Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface

Abstract

The theoretical models for the deformation of a liquid drop impinging on a solid flat surface at the initial and late stages are proposed. It was found that at the initial stage of the drop impact, the thickness of the emerging film decreases rapidly along its radius r, as r −6 , that is similar to the splash jet induced by the blunt-body impact on the liquid surface. The thickness of the film levels off with time due to the viscous force, and the late stage of the drop spreading is controlled by the action of viscous and capillary forces. The influence of the capillary forces is localized in the vicinity of the triple line, and it causes the formation of the thick border ͑blob͒ on the edge of the spreading drop. An analytical solution of the model in viscous limit reveals that the minimum film thickness scales as Re −2/5 and the drop maximum radius in its maximum extension as Re 1/5. The analytical solution for the dynamics of the blob mass growth is also obtained. The kinetic energy of the drop at its maximum extension remains greater than zero in the drop-spreading process even accounting for viscous effect.

Analysis of water drop erosion on turbine blades based on a nonlinear liquid–solid impact model

“…Ref. [14] reported a theoretical model to describe the effect of capillary and viscous force on spreading of a liquid drop impinging on a rigid solid surface, and the stress field in solid was not considered. In the work by Lesser [15], the finite impedance of the solid material was shown to affect both the pressure and the angle at which jetting started [11].…”

First stages of drop impact on a dry surface: asymptotic model

“…At early post-impact times, τ 0 < τ 1, where τ 0 is the dimensionless time of lamella emergence (τ 0 ∼ Re −1 [10]), the radius of the spreading lamella base, r K (τ ), and the maximum spreading radius, r max (τ ), are estimated from simple geometrical considerations [4,6,7,14] to be of order O( √ τ ) with different O(1) prefactors, such that r K < r max . For small τ , the values of the prefactors are obtained only experimentally [10,14].…”

“…For small τ , the values of the prefactors are obtained only experimentally [10,14]. An estimate of the lamella thickness at its base, say z max = h(r K , τ), can be found by equating the volume flux through the impacting spherical drop with that through the lamella [4], with the result z max ∼ 0.5τ .…”

Numerical simulation of capillary deformation of a body implantable device

“…It is interesting to know that not only the normal component of the capillary force but the tangential component also may play an important role to deform the solid [39]. The deformation of a liquid drop colliding with the surface of a solid is studied by using several theoretical models; thereby, it is obvious that the capillary and the viscous forces are major players on spreading of a liquid drop [40]. An experimental study on the capillary motion of liquid drop on a solid surface is conducted in which the velocity of a drop is measured and compared to the result from the theoretical analysis [41].…”