Abstract
Research on the wettability of soft matter is one of the most urgently needed studies in the frontier domains, of which the wetting phenomenon of droplets on soft substrates is a hot subject. Scholars have done considerable studies on the wetting phenomenon of single-layer structure, but it is noted that the wetting phenomenon of stratified structure is ubiquitous in nature, such as oil exploitation from geological structural layers and shale gas recovery from shale formations. Therefore, the wettability of droplets on layered elastic gradient soft substrate is studied in this paper. Firstly, considering capillary force, elastic force and surface tension, the constitutive equation of the substrate in the vector function system is derived by using the vector function system in cylindrical coordinates, and the transfer relation of layered structure is obtained. Further, the integral expressions of displacement and stress of double Bessel function are given. Secondly, the numerical results of displacement and stress are obtained by using the numerical formula of double Bessel function integral. The results show that the deformation of the substrate weakens with the increase of the elastic modulus, also the displacement and stress change dramatically near the contact line, while the variation is flat when the contact radius is far away from the droplet radius.
Highlights
Research on the wettability of soft matter is one of the most urgently needed studies in the frontier domains, of which the wetting phenomenon of droplets on soft substrates is a hot subject
The obvious characteristic of soft matter is very sensitive to external stimuli
It can be seen that this phenomenon is ubiquitous and significantly important, such as oil exploitation, printing and p ainting[5,7], application of superhydrophobic s ubstrates[8,9,10] and so on
Summary
The semispherical droplet is placed on a layered elastic soft substrate, and the bottom is fixed with a rigid surface or a semi-infinite space. The inter-layer contact conditions are as follows ui−(r, θ , hk) = ui+(r, θ , hk), σi−z (r, θ , hk) = σi+z (r, θ , hk), (k = 1, 2, · · ·, n), where ui−(r, θ , hk), ui+(r, θ , hk) denote the displacements of the upper surface of the k-layer and the lower surface of the (k − 1)-layer, respectively, and the stress has similar expression. The deformation of the substrate caused by only the surface normal load is considered, and the stress boundary conditions can be expressed as σrz (r, θ , 0) = σθz(r, θ , 0) = 0, σzz(r, θ , 0) = −γlvδ(r − R) + PH(R − r),.
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