Viscoelastic Reynolds-equation solver for Giesekus thin-film lubrication: code, validation data, and analytical limits

Abstract

This dataset accompanies the article "Viscoelastic squeeze-film lubrication: a Giesekus-based perturbation expansion in λḣ/h" by N. C. Dhlamini and W. H. Ho (Physics of Fluids, 2026; under review at the time of deposit). It contains the solver code, parameter files, validation data, and post-processing scripts used to produce all numerical results and figures in the paper.ABSTRACT (paper). Viscoelastic thin-film flows with time-varying geometry involve three independent dimensionless groups: the Weissenberg number Wi = λU/h, the Deborah number De = λU/L, and the squeeze group De_sq = λ|ḣ|/h, which governs the temporal lag of polymer stress behind a changing flow field. We develop a perturbation expansion in De_sq for the Giesekus constitutive model, deriving a modified Reynolds equation whose volume flux decomposes into five contributions: steady-state viscometric flow, squeeze-film memory, first normal stress gradient, hoop stress, and Giesekus quadratic stress coupling. The framework recovers the Newtonian Reynolds equation, the upper-convected Maxwell model, and second-order fluid theory as limiting cases. Validation against published Boger fluid squeeze-flow data confirms the perturbation method at moderate Wi.ARCHIVE CONTENTS. The archive is organised as follows: /solver/ — Python implementation of the Giesekus thin-film solver, including (i) the steady-state material-function calculation, (ii) the second-order finite-difference discretisation of the modified Reynolds equation with ghost-node boundary conditions, and (iii) the flux-decomposition post-processor. Entry points are documented in solver/README.md. /parameters/ — Input parameter files (.json or .yaml) for each published case: Newtonian baseline, UCM limit, Boger fluid validation against Phan-Thien et al. (1985), and the two illustrative polymer solutions used in the paper. /validation_data/ — Comma-separated tables of the digitised experimental squeeze-flow data from Phan-Thien et al. (1985, J. Non-Newt. Fluid Mech. 18, 227–254) and the corresponding solver outputs. Columns are documented in each file's header row and in the data dictionary described below. /figures/ — Reproduction scripts (Python/matplotlib) for Figures 1–6 of the paper, with the underlying numerical outputs stored as .csv files in the same folder. /docs/ — Supplementary documentation, including the full numerical implementation guide and a data dictionary describing every column heading in the .csv outputs. README.md — Top-level orientation document with installation instructions, dependency versions (Python ≥ 3.10, NumPy, SciPy, matplotlib), and a worked end-to-end reproduction example. LICENSE — CC-BY-4.0 for data; MIT for code.DATA DICTIONARY (representative). Each .csv output file contains a header row naming the columns; the meanings are: Lambda — Dimensionless shear rate λγ̇ (Giesekus auxiliary variable argument). f — Giesekus auxiliary variable, physical root of the quadratic given in §II.B of the paper, dimensionless. eta_over_eta0 — Total viscosity normalised by zero-shear viscosity, dimensionless. Psi1_over_Psi1_0 — First normal stress coefficient normalised by its zero-shear value, dimensionless. De_sq — Squeeze Deborah number λ|ḣ|/h, dimensionless. F_over_F_Newtonian — Ratio of viscoelastic to Newtonian load capacity, dimensionless. Used in the UCM-limit and Boger fluid validation figures. r_over_R — Radial coordinate normalised by disk/pad outer radius, dimensionless. p_over_p_ref — Pressure normalised by the lubrication reference pressure η₀U L / h₀², dimensionless. Q_steady — Steady-state viscometric flux contribution, dimensionless (units: [Q]/(U h₀)). Q_memory — Squeeze-memory flux contribution, dimensionless. Q_N1 — First normal stress gradient flux contribution, dimensionless. Q_hoop — Hoop-stress flux contribution, dimensionless. Q_alpha — Giesekus quadratic stress coupling flux contribution, dimensionless. Q_total — Sum of the five flux contributions, dimensionless.PROVENANCE. The solver was developed at the Centre for Research in Computational and Applied Mechanics (CERECAM), University of Cape Town, between September 2025 and April 2026. Validation against the Phan-Thien et al. (1985) Boger fluid data uses values digitised from the published figures in that article; original measurements were not re-collected. No human or animal subjects were involved.REPRODUCTION. To reproduce all figures in the paper, run the scripts in /figures/ in alphabetical order from a Python ≥ 3.10 environment with the dependencies listed in solver/requirements.txt. Expected runtime on a standard workstation is approximately 0.05 minutes for the full set.CITING THIS DATASET. Please cite both the dataset (DOI https://doi.org/10.25375/uct.32113411) and the accompanying journal article.