新型显示薄膜喷墨打印技术的数学建模与分析

本文将新型显示薄膜喷墨打印技术的关键工艺过程“喷墨打印-干燥/烘烤成膜”中多组分聚合物溶液在压电作用下从喷管内喷出均匀液滴、液滴在基板上着床并融合成均匀的液体薄膜、液体薄膜经过蒸发留下溶质(如有机发光二极管OLED(organic light-emitting diode))形成均匀显示薄膜的3个核心科学问题,在数学上提炼为多组分聚合物流体带移动接触线和动态接触角以及带有蒸发条件的固-液-气多相耦合的自由界面问题.本文首先对这些问题的Newton流的数学模型进行热力学自洽的系统综述和完善,然后对包含相分离、溶剂蒸发和非Newton黏弹性等多物理现象的同类自由界面问题进行成体系的数学建模,对模型的理论分析和数值模拟提出一些研究思路.本文希望通过解决这些数学问题突破新型显示薄膜喷墨打印工艺的关键技术瓶颈,提高打印的良品率,推进产业化,促进数学在解决国家重大需求难题中的应用.本文以新型显示薄膜喷墨打印技术核心科学问题为背景,给数学工作者提出了一些新的重要的数学问题,同时也为相关材料科学家提供了可行的数学方案,为双方搭起了良好的沟通桥梁.

Molecular Hydrodynamics of the Moving Contact Line in Two-Phase Immiscible Flows

The no-slip boundary condition,i.e.,zero fluid velocity relative to the solid at the fluid-solid interface,has been very successful in describing many macroscopic flows.A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line,where the interface separating two immiscible fluids intersects the solid wall.Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition,since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line.In this paper we first present an introductory review of the problem.We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow,from molecular dynamics(MD)simulations to continuum hydrodynamics calculations.Through extensive MD studies and detailed analysis,we have uncovered the slip boundary condition governing the moving contact line,denoted the generalized Navier boundary condition.We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale.These results serve to affirm the validity of the generalized Navier boundary condition,as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces.The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation.This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows(Qian,Wang,and Sheng,J.Fluid Mech.564,333-360(2006)).Physically,the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime.Therefore,the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface.A phase field is employed to model the diffuse interface between two immiscible fluid components,one being the electrolyte and the other a nonconductive fluid,both allowed to slip at solid surfaces.Our model consists of the incompressible Navier-Stokes equation for momentum transport,the Nernst-Planck equation for ion transport,the Cahn-Hilliard phase-field equation for interface motion,and the Poisson equation for electric potential,along with all the necessary boundary conditions.In particular,all the dynamic boundary conditions at solid surfaces,including the generalized Navier boundary condition for slip,are derived together with the equations of motion in the bulk region.Numerical examples in two-dimensional space,which involve overlapped electric double layer fields,have been presented to demonstrate the validity and applicability of the model,and a few salient features of the two-phase immiscible electroosmotic flows at solid surface.The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.

Stick-Slip Motion of Moving Contact Line on Chemically Patterned Surfaces

Based on our continuum hydrodynamic model for immiscible two-phaseflows at solid surfaces, the stick-slip motion has been predicted for moving contactline at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78].In this paper we show that the continuum predictions can be quantitatively verifiedby molecular dynamics (MD) simulations. Our MD simulations are carried out fortwo immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuilleflow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluidinterface to intermittent stick-slip motion of moving contact line, we have quantitativeagreement between the continuum and MD results. This agreement is attributed tothe accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for therelaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysisbased on the Onsager principle of minimum energy dissipation.