Study On Fluid Flow Dynamics In The Fractal Tree-like Microchannels

The fractal tree-like network,such as human respiratory and circulatory system,botanical trees,river networks,and the like,is widely found in nature.The fractal tree provides the optimal solution for mass and energy transfer from point to surface(body)or from surface(body)to point in engineering transport systems.Recently,the fractal tree has been applied broadly in micro-system(such as microelectronic device cooling,micro-reactor,microfluidic,etc.)for channel structure optimization.However,due to the complexity of tree network and the scale effect of fluid flow in micro-system,the microscopic mechanism of fluid flow in the fractal tree network has not been fully revealed.In this context,it is of great importance for scientific research and engineering application to investigate the hydrodynamic behaviors of fluid flow in fractal tree-like network.Currently,the available researches about the application of fractal tree network are mainly focused on the single-phase flow system,in which the channel structure optimization is based on the classical Murray’s law.However,the rarified gas flow and droplet/bubble multiphase flow in the fractal tree-like microscale system are still scarce.In such microscale system,due to the coupling rarefied effect and multi-scale effect,a question arises as to whether the rarified gas flow within fractal tree-like network still obey the Murray’s law.In addition,differing from the macro channels,the surface tension forces dominate over inertial forces for the microscale multiphase flow.The corresponding mechanisms of droplet/bubble multiphase flow in the fractal tree-like microscale system is still unclear.In this context,the dynamic behaviors and mechanisms of fluid flow(including single-phase flow and multiphase flow)in the fractal tree-like microchannels are investigated by means of theoretical model,numerical method and visualization experiment.A model of rarefied gas flow in fractal tree-like microchannels is developed and numerically analyzed to study the multi-scale effect and tree optimization.In addition,the lattice Boltzmann model of droplet flow in the unit T-junction of fractal tree-like network is developed to investigate the droplet dynamic behaviors and the inherent mechanisms.A detailed analysis of the influence of capillary number,the viscosity ratio and the channel width ratio on droplet flow behavior is performed.Then,the droplet/bubble flows in the fractal tree-like network are investigated by means of theoretical model,numerical method and visualization experiment,in an effort to elucidate the effect of system asymmetry on droplet/bubble breakup mechanisms.The results and conclusions are summarized as follows:(1)A lattice Boltzmann model of the rarefied gas flow through a fractal tree-like network is developed and numerically simulated to investigate the gas dynamic behaviors,especially focusing on the rarefaction effect,multi-scale effect and corresponding optimization method.The results indicate that the rarefaction effect and multi-scale effect play important roles in micro gas flow through the fractal tree-like microchannels.In fractal tree-like hierarchical network,increases in branching level lead to larger Knudsen number,which induce larger effective slip length and smaller Poiseuille number.When Kn equals 0.022 lying in the slip flow regime,the optimal width dimension of fractal tree-like microchannels is 1.8,which deviates from the optimal value 2 as per Murray’s law.As Kn increases,the more the gas flow becomes rarefied,the more the optimal width dimension would deviate from Murray’s law.(2)A phase-field multiphase lattice Boltzmann model is developed to systematically investigate the dynamic behavior of a droplet passing through a microfluidic T-junction,especially focusing on the non-breakup of the droplet.Detailed information on the breakup and non-breakup is presented,together with the quantitative evolutions of driving and resistance forces as well as the droplet deformation characteristics involved.Through comparisons between cases of non-breakup and breakup,it is found that the appearance of tunnels(the lubricating film between droplet and channel walls)provides a precondition for the final non-breakup of droplets,which slows down the droplet deformation rate and even induces non-breakup.The vortex flow formed inside droplets plays an important role in determining whether they break up or not.In particular,when the strength of vortex flow exceeds a critical value,a droplet can no longer break up.Additionally,more effort has been devoted to investigating the effects of viscosity ratio between disperse and continuous phases and width ratio between branch and main channels on droplet dynamic behaviors.It is found that a large droplet viscosity results in a small velocity gradient in a droplet,which restricts vortex generation and thus produces lower deformation resistance.Consequently,it is easier to break up a droplet with larger viscosity.This study also reveals that a droplet in small branch channels tends to obstruct the channels and have small vortex flows,which induces easier breakup as well.Eventually,several phase diagrams for droplet flow patterns are provided,and the corresponding power-law correlations(l0/w = βCab,where l0/w is dimensionless initial droplet length and Ca is capillary number)are fitted to describe the boundaries between different flow patterns.(3)A phase-field multiphase lattice Boltzmann model is developed to systematically investigate the dynamic behavior of droplets passing through a fractal tree-like microchannel,especially focusing on the breakup of the droplet.Detailed information on the droplet interaction influences is presented,together with the influence of the system asymmetry on droplet breakup.The results indicate that when a single droplet passes through a T-shaped bifurcation,the droplet gradually deforms and obstructs the flow.After the droplet breakup,the tail of daughter droplets retracts and reforms,which accelerates the flow.When the continuous droplets pass through the fractal tree-like microchannels and break up symmetrically,the droplet behaves periodically with exactly the same flow trajectory.In this symmetrical situation,the acceleration effect occurring in each bifurcation balances each other and so does the obstruction effect,which means the interaction between droplets can be neglected.In addition,if breaking the symmetry pattern by changing one of the outlet pressure values,the acceleration effect and obstruction effect occurring in each bifurcation will act on the flow field alternately,inducing asymmetrical droplet breakup.Note that the partition ratios of asymmetrical droplet breakup could deviate from the theoretical predictions,which are affected by the droplet interaction in squeezing stage during droplet deformation.According to the theoretical analysis,the uniformity of droplet generation mainly depends on two key dimensionless parameters namely Λ1(the ratio of the sum of the pressure drop of the continuous phase and the discrete phase to the pressure drop at two-phase interface within the Oth level channel)and Λ2(the ratio of the outlet pressure to the sum of the pressure drop of the continuous phase and the discrete phase within the 0th level channel).With the help of Λ1 and Λ2,it is found that increasing Ca and the length of continuous phase flow at main channel contributes to enhancing the uniformity of droplet generation,and so does increasing the lengths of each level channels.(4)The visualization experiment on the glass fractal tree-like microfluidic chip is performed to capture the bubble flow patterns with the help of high-speed microscopic camera system,especially focusing on the asymmetry effect on the bubble flow dynamics.The corresponding suppression method is discussed in details.The results indicate that six different bubble flow patterns are found in the experiment,including non-breakup,symmetry breakup,asymmetry breakup,non-breakup after merging,merging symmetrical breakup,and merging asymmetrical breakup.When the adjacent bubbles approach each other,they get merged.Due to the flow asymmetry,bubbles will not break or break up asymmetrically.For the asymmetrical cases,the statistical average diameter of bubbles in the higher branch level channels will deviate from the designed value more greatly,contributing to bigger special coefficient of variation.To reduce the asymmetrical effect,the dimensionless parameter Ai should get larger by increasing the capillary number and the length of continuous phase flow at main channel,which is favorable for the generation of desired bubbles.In summary,the above investigations systematically gains an insight into the micro gas flow and droplet/bubble multiphase flow through the fractal tree-like microchannels.The corresponding research results provide a strong theoretical support for the design and optimization of micro systems,and also supplement and perfect the theory of micro-scale fluid dynamics.