1. ABOUT THE DATASET -------------------- Title: Supplementary Material - Hydrodynamic Interactions Between Pairs of Sedimenting Semi-Flexible Brownian Fibres Creator(s): Nasrollah Hajaliakbari, David Head, Oliver Harlen Organisation(s): University of Leeds Rights-holder(s): Copyright 2025 University of Leeds Publication Year: 2025 Description: The results for a pair of sedimenting semiflexible fibres with initially both horizontal and vertical configurations have been reported here. These include the rho-value, cos2 (tetha), the nondimensional interaction velocity and rate of rotation, sedimentation velocity, eigenvalues of gyration matrix. In addition to that, the results of the Phi changes and the ratio of maximum deflection (A) to the length of the fibre (l) for a single sedimenting fibre has been put in the dataset. Cite as: Nasrollah Hajaliakbari, David Head, Oliver Harlen (2025): Supplementary Material-Hydrodynamic Interactions Between Pairs of Sedimenting Semi-Flexible Brownian Fibres. [Dataset]. https://doi.org/10.5518/1731. Related publication: [1] L. Li, H. Manikantan, D. Saintillan, andS. E. Spagnolie, "The sedimentation of flexible filaments," Journal of Fluid Mechanics 735, 705 (2013). [2] M. Cosentino Lagomarsino, I. Pagonabarraga, andC. Lowe, "Hydrodynamic induced deformation and orientation of a microscopic elastic filament," Physical review letters 94, 148104 (2005). [3] G. B. Jeffery, "The motion of ellipsoidal particles immersed in a viscous fluid," Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character 102, 161 (1922). Contact: D.Head@leeds.ac.uk 2. TERMS OF USE --------------- Copyright 2025, University of Leeds. This dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/. 3. PROJECT AND FUNDING INFORMATION ---------------------------------- Title: Rheology of crosslinked assemblies of flexible fibres in viscous flow Dates: 2023-2026 Funding organisation: EPSRC Grant no.: RTSG 95534477 We thank you EPSRC to provide funding and support for this research work. 4. CONTENTS ----------- File listing The data has been included into four subfolders, 1- Continuum model&RPY: All the data reported in Figs 7 and 8 regarding the nondimensional interaction velocity and rate of rotation (Omega*=NormOMY) against nondimensional distance paramter (D*) for both horizontal and vertical configurations. ( Horizontal: 8 variables, 8 rows, VARIABLES = "D*", "NormOMY(Con)", "NormOMY(RPY)", "NormIntVel(Con)", "Vel_pair(RPY)", "Vel_single(RPY)", "NormIntVel(RPY)", "OM_ThermalDiffusion(Rot)" - Vertical: 8 variables, 8 rows, VARIABLES = "D*", "NormOMY(Con)", "NormOMY(RPY)", "NormIntVel(Con)", "Vel_pair(RPY)", "Vel_single(RPY)", "NormIntVel(RPY)", "OM_ThermalDiffusion(Rot)") 2- Contours: All the data reported in Figs 4, 5 and 6 regarding the rho-value(RoXX) and Cos2(tetha) against nondimensional distance paramter (D*=d0/l) and Peclet number (Pe) for both horizontal and vertical configurations. ( Horizontal: 3 variables, 28 rows, VARIABLES = "Pe", "d0/l", "RhoXX" - 3 variables, 20 rows VARIABLES = "Pe", "lp/l", "Cos2(Tetha)" - Vertical: 3 variables, 16 rows VARIABLES = "Pe", "d0/L", "Cos2(tetha)" - 3 variables, 16 rows VARIABLES = "Pe", "d0/l", "RhoXX" - 3 variables, 20 rows VARIABLES = "Pe", "lp/l", "Cos2(Tetha)"") 3- Sedimentation Velocity&GyrationMatrix: All the data reported in Figs 9 and 10 regarding the sedimentation velocity and Eigen value of gyration matrix ( both horizontal and vertical configurations). 4- Validation: All the data reported in Figs A2 and A3 regarding the phi value against time (for Jeffery orbit) and A/l against B* (for sedimentation of single fibre). 5. METHODS ---------- -Tools: The data was created by using some analytical tools (detailed in the article) and the first version of this open-source code in github: https://github.com/stochasticHydroTools/SlenderBody Also, there are some data, which was extracted from some published articles for validation purposes such as: [1] L. Li, H. Manikantan, D. Saintillan, andS. E. Spagnolie, "The sedimentation of flexible filaments," Journal of Fluid Mechanics 735, 705 (2013). [2] M. Cosentino Lagomarsino, I. Pagonabarraga, andC. Lowe, "Hydrodynamic induced deformation and orientation of a microscopic elastic filament," Physical review letters 94, 148104 (2005). [3] G. B. Jeffery, "The motion of ellipsoidal particles immersed in a viscous fluid," Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character 102, 161 (1922). -Methods: To analyse the data, you need to use the Excel from Microsoft Office 2024 package and Notepad/Notepad++ any version. The Tecplot 2023 was used to plot the images. Further details about analysed data can be found in: Hajaliakbari, Nasrollah; Head, David; Harlen, Oliver; 2025; Hydrodynamic Interactions Between Pairs of Sedimenting Semi-Flexible Brownian Fibres; University of Leeds.