System and method of obtaining entrained cylindrical fluid flow

Abstract

A method and system for entraining fluids is provided. The method and system may be used to create filaments. As one example, a filament may be produced by entraining a first fluid within a second fluid by flowing a third fluid, the flowing third fluid at least partly constraining the second fluid in at least one dimension. As another example, a filament may be produced by entraining a first fluid within a second fluid based on a model of a dynamic response of the first and second fluids as functions of densities of the first and second fluids, viscosities of the first and second fluids, Reynolds numbers of the first and second fluids, and Weber numbers of the first and second fluids.

1 . A filament being produced by: 
 entraining a first fluid within a second fluid by flowing a third fluid, the flowing third fluid at least partly constraining the second fluid in at least one dimension.    
   
   
       2 . The filament of  claim 1 , further comprising solidifying at least a part of the second fluid to form a fiber.  
   
   
       3 . The filament of  claim 2 , further comprising solidifying at least a part of the first fluid to form the fiber.  
   
   
       4 . The filament of  claim 1 , wherein entraining a first fluid within a second fluid is based only on fluid properties of the first fluid and the second fluid  
   
   
       5 . The filament of  claim 4 , wherein the fluid properties are viscosity of the first fluid and the second fluid; and 
 wherein the second fluid is more viscous than the first fluid.    
   
   
       6 . The filament of  claim 1 , wherein the first fluid comprises a liquid or a gas that is immiscible with the second fluid.  
   
   
       7 . The filament of  claim 1 , wherein a plurality of fluids are entrained within the second fluid.  
   
   
       8 . The filament of  claim 7 , wherein the third fluid flows at least partly by co-electrospinning.  
   
   
       9 . The filament of  claim 7 , wherein the third fluid flows at least partly by pressure applied to the third fluid.  
   
   
       10 . The filament of  claim 7 , wherein the second fluid is axisymmetrically constrained by the flowing of the third fluid to surround the second fluid.  
   
   
       11 . The filament of  claim 7 , wherein the first fluid flows from a first nozzle and the second fluid flows from a second nozzle; and 
 wherein the first nozzle is concentric with the second nozzle.    
   
   
       12 . The filament of  claim 7 , wherein the second fluid flows to entrain the first fluid; and 
 wherein the flow of the second fluid is due more to drawing of the second fluid by the flowing of the third fluid than to pressure applied to the second fluid.    
   
   
       13 . The filament of  claim 12 , wherein the entraining of the first fluid within the second fluid is due more to drawing of the first fluid by the flowing of the second fluid than to pressure applied to the first fluid.  
   
   
       14 . A filament being produced by: 
 entraining a first fluid within a second fluid based on a model of a dynamic response of the first and second fluids as functions of densities of the first and second fluids, viscosities of the first and second fluids, Reynolds numbers of the first and second fluids, and Weber numbers of the first and second fluids.    
   
   
       15 . The filament of  claim 14 , wherein the model of the dynamic response defines a phase space of a stable entraining of the first fluid within the second fluid; and 
 wherein values of the Reynolds numbers of the first and second fluid and Weber numbers of the first and second fluid are selected to be in the phase space of the stable entraining of the first fluid within the second fluid.    
   
   
       16 . The filament of  claim 15 , wherein the entraining of the first fluid within the second fluid is performed by a system that controls velocity of the first fluid and second fluid; and 
 wherein the velocity of the first fluid and the second fluid are selected such that the model is in the phase space of the stable entraining of the first fluid within the second fluid.    
   
   
       17 . The filament of  claim 15 , wherein the model is derived numerically.  
   
   
       18 . The filament of  claim 15 , wherein the model is derived analytically.  
   
   
       19 . The filament of  claim 18 , wherein the model is a function of: 
 the ratio of the densities of the first and second fluid,    the ratio of the viscosities of the first and second fluid,    the Reynolds number of the first fluid        Re   1 =ρ 1   VR   1 /μ 1      with ρ 1  being the density of the first fluid, μ 1  being the viscosity of the first fluid, R 1  being the radius of a cylindrical jet through which the first fluid flows, and Vbeing the uniform velocity of the first and second fluids relative to an observer,    the Reynolds number of the second fluid        Re   2 =ρ 2   VR   2 /μ 2      with ρ 2  being the density of the first fluid, μ 2  being the viscosity of the first fluid, and R 2  being the radius of a cylindrical jet through which the second fluid flows,    the Weber number of the first fluid        We   1 =ρ 1   V   2   R   1 /σ   where σ being the surface tension, and    the Weber number of the second fluid        We   2 =ρ 2   V   2   R   2 /σ.    
   
   
       20  The filament of  claim 14 , further comprising solidifying at least a part of the second fluid to form a fiber.  
   
   
       21 . The filament of  claim 14 , wherein operating conditions are selected in order to be in a specific phase space within the model so that the flow of the first fluid is continuous for a predetermined time.  
   
   
       22 . The filament of  claim 21 , wherein the operating condition comprises pressure; and 
 wherein the pressure to at least one of the first and second fluids is dynamically adjusted to maintain a shape of an interface between the first fluid and the second fluid for the predetermined time.