Axisymmetric drop impact dynamics on a wall film of the same liquid

Measurement quantities and techniques

Experiment

When carrying out the experiments, a uniform film of 500 μm thickness is prepared utilizing the film thickness sensor. In the next step, the film thickness sensor is moved and a drop is generated. During the drop impact onto the liquid film shadowgraphy images are taken. A synchronized high-performance LED (Constellation 120E) in combination with a diffuser plate provides a uniform background illumination. Images are taken with a high-speed CMOS camera (Photron SA-X2), recording the impact at a frame rate of 20000 fps with a resolution of 31 μm/px.

The dynamics of the drop-film interaction is characterized by three parameters as indicated in Fig. 4.

The crown diameter at the crown base d_CB, measured 0.13 mm above the film surface
The crown diameter at the free rim forming the crown top d_CT
The crown height h_C

These parameters are obtained from preprocessed images with the help of the MATLAB Image-Processing Toolbox. For this, a background subtraction from raw images is first performed to be able to distinguish the crown from the background. Then the images are binarised, using a global thresholding method, as shown on the left side of Fig. 4. From the evaluation of consecutive binarised images, the temporal evolution of d_CB, d_CT and h_C can be determined. Reflections on the crown surface can lead to nonphysical interpretations of the crowns dimensions in individual frames. To eliminate erroneous values from the results, all values with a deviation of more than three standard deviations from a running median of 20 consecutive frames are considered as outlier.

Fig. 4: Montage of binarized picture on the left and a raw picture on the right. The crown diameter at the free rim d_CT and the crown diameter at the base d_CB are depicted in red. The crown height h_C is depicted in green. The dashed blue line indicates the film level.

Numerical method and computational setup

The numerical simulations are performed with a diffuse-interface phase-field method which solves the coupled Cahn-Hilliard Navier-Stokes equations by a finite volume method using OpenFOAM (code phaseFieldFoam). The computational setup is shown in Fig. 5. In OpenFOAM, axisymmetric calculations are realized by a wedge-shaped domain with small opening angle (Fig. 5 a). The domain size and the initial conditions are displayed in Fig. 5 (b). In the diffuse-interface region, the mesh is adaptive as illustrated in Fig. 5 (c) for the initial configuration. In the azimuthal direction, the wedge is discretized by one mesh cell.

Fig. 5: Illustration of a suitable computational setup: a) Wedge-shaped domain with boundary conditions, b) Domain size and initial phase distribution, c) Typical initial configuration of the adaptive grid.

In the numerical simulations, two different models for the surface tension force (equilibrium/relaxation) are employed in combination with different spatial resolutions. In the phase field method, the surface tension force is related to the profile of the phase-discriminating order parameter (C) and depends in particular on the gradient of C within the diffuse interface region. In the standard (equilibrium) formulation, C is assumed to follow the tanh profile of the equilibrium state whereas the relaxation model accounts for the deviation of the actual profile of C from the equilibrium profile. The spatial resolution is quantified by the number of mesh cells N_c used to resolve the thickness of the diffuse interface at equilibrium as illustrated in Fig. 6.

Fig. 6: Initial phase distribution with magnified views of the diffuse interface for different grid resolutions employed in numerical simulations.

Further details can be found in the following publication:

M. Bagheri, B. Stumpf, I.V. Roisman, C. Tropea, J. Hussong, M. Wörner, H. Marschall, Interfacial relaxation – Crucial for phase-field methods to capture low to high energy drop-film impacts, Int. J. Heat Fluid Flow 94 (2022) 108943, https://doi.org/10.1016/j.ijheatfluidflow.2022.108943

Contributed by: Milad Bagheri, Bastian Stumpf, Ilia V. Roisman, Cameron Tropea, Jeanette Hussong, Martin Wörner, Holger Marschall — Technical University of Darmstadt and Karlsruhe Institute of Technology

Front Page

Introduction

Review of experimental studies

Description

Experimental Set Up

Measurement Quantities and Techniques

Data Quality and Accuracy

Measurement Data and Results