Surface Charge Density Gradient Printing To Drive Droplet Transport: A Numerical Study

Abstract

Traditional strategies, such as morphological or chemical gradients, struggle to realize the high-velocity and long-distance transport for droplets on a solid surface because of the pinning hydrodynamic equilibrium. Thus, there is a continuing challenge for practical technology to drive droplet transport over the last decades. The surface charge density (SCD) gradient printing method overcame the theoretical limit of traditional strategies and tackled this challenge [Nat. Mater. 2019, 18: 936], which utilized the asymmetric electric force to realize the high-velocity and long-distance droplet transport along a preprinted SCD gradient pathway. In the present work, by coupling the electrostatics and the hydrodynamics, we developed an unexplored numerical model for the water droplet transporting along the charged superhydrophobic surface. Subsequently, the effects of SCD gradients on the droplet transport were systematically discussed, and an optimized method for SCD gradient printing was proposed according to the numerical results. The present approach can provide early guidance for the SCD gradient printing to drive droplet transport on a solid surface.

Development of a MoS2/Ag NP Nanopocket to Trap Target Molecules for Surface-Enhanced Raman Scattering Detection with Long-Term Stability and High Sensitivity

“…The level-set function ϕ is a signed distance function in terms of the liquid–gas interface location. The transport equation of the liquid–gas interface is as follows: ∂ ϕ ∂ t + bold-italicu · ∇ ϕ = γ ∇ · true( scriptϵ l s ∇ ϕ − ϕ ( 1 − ϕ ∇ ϕ | ∇ ϕ | ) ) where γ is the stabilization parameter of the level-set function and was set to 1 by default. The interface thickness ϵ ls was defined as half of the maximum elemental size of the component.…”

Triboelectric ‘electrostatic tweezers’ for manipulating droplets on lubricated slippery surfaces prepared by femtosecond laser processing

“…The electrostatic force, F e , acting on an object is the sum of the Maxwell stress working on the surface of the object, and such a surface force is the integral of the surface of the object. For a liquid droplet under an electrostatic field, the electrostatic force can be expressed as [63,64]:…”

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“…The uneven distribution of charge causes the droplet to be subjected to electrostatic force (Figure d and k). The Coulomb force is the sum of the Maxwell stresses acting on the surface of the droplet: ,− bold-italicF normale = prefix∮ [ ε E false( bold-italicE bold-italicn false) − ε 2 E 2 n ] normald S where ε and E are the permittivity of the liquid and the electric field strength at the droplet surface, respectively, and n and S are the surface unit normal and surface area of the droplet, respectively. This electrostatic force can be quantified in tensor form: ,, bold-italicF normale = prefix∮ T normale , i j · bold-italicn normald S , goodbreak.25em normalw normali normalt normalh .25em T normale , i j = ε 0 ( E i E j − δ i j 2 E 2 ) goodbreak, i , j = x , y badbreak, z where T e , ε 0 , E , and δ ij are the Maxwell stress tensor, the permittivity of air, the magnitude of E , and the Kronecker delta function, respectively.…”

“…The uneven distribution of charge causes the droplet to be subjected to electrostatic force (Figure d and k). The Coulomb force is the sum of the Maxwell stresses acting on the surface of the droplet: ,− where ε and E are the permittivity of the liquid and the electric field strength at the droplet surface, respectively, and n and S are the surface unit normal and surface area of the droplet, respectively. This electrostatic force can be quantified in tensor form: ,, where T e , ε 0 , E , and δ ij are the Maxwell stress tensor, the permittivity of air, the magnitude of E , and the Kronecker delta function, respectively.…”