Viscous Energy Dissipation Of The Two Touching/self-assembly Droplets In Uniform Stokes Flow

Microfluidics based on droplets have many dynamic phenomena,one of which is that monodisperse or polydisperse droplets will self-assemble into a relatively stable and regular arrangement structure when they move in microchannels.The significance of droplet self-assembly includes the synthesis of new particles or materials,the expression of information through the assembly structure of droplets,and the orderly encapsulation of cells.The study of the law of droplet self-assembly can bring new ideas for manufacturing science.By changing the experimental conditions such as microchannel structure,flow resistance,pressure or flow rate and other conditions,different assembly results of droplets can be obtained.It is worth noting that the droplets are self-assembled in the flow field.The droplet assembly structure is also called "flowing crystal".And the flow field is always energy-dissipating,including the internal flow of the droplet.So the droplet micro-flow system is an energy dissipation system,and droplet assembly is performed in the dissipation system.However,there is still lack of researches on the energy dissipation in the flow of droplet self-assembly.This paper focuses on the energy dissipation of fluid internal flow in droplets during self-assembly in order to understand the phenomenon of droplet self-assembly.Viscous energy dissipation of two touching or self-assembly droplets in uniform Stokes flow was investigated in this paper.Based on the solution of Stokes flow,the Chebyshev spectrum method and the Filon integration method were used to calculate the energy dissipation per unit time of two droplets.Through changing the size of droplets,the energy dissipation of the two contact self-assembled droplets and the energy disspation of the single droplet were obtained and compared.And the theoretical calculation model for viscous dissipation energy of self-assembled droplets were obtained.The investigation reveals that the energy dissipation per unit time of either droplet increases with the increasing droplet viscosity at constant continuous fluid viscosity of extenal continuous phase.And the energy dissipation reaches a peak value when the viscosity of two pahses are equal.Moreover,when the sizes of two contacts self-assembled droplets are determined,interchanging their positions could not change their energy dissipation value per unit time.The energy dissipation per unit time of either droplet changes with the sizes of both droplets.The total energy dissipation per unit time of the two touching or self-assembly droplets is less than the sum of the energy dissipation per unit time of the two droplets at nature state.In particular,it reaches the minimum value,which is about 1/6 of the energy disspation of the sigle droplet flow with same droplet size,when the two droplets’ sizes are equal in the touching or self-assembly droplets system.Therefore,two droplets’ contact or self-assembly will minimize the energy dissipation of droplets internal flow,it can save energy for the flow system.This study proposes a new perspective for droplet self-assembly study and can promote the studies of droplet collision and coalescence,as well as can bring benefits to relevant applications.