Introduction This folder structure contains the relevant references to data and scripts used for the following publication: Steffen Bisswanger, Henning Bonart, Pyi Thein Khaing, and Steffen Hardt. "Liquid Surfaces with Chaotic Capillary Waves Exhibit an Effective Surface Tension." Physical Review Letters 133, no. 3 (2024): 034001 Please follow the publication to understand the experimental setup and the procedure for data evaluation.

Experimental raw data Due to the size of the raw data, it is only available upon request from the authors, and not deposited on the public repository except from the data corresponding to a single experimental run as an example. The experimental data has the following structure: Naming scheme: YYMMDD/ ├─ session_xx/ │ ├─ run_01/ │ │ ├─ YYMMDD_sxx_r01.nd2 # contains raw image data (1 fps); proprietary format readable with imagej plugin │ │ ├─ jpg/ # contains unpacked frames (.jpg-files) │ │ ├─ eval/ # contains marked holes to check post processing for screw-ups (.jpg-files) │ │ ├─ YYMMDD_sxx_r01.csv # contains raw data from laser line sensor │ │ ├─ eval.csv # contains the evaluated data of the experiment, including wave energy density measurement │ │ ├─ energy_density_spectra_rel.csv # contains the energy density spectra for each point in the laser line (rel = rigid body motion of substrate is already substracted) │ │ ├─ spectrum_noise_reduction_rel.csv # contains the (over many points on the laser line) averaged spectrum, with white noise background substraction applied │ │ ├─ │ ├─ run_02/ │ ├─ ... │ ├─ run_11/ │ ├─ vibration_data/

Each session is conducted at a constant volume (except from the experiments with constant amplitude available upon request). Each run can be seen as a quasi static experiment corresponding to a specific set of parameters. The folder "YYMMDD_sxx_vibration_data" is session-specific amd contains the vibration data (frequency and amplitude) corresponding to all the runs.

Scripts to process and evaluate experimental data as well as to obtain numerical solutions

• iso_lc_data - Contains the script used for calculating the iso lc-lines (constant capillary length) shown in figure 2.

• wave energy measurement - Contains the scripts used for the postprocessing of the laser sheet sensor data, giving the wave energy density measurement.

• bayesian_inference Contains the scripts for the inference of the capillary lengths from the experimental data used for figure 5 including the forward model, its surrogate model, likelihood functions, Bayesian inference via ADVI, as well as the visualization of intermediate results and the figures in the supplemental material.

results.csv Contains the summarized results. Day # day of the recorded data Volume # liquid volume inside the reservoir in units of ml Velocity_Amplitude # velocity amplitude of the shaker in m/s Frequency # frequency of the shaker in Hz Wave_Energy_1000 # wave enegry density (integrared up to 1000 Hz) in N / m * s Apparent_Defect_Radius # radius of the dry spot as seen from above (smaller than acual due to meniscus) in mm Apparent_Contact_Line_Length # bounding length of the (not exactly circular) dry spot in mm Apparent_Defect_Radius_px # radius of the dry spot as seen from above (smaller than acual due to meniscus) in px Defect_Location_x # x-location of the center of the dry spot in mm Defect_Location_y # y-location of the center of the dry spot in mm Acceleration_Amplitude # acceleration amplitude of the shaker in m / s^2 Wave_Energy_1000_std # standard deviation of the energy density spectra (integrated up to 1000 Hz) in N / m * s Wave_Energy_1414 # averaged wave energy density (if integrated up to 1414 Hz) in N / m * s Wave_Energy_1414_noise_reducted Wave_Energy_1414_std # averaged, noise reduced wave energy density (if integrated up to 1414 Hz) in N / m * s image # name of corresponding image caS_mean DeltaV_mean caS_low caS_high DeltaV_low DeltaV_high lc_static_mean lc_static_low lc_static_high lc_mean lc_low lc_high Srad_mean Srad_low Srad_high