1
|
Quenta J, Vasquez DA. Thermal and compositional driven convection in thin reaction fronts. Phys Rev E 2024; 109:035104. [PMID: 38632785 DOI: 10.1103/physreve.109.035104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 02/29/2024] [Indexed: 04/19/2024]
Abstract
Chemical reaction fronts separate regions of reacted and unreacted substances as they propagate in liquids. These fronts may induce density gradients due to different chemical compositions and temperatures across the front. In this paper, we investigate buoyancy-induced convection driven by both types of gradients. We consider a thin front approximation where the normal front velocity depends only on the front curvature. This model applies for small curvature fronts independent of the specific type of chemical reaction. For density changes due only to heat variations near the front, we find that convection can take place for either upward or downward propagating fronts if density gradients are above a threshold. Convection can set in even if the fluid with lower density is above the higher density fluid. Our model consists of Navier-Stokes equations coupled to the front propagation equation. We carry out a linear stability analysis to determine the parameters for the onset of convection. We study the nonlinear front propagation for liquids confined in narrow two-dimensional domains. Convection leads to fronts of steady shape, propagating with constant velocities.
Collapse
Affiliation(s)
- Johann Quenta
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel, Lima 32, Perú
| | - Desiderio A Vasquez
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel, Lima 32, Perú
- Department of Physics, Purdue University Fort Wayne, Fort Wayne, Indiana 46805, USA
| |
Collapse
|
2
|
Influence of fast advective flows on pattern formation of Dictyostelium discoideum. PLoS One 2018; 13:e0194859. [PMID: 29590179 PMCID: PMC5874059 DOI: 10.1371/journal.pone.0194859] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2017] [Accepted: 03/12/2018] [Indexed: 12/05/2022] Open
Abstract
We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction. While the wave period and transverse propagation velocity are constant, parallel wave velocity and the wave width increase linearly with the imposed flow. We also observe that the acquired wave shape is highly dependent on the wave generation site and the strength of the imposed flow. We compared the wave shape and velocity with numerical simulations performed using a reaction-diffusion model and found excellent agreement. These results are expected to play an important role in understanding the process of pattern formation and aggregation of D. discoideum that may experience fluid flows in its natural habitat.
Collapse
|
3
|
Yildiz-Ozturk E, Yucel M, Muderrisoglu C, Sargin S, Yesil-Celiktas O. Modelling coupled dynamics of diffusive–convective mass transfer in a microfluidic device and determination of hydrodynamic dispersion coefficient. J Taiwan Inst Chem Eng 2017. [DOI: 10.1016/j.jtice.2017.08.033] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
4
|
Chevalier T, Dubey AK, Atis S, Rosso A, Salin D, Talon L. Avalanches dynamics in reaction fronts in disordered flows. Phys Rev E 2017; 95:042210. [PMID: 28505739 DOI: 10.1103/physreve.95.042210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2016] [Indexed: 11/07/2022]
Abstract
We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.
Collapse
Affiliation(s)
- T Chevalier
- Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| | - A K Dubey
- Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| | - S Atis
- Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| | - A Rosso
- LPTMS, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| | - D Salin
- Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| | - L Talon
- Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France
| |
Collapse
|
5
|
Atis S, Saha S, Auradou H, Martin J, Rakotomalala N, Talon L, Salin D. CHEMO-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. CHAOS (WOODBURY, N.Y.) 2012; 22:037108. [PMID: 23020499 DOI: 10.1063/1.4734489] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.
