Many numerical studies validate droplet wall impact using only maximum spreading diameter, yet this metric alone cannot ensure correct droplet dynamics. We present a combined dynamic contact angle (DCA) model that merges the geometric accuracy of the generalized Hoffman-Voinov-Tanner law with the kinematic consistency of a Hoffman function-based approach, improving predictions of droplet spreading and receding. We simulate water-glycerol droplet impact on sapphire glass at Weber numbers 20 -- 250 and assess both contact angle formulations. Simulated radial velocity fields are processed in Python using SciPy and compared with Particle Image Velocimetry measurements in the longitudinal section of the spreading droplet. The Hoffman function-based model captures the main droplet kinematic trends and provides more consistent receding dynamics. The generalized Hoffman-Voinov-Tanner law matches the maximum spreading diameter within 7%. However, during receding, it shows a median absolute error in radial velocity up to three times higher than that of the Hoffman function-based solution. Average radial velocity and spreading velocity can differ from experimental trends even when maximum spreading is reproduced. These findings support validation combining geometric and kinematic metrics and motivate the combined model for predicting spreading and receding. Using the maximum spreading factor $β_{max}$ as the ratio of the maximum spreading diameter over the initial droplet diameter and the characteristic capillary number $Ca_{char}$ defined from the mean internal horizontal velocity at 300 micrometer above the substrate, we introduce a $(β_{max},\,Ca_{char})$ diagram to relate spreading characteristics to internal flow dynamics. We hypothesize that, given sufficient data, the contact-line geometry may be used to estimate internal kinematics.
The process of droplet impact with a solid substrate [31] plays an important role in a wide range of applications, such as high-temperature surface cooling [21], spray coating [39], 3D-bioprinting [27], inkjet printing [24], precision agricultural spraying and crop protection [38], anti-icing surface engineering [16] and drop-on-demand metal additive manufacturing [11]. The dynamics of droplet impact on solid substrates are governed by a complex interplay of inertial, viscous, capillary, and thermal forces, each contributing to different phases of droplet dynamics [17,41]. All possible outcomes of droplet collision are highly sensitive to parameters such as droplet velocity, surface roughness, wettability, and ambient conditions [17].
Computational fluid dynamics (CFD) simulation of these processes remains a challenging and actively investigated topic, since it must capture multiphase flow and moving interfaces. Reliable predictions require careful numerical setup and validation against experiments. In particular, validation should include not only droplet shape and spreading, but also internal flow metrics.
A great number of CFD simulations [22,44,3,9,45] of droplet impact on a solid surface involve validating through maximum droplet spreading diameter. However, it is questionable whether focusing solely on geometric parameters provides an accurate representation of droplet impact dynamics. Furthermore, important kinematic parameters of the liquid, such as the internal velocity fields, radial velocity and droplet spreading velocity are not considered in the vast majority of the earlier simulations.
More recently, Shu et al. [32] investigated the impact dynamics of droplets with initial angular velocity on superhydrophobic surfaces. They used numerical simulations to explore the effect of droplet rotation on impact behavior. They found that increasing the initial angular velocities leads to greater centrifugal forces, which enhances droplet spreading and reduces contact time. To validate the numerical model, they used geometrical and dynamic parameters including the spreading factor, droplet height, droplet shape evolution over time, rotation angle, and contact time.
Ye et al. [42] used the CFD simulation to find out that a dynamic contact angle model accurately predicts the paint droplet impact on dry surfaces. At the same time, the impact on wet surfaces results in the creation of the craters, whose size strongly correlates with the Reynolds number. The researchers developed a model to simulate the motion of pigment flakes within the droplet, which is crucial for understanding and improving the final quality of metallic paint finishes. The numerical results were validated against experimental data by comparing the droplet contour evolution, droplet spread factor and height ratio.
Wang et al. [40] studied the spreading of liquid droplets on coal dust surfaces to optimize spray dust removal. Increasing coal-dust surface roughness promotes spreading, yielding a larger maximum spread ratio. The authors employed high-speed imaging to capture the transient wetting behavior of droplets impacting coal dust and built a two-phase CFD model simulating droplet-particle interactions, including spreading, bouncing, and fragmentation. The experimentally observed dynamics were then used to validate the CFD model, which demonstrated high accuracy in reproducing the droplet impact and spreading behavior.
The combination of CFD simulations and Particle Image Velocimetry [23] (PIV) is a powerful yet challenging approach to studying fluid mechanics. PIV provides highly detailed velocity field measurement, which can help validate numerical models. On the other hand, coupling these techniques is not trivial. The two approaches are affected by fundamentally different sources of uncertainty. PIV is limited by measurement error and experimental biases, whereas CFD accuracy depends on modelling setup and discretization techniques.
Gultekin et al. [12] investigated the internal flow dynamics of single and two-component droplets impacting on the sapphire glass solid surface using PIV. The velocity fields revealed a nonlinear behavior at the lamella edges for experiments with moderate Weber numbers, while test with high Weber numbers showed more linear profiles. Subsequently, they calibrated CFD simulations using the experimental spreading diameters and PIV velocity measurements to match them. They compared these characteristics with those obtained by an analytical model. The linear model agreed well with the linear parts of the velocity profiles in the early stage of spreading, while CFD simulations reproduced both radial velocity distributions and droplet shapes. The authors also matched the radial velocity distributions, the non-dimensional spreading diameter over time, and the shape of the droplet.
Erkan [10] described the velocity fields inside water droplets impacting heated sapphire surfaces using time-resolved PIV and
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