Mathematical Model for Mixing Reactants in a Capillary Microreactor by Transverse Diffusion of Laminar Flow Profiles

To overcome the problem of fluid mixing in capillary tubes, the induction of radial diffusion of laminar flow profiles (RDLFP) was proposed recently, together with a mathematical. Since, under realistic conditions, continuous flow capillary reactors are influenced by noise in the feed streams, the stability of such a reactor for a system of three liquids was analyzed through its largest Lyapunov exponents. Simulations showed that although the aim of RDLFP is to improve mixing, poorly mixed microreactors are more robust to the influx of noise than well-mixed tubes. Therefore, these contrasting requirements have to be balanced to decide the besy operating conditions. Multi-component noise in multi-fluid systems can also induce stochastic resonance, which may either enhance or reduce stability. Thus, it is important and useful to filter the noise judiciously to promote reactor stability.

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A model for the longitudinal patterns shaped by water on erodible rocks

10.5194/egusphere-egu2020-7031 ◽

2020 ◽

Author(s):

Matteo Bernard Bertagni ◽

Carlo Camporeale

Keyword(s):

Mathematical Model ◽

Pattern Formation ◽

Laminar Flow ◽

Spatial Scales ◽

Concentration Field ◽

Water Film ◽

Time And Space ◽

Longitudinal Patterns ◽

Flow Intensity ◽

Alpine Environments

<p>The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).</p>

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Diffusive, Electrostatic, and Gravitational Deposition of Suspensions in the Entrance of a Nozzle

Journal of Applied Mechanics ◽

10.1115/1.3166993 ◽

1983 ◽

Vol 50 (1) ◽

pp. 1-7

Author(s):

T. A. Korjack

Keyword(s):

Mathematical Model ◽

Brownian Motion ◽

Laminar Flow ◽

Gravity Field ◽

Deposition Rate ◽

Flow Parameter ◽

Deposition Process ◽

Electrostatic Charge ◽

Analytical Investigation ◽

Nozzle Inlet

An analytical investigation of the mechanics of deposition affected by gravity, electrostatic charge, and Brownian motion in an effuser from the nozzle inlet to a distance where incompressible effects are still valid has been made and a mathematical model developed for the deposition process. The analysis was restricted to laminar flow of dilute, nonreactive suspensions contained within an incompressible, viscous carrier. The results show that increasing the nozzle angle causes a decrease in deposition rate regardless of the diffusive Peclet number and gravity flow parameter. Furthermore, an increase in gravity field causes an increase in bottom deposition rate and decrease in top deposition rate.

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Streamline's Shape Theory

10.20944/preprints201904.0067.v1 ◽

2019 ◽

Author(s):

Yuvaraj George

Keyword(s):

Mathematical Model ◽

Laminar Flow ◽

Historical Data ◽

Incidence Angle ◽

Open Circuit ◽

The Body ◽

Separation Flow ◽

Continuous Surface ◽

Theoretical Mechanics ◽

Shape And Size

This article attempts to propose a mathematical model and potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena. These typical phenomena in laminar flow are explained using the proposed theory rather than conventional approximations or several partial theories. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. To formulate a more realistic and simplified mathematical model for open circuit laminar flow over a body, a mathematical model is proposed based on the historical data of aerodynamics and theoretical mechanics. This mathematical model is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict various phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. Most of all a mathematical model and the mechanism of streamline formation in an open-circuit laminar with respect to the shape and size of the body are illustrated.

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