Experimental studies on the effect of Reynolds and Weber numbers on the impact forces of low-speed droplets colliding with a solid surface

Zhang, Bin; Li, Jingyin; Guo, Penghua; Liu, Qian

doi:10.1007/s00348-017-2413-z

Cited by 46 publications

(29 citation statements)

References 46 publications

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“…Accordingly, F max should scale with the inertial force, ρD 2 U 2 0 , instead of the water-hammer force, ρD 2 cU 0 , where c is the speed of sound in the liquid. This argument is indeed supported by both previous studies (Grinspan & Gnanamoorthy 2010;Soto et al 2014;Li et al 2014;Zhang et al 2017) and our experiments (figure 4b). Thus, the maximum impact force of subsonic liquid drops at high Re, relevant to most natural and industrial processes, arises from the development of upward expanding self-similar pressure fields, rather than water-hammer pressures assumed in several recent studies (Deng et al 2009;Kwon et al 2011;Thanh-Vinh et al 2016).…”

Section: Resultssupporting

confidence: 93%

“…Through this study, we experimentally verify the existence of an upward propagating self-similar structure during the initial impact of liquid drops at high Re (Eggers et al 2010;Philippi et al 2016). Our quantitative analysis on the temporal variation of impact forces also predicts the maximum impact force and the associated peak time as a function of Re, which have been extensively studied in experiments (Nearing et al 1986;Grinspan & Gnanamoorthy 2010;Li et al 2014;Soto et al 2014;Zhang et al 2017). Second, we generalise the self-similar solution of drop spreading proposed by Eggers and co-workers (Eggers et al 2010) and find an exact parameter-free closed-form self-similar solution for inertia-driven drop spreading following the initial impact.…”

Section: Introductionmentioning

confidence: 56%

“…Although the maximum impact force of liquid drops has been measured in previous studies, the presence of strong resonant ringing and the abnormal slow decay of impact forces have limited the application of piezoelectric force sensors in resolving the temporal evolution of impact forces (Nearing et al 1986;Grinspan & Gnanamoorthy 2010;Li et al 2014;Soto et al 2014;Zhang et al 2017). Here, we solved these problems by targeting the impinging drops slightly off the centre of the force sensor, which significantly reduced resonant ringing.…”

Section: Methodsmentioning

confidence: 97%

“…Nevertheless, compared with the large number of studies on the morphology of impacting liquid drops, comparatively fewer experiments have been conducted to investigate the impact force of liquid drops. Most of the existing works have focused on the maximum impact force of liquid drops (Nearing et al 1986;Grinspan & Gnanamoorthy 2010;Li et al 2014;Soto et al 2014;Zhang et al 2017). The temporal evolution of impact forces during impacts remains largely unexplored.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

2018

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We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers (Re). At high Re, when inertia dominates the impact processes, we show that the early-time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high Re. When viscous forces gradually set in with decreasing Re, we analyse the early-time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing Re. Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high Re following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high Re. The limit of the selfsimilar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop impact processes.

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Section: Resultssupporting

confidence: 93%

Section: Introductionmentioning

confidence: 56%

Section: Methodsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

2018

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“…Shen and Bi [5] studied the effects of several dimensionless parameters on the deformation of a droplet impacting on a 2D round surface by using lattice Boltzmann algorithm and revealed that initial impacting velocity plays a significant role in impact dynamic. Li and Zhang [6][7] experimentally and numerically measured the impact forces of the low-speed water droplet colliding on a light and tiny aluminum plate and investigated the effects of impact velocity and diameter of droplets, Reynolds and Weber numbers on the impact forces. Blake and Thompson [8] employed an enthalpy-porosity method to numerically simulate the impact and solidification of a super-cooled water droplet on a cooled substrate.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of low-speed droplets impacting on the fabric surface

Guo

Sun

Chen

et al. 2019

mech

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In this approach, the numerical model of the fluid dynamics of liquid droplets impacting on the fabric surface with VOF method is proposed. The results obtained by the proposed model are well in agreement with the experimental results. The mechanism of the liquid droplet morphological evolution is investigated by pressure distribution and velocity vector, and the obvious bubble entrapment, which cannot be observed in experimenal results, is captured by the proposed model. The evolution laws of the spreading factor and the contact angle at the liquid-porous interface are obtained and the reason why the contact angle is dynamic is analyzed. The effects of droplet diameter and impact velocity on the fluid flow characteristics are also discussed. Usually, droplet diameter increasing leads more dramatic shape distortion of the liquid droplet, and impact velocity increasing leads shorter time to reach the maximum spreading stage. Finally, based on the properties of the impacting droplet by the proposed model, the important references of optimizing the parachute design for severe weather are built.

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Experimental determination of forces applied by liquid water drops at high drop velocities impacting a glass plate with and without a shallow water layer using wavelet deconvolution

Hopkins

2018

Exp Fluids

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Time-dependent forces applied by 2 and 4.5 mm diameter drops of water (with velocities up to terminal velocity) impacting upon a glass plate with or without a water layer (up to 10 mm depth) have been measured using two different approaches, force transduction and wavelet deconvolution. Both approaches are in close agreement for drops falling on dry glass. However, only the wavelet approach is able to measure natural features of the splash on shallow water layers that impart forces to the plate after the initial impact. At relatively high velocities (including terminal velocity) the measured peak force from the initial impact is significantly higher than that predicted by idealised drop shape models and models from Roisman et al. and Marengo et al. Hence empirical formulae are developed for the initial time-dependent impact force from drops falling at (a) different velocities up to and including terminal velocity onto a dry glass surface, (b) terminal velocity onto dry glass or glass with a water layer and (c) different velocities below terminal velocity onto dry glass or glass with a water layer. For drops on dry glass, the empirical formulae are applicable to a glass plate or a composite layered plate with a glass surface, although they apply to other plate thicknesses and are applicable to any plate material with a similar surface roughness and wettability. The measurements also indicate that after the initial impact there can be high level forces when bubbles are entrained in the water layer.

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Experimental studies on the effect of Reynolds and Weber numbers on the impact forces of low-speed droplets colliding with a solid surface

Cited by 46 publications

References 46 publications

Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

Numerical study of low-speed droplets impacting on the fabric surface

Experimental determination of forces applied by liquid water drops at high drop velocities impacting a glass plate with and without a shallow water layer using wavelet deconvolution

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