Hierarchical networks for optimal or improved delivery of fluid to porous electrochemical / chemical media

Abstract

Aspects of the subject disclosure may include, for example, a porous device, comprising a porous material, and a hierarchical network of flow channels defined in the porous material, wherein at least one flow channel in the hierarchical network of flow channels has a shape that at least partially approximates a cube-root profile or a quartic-root profile. Additional embodiments are disclosed.

What is claimed is: 
     
         1 . A porous device, comprising:
 a porous material; and   a hierarchical network of flow channels defined in the porous material, wherein at least one flow channel in the hierarchical network of flow channels has a shape that at least partially approximates a cube-root profile or a quartic-root profile.   
     
     
         2 . The porous device of  claim 1 , wherein the hierarchical network of flow channels comprises a primary set of flow channels and at least one additional set of flow channels that are smaller than the primary set of flow channels and that extend from the primary set of flow channels. 
     
     
         3 . The porous device of  claim 2 , wherein each of the flow channels in the primary set of flow channels and the at least one additional set of flow channels has a shape that approximates the cube-root profile or the quartic-root profile. 
     
     
         4 . The porous device of  claim 1 , wherein the hierarchical network of flow channels is arranged with size scales that are self-similar, thereby yielding a particular fractal dimension. 
     
     
         5 . The porous device of  claim 1 , wherein the porous material is electrochemically or chemically reactive. 
     
     
         6 . A method, comprising:
 obtaining a first porous electrode; and   embedding a hierarchy of flow channels in a surface of the first porous electrode, wherein at least one flow channel in the hierarchy of flow channels comprises a tapered profile or a linear or straight profile.   
     
     
         7 . The method of  claim 6 , wherein the embedding is performed via laser machining, mechanical milling, microfabrication, embossing, additive manufacturing, or a combination thereof, wherein the hierarchy of flow channels comprises a hierarchical interdigitated arrangement of inlet channels and outlet channels, and wherein each channel in a finest scale of the hierarchy has a cross-section that spans an entire expanse between inlet and outlet channels of a next finest scale of the hierarchy, resulting in capillaries that facilitate flow through the capillaries, thereby reducing or preventing scaling, fouling, and/or pore blockage. 
     
     
         8 . The method of  claim 6 , wherein the hierarchy of flow channels comprises a hierarchical interdigitated arrangement of inlet channels and outlet channels. 
     
     
         9 . The method of  claim 8 , wherein a first inlet channel of the inlet channels is defined such that there exists a gap distance between an end of the first inlet channel and an edge of the first porous electrode. 
     
     
         10 . The method of  claim 6 , wherein the embedding is performed in accordance with design parameters determined from modeling, and wherein the modeling involves a Pareto plot that defines a performance of hierarchical networks based on an apparent permeability factor relative to a flow path length. 
     
     
         11 . The method of  claim 10 , wherein one or more of the design parameters are obtained based on identifying a reduced or minimum flow path length in the Pareto plot. 
     
     
         12 . The method of  claim 10 , wherein the design parameters include a width of each secondary channel in the hierarchy of flow channels and a spacing between secondary channels in the hierarchy of flow channels. 
     
     
         13 . The method of  claim 12 , wherein a plurality of constraints are assumed for the modeling, and wherein the plurality of constraints include a permeability of the first porous electrode, a macroporosity constituted by channels, a length of the first porous electrode, a width of each primary channel in the hierarchy of flow channels, or a combination thereof. 
     
     
         14 . The method of  claim 13 , wherein a spacing between primary channels in the hierarchy of flow channels is defined based on the macroporosity, the width of each primary channel, the width of each secondary channel, and the spacing between secondary channels. 
     
     
         15 . The method of  claim 12 , wherein the width of each secondary channel in the hierarchy of flow channels corresponds to a secondary channel width of a terminal design on a Pareto front in the Pareto plot. 
     
     
         16 . The method of  claim 12 , wherein the width of each secondary channel in the hierarchy of flow channels corresponds to a secondary channel width that is within a threshold range from a secondary channel width of a terminal design on a Pareto front in the Pareto plot. 
     
     
         17 . The method of  claim 16 , wherein a flow path length associated with the secondary channel width that is within the threshold range from the secondary channel width of the terminal design is greater than a flow path length associated with the terminal design by no more than a threshold amount. 
     
     
         18 . The method of  claim 10 , wherein the design parameters are selected based at least in part on identifying a point of a Pareto front in the Pareto plot at which secondary channel widths transition from being within range of a secondary channel width of a terminal design on the Pareto front to being outside of the range and approaching a defined width of each primary channel in the hierarchy of flow channels. 
     
     
         19 . The method of  claim 6 , further comprising:
 obtaining a second porous electrode;   embedding a second hierarchy of flow channels in a surface of the second porous electrode, wherein at least one flow channel in the second hierarchy of flow channels comprises the tapered profile or the linear or straight profile; and   assembling the first porous electrode and the second porous electrode together with a separator layer therebetween.   
     
     
         20 . A system, comprising:
 a pair of porous electrodes; and   a separator disposed between the pair of porous electrodes, wherein each porous electrode of the pair of porous electrodes comprises a hierarchical network of interdigitated flow channels, and wherein each of the flow channels comprises a tapered profile.