TY - GEN A1 - Niedl, Robert Raimund A1 - Berenstein, Igal A1 - Beta, Carsten T1 - How imperfect mixing and differential diffusion accelerate the rate of nonlinear reactions in microfluidic channels N2 - In this paper, we show experimentally that inside a microfluidic device, where the reactants are segregated, the reaction rate of an autocatalytic clock reaction is accelerated in comparison to the case where all the reactants are well mixed. We also find that, when mixing is enhanced inside the microfluidic device by introducing obstacles into the flow, the clock reaction becomes slower in comparison to the device where mixing is less efficient. Based on numerical simulations, we show that this effect can be explained by the interplay of nonlinear reaction kinetics (cubic autocatalysis) and differential diffusion, where the autocatalytic species diffuses slower than the substrate. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 253 KW - arsenious acid KW - fronts KW - paper KW - poly(dimethylsiloxane) KW - scale KW - systems Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95810 SP - 6451 EP - 6457 ER - TY - JOUR A1 - Niedl, Robert Raimund A1 - Berenstein, Igal A1 - Beta, Carsten T1 - How imperfect mixing and differential diffusion accelerate the rate of nonlinear reactions in microfluidic channels JF - Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies N2 - In this paper, we show experimentally that inside a microfluidic device, where the reactants are segregated, the reaction rate of an autocatalytic clock reaction is accelerated in comparison to the case where all the reactants are well mixed. We also find that, when mixing is enhanced inside the microfluidic device by introducing obstacles into the flow, the clock reaction becomes slower in comparison to the device where mixing is less efficient. Based on numerical simulations, we show that this effect can be explained by the interplay of nonlinear reaction kinetics (cubic autocatalysis) and differential diffusion, where the autocatalytic species diffuses slower than the substrate. KW - arsenious acid KW - systems KW - poly(dimethylsiloxane) KW - fronts KW - scale KW - paper Y1 - 2016 U6 - https://doi.org/10.1039/c6cp00224b SN - 1463-9076 SN - 1463-9084 VL - 18 SP - 6451 EP - 6457 PB - Royal Society of Chemistry CY - Cambridge ER - TY - GEN A1 - Berenstein, Igal A1 - Beta, Carsten A1 - De Decker, Yannick T1 - Comment on "Flow-induced arrest of spatiotemporal chaos and transition to a stationary pattern in the Gray-Scott model" T2 - Physical review : E, Statistical, nonlinear and soft matter physics N2 - In this Comment, we review the results of pattern formation in a reaction-diffusion-advection system following the kinetics of the Gray-Scott model. A recent paper by Das [Phys. Rev. E 92, 052914 (2015)] shows that spatiotemporal chaos of the intermittency type can disappear as the advective flow is increased. This study, however, refers to a single point in the space of kinetic parameters of the original Gray-Scott model. Here we show that the wealth of patterns increases substantially as some of these parameters are changed. In addition to spatiotemporal intermittency, defect-mediated turbulence can also be found. In all cases, however, the chaotic behavior is seen to disappear as the advective flow is increased, following a scenario similar to what was reported in our earlier work [I. Berenstein and C. Beta, Phys. Rev. E 86, 056205 (2012)] as well as by Das. We also point out that a similar phenomenon can be found in other reaction-diffusion-advection models, such as the Oregonator model for the Belousov-Zhabotinsky reaction under flow conditions. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.94.046201 SN - 2470-0045 SN - 2470-0053 VL - 94 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Cross-diffusion in the two-variable Oregonator model JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We explore the effect of cross-diffusion on pattern formation in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction. For high negative cross-diffusion of the activator (the activator being attracted towards regions of increased inhibitor concentration) we find, depending on the values of the parameters, Turing patterns, standing waves, oscillatory Turing patterns, and quasi-standing waves. For the inhibitor, we find that positive cross-diffusion (the inhibitor being repelled by increasing concentrations of the activator) can induce Turing patterns, jumping waves and spatially modulated bulk oscillations. We qualitatively explain the formation of these patterns. With one model we can explain Turing patterns, standing waves and jumping waves, which previously was done with three different models. Y1 - 2013 U6 - https://doi.org/10.1063/1.4816937 SN - 1054-1500 VL - 23 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Flow-induced transitions in bistable systems JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We studied transitions between spatiotemporal patterns that can be induced in a spatially extended nonlinear chemical system by a unidirectional flow in combination with constant inflow