Applying the Shearlet-Based Complexity Measure for Analyzing Mass Transfer in Continuous-Flow Microchannels

Continuous-flow microchannels are widely employed for synthesizing various materials,including nanoparticles,polymers,and metal-organic frameworks(MOFs),to name a few.Microsystem technology allows precise control over reaction parameters,resulting in purer,more uniform,and structurally stable products due to more effective mass transfer manipulation.However,continuous-flow synthesis processes may be accompanied by the emergence of spatial convective structures initiating convective flows.On the one hand,convection can accelerate reactions by intensifying mass transfer.On the other hand,it may lead to non-uniformity in the final product or defects,especially in MOF microcrystal synthesis.The ability to distinguish regions of convective and diffusive mass transfer may be the key to performing higher-quality reactions and obtaining purer products.In this study,we investigate,for the first time,the possibility of using the information complexity measure as a criterion for assessing the intensity of mass transfer in microchannels,considering both spatial and temporal non-uniformities of liquid’s distributions resulting from convection formation.We calculate the complexity using shearlet transform based on a local approach.In contrast to existing methods for calculating complexity,the shearlet transform based approach provides a more detailed representation of local heterogeneities.Our analysis involves experimental images illustrating the mixing process of two non-reactive liquids in a Y-type continuous-flow microchannel under conditions of double-diffusive convection formation.The obtained complexity fields characterize the mixing process and structure formation,revealing variations in mass transfer intensity along the microchannel.We compare the results with cases of liquid mixing via a pure diffusive mechanism.Upon analysis,it was revealed that the complexity measure exhibits sensitivity to variations in the type of mass transfer,establishing its feasibility as an indirect criterion for assessing mass transfer intensity.The method presented can extend beyond flow analysis,finding application in the controlling of microstructures of various materials(porosity,for instance)or surface defects in metals,optical systems and other materials that hold significant relevance in materials science and engineering.

Mathematical modeling of evolution of cell networks in epithelial tissues

Epithelial cell networks imply a packing geometry characterized by various cell shapes and distributions in terms of number of cell neighbors and areas.Despite such simple characteristics describing cell sheets,the formation of bubble-like cells during the morphogenesis of epithelial tissues remains poorly understood.This study proposes a topological mathematical model of morphogenesis in a squamous epithelial.We introduce a new potential that takes into account not only the elasticity of cell perimeter and area but also the elasticity of their internal angles.Additionally,we incorporate an integral equation for chemical signaling,allowing us to consider chemo-mechanical cell interactions.In addition to the listed factors,the model takes into account essential processes in real epithelial,such as cell proliferation and intercalation.The presented mathematical model has yielded novel insights into the packing of epithelial sheets.It has been found that there are two main states:one consists of cells of the same size,and the other consists of“bubble”cells.An example is provided of the possibility of accounting for chemo-mechanical interactions in a multicellular environment.The introduction of a parameter determining the flexibility of cell shapes enables the modeling of more complex cell behaviors,such as considering change of cell phenotype.The developed mathematical model of morphogenesis of squamous epithelium allows progress in understanding the processes of formation of cell networks.The results obtained from mathematical modeling are of significant importance for understanding the mechanisms of morphogenesis and development of epithelial tissues.Additionally,the obtained results can be applied in developing methods to influence morphogenetic processes in medical applications.