourescence Studies of Levels in 206Pb, 207Pb, 208Pb and 209Bi below about 5MeV     

C.P. Swann 《Journal of The Franklin Institute》1974,298(4):321-332

Capabilities of the resonance flourescence technique are discussed. Specific reference is given to the study of ground state dipole and electric quadrople transitions below about 5 MeV in ²⁰⁶Pb, ²⁰⁷Pb, ²⁰⁸Pb and ²⁰⁹Bi. It is suggested that many of the states observed in ²⁰⁷Pb and ²⁰⁹Bi arise from the weak-coupling of a p_{$\text{1}\text{2}$} neutron hole or an h_{$\text{9}\text{2}$} proton to collective levels of ²⁰⁸Pb.  相似文献