The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model ...The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.展开更多
The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich de...The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich deposition patterns of solutes on the substrate.Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection.This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets.We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets.We then summarize the development of the corresponding theory.Particular attention herein is focused on advances and issues related to applying the Onsager variational principle(OVP)theory to the study of the deposition patterns of drying droplets.The main obstacle to conventional theory is the requirement of complex numerical solutions,but fortunately there has been recent groundbreaking progress due to the OVP theory.The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems.As such,OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.展开更多
This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In t...This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In this paper,different structures of polymer can be considered,such as homopolymer,block copolymer,polydisperse polymer and charged polymer.Several systems,micro/macro phase separation,interface,self-assembly,are presented as examples to demonstrate its applications in details.Besides,the fluctuation effects are considered.The first order is Gaussian fluctuation theory,which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure.The derivation and applications of Gaussian fluctuation theory are presented as well.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.21822302)the joint NSFC-ISF Research Program,China(Grant No.21961142020)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe National College Students'Innovative and Entrepreneurial Training Plan Program,China(Grant No.201910006142).
文摘The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.
基金supported by the National Natural Science Foundation of China(Grant No.21822302)the joint NSFCISF Research Program,China(Grant No.21961142020)the Fundamental Research Funds for the Central Universities,China。
文摘The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich deposition patterns of solutes on the substrate.Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection.This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets.We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets.We then summarize the development of the corresponding theory.Particular attention herein is focused on advances and issues related to applying the Onsager variational principle(OVP)theory to the study of the deposition patterns of drying droplets.The main obstacle to conventional theory is the requirement of complex numerical solutions,but fortunately there has been recent groundbreaking progress due to the OVP theory.The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems.As such,OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant Nos.20973176,20990234,50821062,and 20874111)973 Program of the Ministry of Science and Technology(MOST)(Grant No.2011CB808502)the Fundamental Research Funds for the Central Universities.
文摘This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In this paper,different structures of polymer can be considered,such as homopolymer,block copolymer,polydisperse polymer and charged polymer.Several systems,micro/macro phase separation,interface,self-assembly,are presented as examples to demonstrate its applications in details.Besides,the fluctuation effects are considered.The first order is Gaussian fluctuation theory,which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure.The derivation and applications of Gaussian fluctuation theory are presented as well.