Collapse
Affiliation(s)
- S Atis
- Laboratoire Fluides Automatique et Systèmes Thermiques, Universités P. et M. Curie and Paris Sud, C.N.R.S. (UMR7608), Bâtiment 502, Campus Universitaire, 91405 Orsay Cedex, France
| | | | | | | | | | | | | |
Collapse
|
6
|
Malham IB, Jarrige N, Martin J, Rakotomalala N, Talon L, Salin D. Lock-exchange experiments with an autocatalytic reaction front. J Chem Phys 2010; 133:244505. [DOI: 10.1063/1.3507899] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
7
|
Jarrige N, Bou Malham I, Martin J, Rakotomalala N, Salin D, Talon L. Numerical simulations of a buoyant autocatalytic reaction front in tilted Hele-Shaw cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:066311. [PMID: 20866526 DOI: 10.1103/physreve.81.066311] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2010] [Indexed: 05/29/2023]
Abstract
We present a numerical analysis of solutal buoyancy effects on the shape and the velocity of autocatalytic reaction fronts, propagating in thin tilted rectangular channels. We use two-dimensional (2D) lattice Bathnagar-Gross-Krook (BGK) numerical simulations of gap-averaged equations for the flow and the concentration, namely a Stokes-Darcy equation coupled with an advection-diffusion-reaction equation. We do observe stationary-shaped fronts, spanning the width of the cell and propagating along the cell axis. We show that the model accounts rather well for experiments we performed using an Iodate Arsenous Acid reaction propagating in tilted Hele-Shaw cells, hence validating our 2D modelization of a three-dimensional problem. This modelization is also able to account for results found for another chemical reaction (chlorite tetrathionate) in a horizontal cell. In particular, we show that the shape and the traveling velocity of such fronts are linked with an eikonal equation. Moreover, we show that the front velocity varies nonmonotonically with the tilt of the cell, and nonlinearly with the width of the cell.
Collapse
Affiliation(s)
- N Jarrige
- Lab FAST, Universite Pierre et Marie Curie-Paris 6-Universite Paris-Sud-CNRS, Campus Universitaire, Orsay F-91405, France
| | | | | | | | | | | |
Collapse
|
8
|
Koptyug IV, Zhivonitko VV, Sagdeev RZ. Advection of Chemical Reaction Fronts in a Porous Medium. J Phys Chem B 2008; 112:1170-6. [DOI: 10.1021/jp077612r] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Igor V. Koptyug
- International Tomography Center SB RAS, 3A Institutskaya St., Novosibirsk 630090, Russia
| | - Vladimir V. Zhivonitko
- International Tomography Center SB RAS, 3A Institutskaya St., Novosibirsk 630090, Russia
| | - Renad Z. Sagdeev
- International Tomography Center SB RAS, 3A Institutskaya St., Novosibirsk 630090, Russia
| |
Collapse
|
9
|
Edwards BF. Propagation velocities of chemical reaction fronts advected by Poiseuille flow. CHAOS (WOODBURY, N.Y.) 2006; 16:043106. [PMID: 17199384 DOI: 10.1063/1.2358954] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Poiseuille flow between parallel plates advects chemical reaction fronts, distorting them and altering their propagation velocities. Analytical solutions of the cubic reaction-diffusion-advection equation resolve the chemical concentration for narrow gaps, wide gaps, and small-amplitude flow. Numerical solutions supply a general description for fluid flow in the direction of propagation of the chemical reaction front, and for flow in the opposite direction. Empirical relations for the velocity agree with numerical solutions to within a few percent, and agree exactly with the analytical limits. Applications to nonlinear fingering are discussed.
Collapse
Affiliation(s)
- Boyd F Edwards
- Department of Physics, West Virginia University, Morgantown, West Virginia 26506-6315, USA
| |
Collapse
|
10
|
Karnik R, Castelino K, Duan C, Majumdar A. Diffusion-limited patterning of molecules in nanofluidic channels. NANO LETTERS 2006; 6:1735-40. [PMID: 16895365 DOI: 10.1021/nl061159y] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Diffusion-limited patterning (DLP) is a new technique that enables patterning of labile molecular species in solution phase onto surfaces that are not easily accessible. This technique is self-aligning and is simple to implement for patterning multiple species. We demonstrated DLP by patterning alternating bands of fluorescently labeled and unlabeled streptavidin in biotin-functionalized nanofluidic channels with spatial resolution better than 1 microm. The methodology of DLP also enables experimental measurement of a unique parameter that relates molecular surface grafting density, concentration, diffusivity, and channel geometry.
Collapse
Affiliation(s)
- Rohit Karnik
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | | | | | | |
Collapse
|
11
|
Sullivan S, Sani F, Johns M, Gladden L. Simulation of packed bed reactors using lattice Boltzmann methods. Chem Eng Sci 2005. [DOI: 10.1016/j.ces.2005.01.038] [Citation(s) in RCA: 113] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|