Dissolution-driven transport in a rotating horizontal cylinder
Pith reviewed 2026-05-22 21:16 UTC · model grok-4.3
The pith
The symmetry breaking of the dissolving interface in a rotating cylinder is captured by the ratio Ra over Omega squared.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Using numerical simulations for Schmidt number of 1, Rayleigh numbers between 10^5 and 10^8, and rotation rates up to 2.5, the authors demonstrate that the interface symmetry breaking is best described in terms of Ra/Ω². In the absence of rotation and buoyancy, the interface distance follows a square root of time relation until finite domain effects dominate.
What carries the argument
The parameter Ra/Ω², which collapses data on interface symmetry breaking across different buoyancy strengths and rotation frequencies in the dissolution model.
If this is right
- The area of the dissolved solute varies nonlinearly with time depending on Ra and Ω.
- Rotation affects flow regimes and mixing of the dissolved solute relative to the buoyancy timescale.
- Without rotation or buoyancy, the interface advances as the square root of time before finite-size effects appear.
Where Pith is reading between the lines
- If Ra/Ω² is held fixed while changing individual values, the symmetry properties of the interface should remain similar.
- This scaling may help predict how rotation modifies buoyancy-driven dissolution in other confined fluid geometries.
Load-bearing premise
The Oberbeck-Boussinesq approximation accurately models the density increase with solute concentration to drive buoyancy in the Navier-Stokes equations.
What would settle it
A direct numerical simulation or laboratory experiment measuring the interface asymmetry for various Ra and Ω values that fails to show collapse when rescaled by Ra/Ω².
read the original abstract
We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we model this using the Oberbeck-Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier-Stokes equations with the advection-diffusion equation and a Stefan condition for the evolving solute-fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates, and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $\Omega \in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt{t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency -- from smaller to larger, relative to the inverse of the buoyancy-induced timescale -- and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $\Omega$. The symmetry breaking of the interface is best described in terms of $Ra/\Omega^2$.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript studies dissolution-driven flows in a rotating horizontal cylinder by solving the Navier-Stokes and advection-diffusion equations coupled to a Stefan condition under the Oberbeck-Boussinesq approximation. For Sc=1, Ra ∈ [10^5,10^8] and Ω ∈ [0,2.5], highly resolved simulations are used to examine flow regimes, dissolution rates, mixing, and interface evolution; the central claim is that symmetry breaking of the interface is best described by the ratio Ra/Ω².
Significance. If the numerical results are reliable, the identification of Ra/Ω² as the controlling parameter for interface symmetry breaking offers a compact description of the combined buoyancy-rotation effects. The work employs direct numerical solution of the standard governing equations without fitted parameters or self-referential reductions, which strengthens the internal consistency of the reported scalings.
major comments (1)
- [Abstract] Abstract: the statement that the results rest on 'highly resolved numerical simulations' is not accompanied by any grid-convergence data, validation against known benchmarks (e.g., the non-rotating diffusive limit or published dissolution rates), or quantitative error estimates. Because the central claim concerns quantitative interface evolution and the collapse onto Ra/Ω², the absence of these checks is load-bearing for the reliability of all reported regimes.
Simulated Author's Rebuttal
We thank the referee for their careful reading and constructive comments. We address the single major comment below.
read point-by-point responses
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Referee: [Abstract] Abstract: the statement that the results rest on 'highly resolved numerical simulations' is not accompanied by any grid-convergence data, validation against known benchmarks (e.g., the non-rotating diffusive limit or published dissolution rates), or quantitative error estimates. Because the central claim concerns quantitative interface evolution and the collapse onto Ra/Ω², the absence of these checks is load-bearing for the reliability of all reported regimes.
Authors: We agree that the abstract claim of 'highly resolved numerical simulations' requires supporting evidence given the quantitative nature of the interface evolution and Ra/Ω² collapse. In the revised manuscript we will add grid-convergence studies with quantitative error estimates, explicit validation against the non-rotating diffusive limit (confirming r_d ∝ √t at early times), and comparisons to any available literature dissolution rates for the non-rotating case. These will be presented in a new methods subsection or appendix to underpin all reported regimes. revision: yes
Circularity Check
No significant circularity
full rationale
The paper reports direct numerical simulations of the standard Navier-Stokes equations coupled to advection-diffusion and a Stefan condition, under the Oberbeck-Boussinesq approximation, for given ranges of Sc, Ra and Ω. The reported collapse of interface symmetry onto Ra/Ω² is an observed outcome of those simulations, not a fitted parameter renamed as a prediction, not a self-definitional relation, and not justified by any load-bearing self-citation. No derivation step reduces to its own inputs by construction.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Oberbeck-Boussinesq approximation for density variation with concentration
discussion (0)
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