concentrations. Three different scenarios were investigated. (i) Under conditions where the system exhibited two stable fixed points, the propagation direction of trigger fronts could be reversed, so that domains of the less stable fixed point invaded the system. (ii) For bistability between a stable fixed point and a limit cycle we observed that above a critical flow velocity, the unstable focus at the center of the limit cycle could be stabilized. Increasing the flow speed further, a regime of damped flow-distributed oscillations was found and, depending on the boundary values at the inflow, finally the stable fixed point dominated. Similarly, also in the case of spatiotemporal chaos (iii), the unstable steady state could be stabilized and was replaced by the stable fixed point with increasing flow velocity. We finally outline a linear stability analysis that can explain part of our findings. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.86.056205 SN - 1539-3755 VL - 86 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We show that quasi-standing wave patterns appear in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction when a cross-diffusion term is added, no wave instability is required in this case. These standing waves have a frequency that is half the frequency of bulk oscillations displayed in the absence of diffusive coupling. The standing wave patterns show a dependence on the systems size. Regular standing waves can be observed for small systems, when the system size is an integer multiple of half the wavelength. For intermediate sizes, irregular patterns are observed. For large sizes, the system shows an irregular state of spatiotemporal chaos, where standing waves drift, merge, and split, and also phase slips may occur. Y1 - 2012 U6 - https://doi.org/10.1063/1.3676577 SN - 0021-9606 VL - 136 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Berenstein, Igal A1 - Beta, Carsten T1 - Flow-induced control of chemical turbulence JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We report spatiotemporal chaos in the Oregonator model of the Belousov-Zhabotinsky reaction. Spatiotemporal chaos spontaneously develops in a regime, where the underlying local dynamics show stable limit cycle oscillations (diffusion-induced turbulence). We show that spatiotemporal chaos can be suppressed by a unidirectional flow in the system. With increasing flow velocity, we observe a transition scenario from spatiotemporal chaos via a regime of travelling waves to a stationary steady state. At large flow velocities, we recover the known regime of flow distributed oscillations. KW - chaos KW - chemical equilibrium KW - chemically reactive flow KW - reaction kinetics theory KW - spatiotemporal phenomena KW - turbulence Y1 - 2011 U6 - https://doi.org/10.1063/1.3656248 SN - 0021-9606 VL - 135 IS - 16 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Berenstein, Igal T1 - Distinguishing similar patterns with different underlying instabilities Effect of advection on systems with Hopf, Turing-Hopf, and wave instabilities JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Systems with the same local dynamics but different types of diffusive instabilities may show the same type of patterns. In this paper, we show that under the influence of advective flow the scenario of patterns that is formed at different velocities change; therefore, we propose the use of advective flow as a tool to uncover the underlying instabilities of a reaction-diffusion system. Y1 - 2012 U6 - https://doi.org/10.1063/1.4766591 SN - 1054-1500 VL - 22 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Berenstein, Igal T1 - Pattern formation in a reaction-diffusion-advection system with wave instability JF - Chaos : an interdisciplinary journal of nonlinear science N2 - In this paper, we show by means of numerical simulations how new patterns can emerge in a system with wave instability when a unidirectional advective flow (plug flow) is added to the system. First, we introduce a three variable model with one activator and two inhibitors with similar kinetics to those of the Oregonator model of the Belousov-Zhabotinsky reaction. For this model, we explore the type of patterns that can be obtained without advection, and then explore the effect of different velocities of the advective flow for different patterns. We observe standing waves, and with flow there is a transition from out of phase oscillations between neighboring units to in-phase oscillations with a doubling in frequency. Also mixed and clustered states are generated at higher velocities of the advective flow. There is also a regime of "waving Turing patterns" (quasi-stationary structures that come close and separate periodically), where low advective flow is able to stabilize the stationary Turing pattern. At higher velocities, superposition and interaction of patterns are observed. For both types of patterns, at high velocities of the advective field, the known flow distributed oscillations are observed. Y1 - 2012 U6 - https://doi.org/10.1063/1.4704809 SN - 1054-1500 VL - 22 IS - 2 PB - American Institute of Physics CY - Melville ER -