Influence of the Péclet number on reactive viscous fingering

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Priyanka Shukla ◽  
A. De Wit
Keyword(s):  
Peclet Number ◽  
Viscous Fingering ◽  
Péclet Number

scholarly journals The dynamics of miscible viscous fingering from onset to shutdown

2018 ◽  
Vol 837 ◽  
pp. 520-545 ◽  
Author(s):  
Japinder S. Nijjer ◽  
Duncan R. Hewitt ◽  
Jerome A. Neufeld
Keyword(s):  
Numerical Simulations ◽  
Flow Regime ◽  
Peclet Number ◽  
Viscous Fingering ◽  
Linear Stability Theory ◽  
Late Time ◽  
Exchange Flow ◽  
Mixing Rate ◽  
Péclet Number ◽  
Single Finger

We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions.

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

2015 ◽  
Vol 782 ◽  
Author(s):  
Satyajit Pramanik ◽  
A. De Wit ◽  
Manoranjan Mishra
Keyword(s):  
Porous Media ◽  
Parameter Space ◽  
Peclet Number ◽  
Viscous Fingering ◽  
Mobility Ratio ◽  
Péclet Number ◽  
Initial Curvature ◽  
Instability Zone

The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

Convective diffusion toward the sphere in laminar flow around the sphere

1979 ◽  
Vol 44 (4) ◽  
pp. 1218-1238
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number ◽  
Stability Of The Solution

The problem of convective diffusion toward the sphere in laminar flow around the sphere is solved by combination of the analytical and net methods for the region of Peclet number λ ≥ 1. The problem was also studied for very small values λ. Stability of the solution has been proved in relation to changes of the velocity profile.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Modeling temperature rise in multi-track reciprocating frictional sliding

2021 ◽  
pp. 135065012098823
Author(s):  
Thierry A Blanchet
Keyword(s):  
Temperature Rise ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Uniform Heat Flux ◽  
Heat Accumulation ◽  
Stroke Length ◽  
Péclet Number ◽  
Maximum Temperature Rise ◽  
Rectangular Patch ◽  
Accumulation Effect

As in various manufacturing processes, in sliding tests with scanning motions to extend the sliding distance over fresh countersurface, temperature rise during any pass is bolstered by heating during prior passes over neighboring tracks, providing a “heat accumulation effect” with persisting temperature rises contributing to an overall temperature rise of the current pass. Conduction modeling is developed for surface temperature rise as a function of numerous inputs: power and size of heat source; speed and stroke length, and track increment of scanning motion; and countersurface thermal properties. Analysis focused on mid-stroke location for passes of a square uniform heat flux sufficiently far into the rectangular patch being scanned from the first pass at its edge that steady heat accumulation effect response is adopted, focusing on maximum temperature rise experienced across the pass' track. The model is non-dimensionalized to broaden the applicability of the output of its runs. Focusing on practical “high” scanning speeds, represented non-dimensionally by Peclet number (in excess of 40), applicability is further broadened by multiplying non-dimensional maximum temperature rise by the square root of Peclet number as model output. Additionally, investigating model runs at various non-dimensional speed (Peclet number) and reciprocation period values, it appears these do not act as independent inputs, but instead with their product (non-dimensional stroke length) as a single independent input. Modified maximum temperature rise output appears to be a function of only two inputs, increasing with decreasing non-dimensional values of stroke length and scanning increment, with outputs of models runs summarized compactly in a simple chart.

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