Flow-induced shear stress and deformation of a core–shell-structured microcapsule in a microchannel

A numerical model was developed and validated to investigate the fluid–structure interactions between fully developed pipe flow and core–shell-structured microcapsule in a microchannel. Different flow rates and microcapsule shell thicknesses were considered. A sixth-order rotational symmetric distribution of von Mises stress over the microcapsule shell can be observed on the microcapsule with a thinner shell configuration, especially at higher flow rate conditions. It is also observed that when being carried along in a fully developed pipe flow, the microcapsule with a thinner shell tends to accumulate stress at a higher rate compared to that with a thicker shell. In general, for the same microcapsule configuration, higher flow velocity would induce a higher stress level over the microcapsule shell. The deformation gradient was used to capture the microcapsule's deformation in the present study. The effect of Young's modulus on the microcapsule shell on the microcapsule deformation was investigated as well. Our findings will shed light on the understanding of the stability of core–shell-structured microcapsule when subjected to flow-induced shear stress in a microfluidic system, enabling a more exquisite control over the breakup dynamics of drug-loaded microcapsule for biomedical applications.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Unsymmetrical Pyrene‐Fused Phthalocyanine Derivatives: Synthesis,Structure, and Properties

Novel pyrene‐fused unsymmetrical phthalocyanine derivatives 2,3,9,10,16,17‐hexakis(2,6‐dimethylphenoxy)‐22,25‐diaza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc complex Zn[Pc(Pz‐pyrene)(OC₈H₉)₆] ( 1 ) and 2,3,9,10‐tra(2,6‐dimethylphenoxy)‐15,18,22,25‐traza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc compound Zn[Pc(Pz‐pyrene)₂(OC₈H₉)₄] ( 2 ) were isolated for the first time. These unsymmetrical pyrene‐fused phthalocyanine derivatives have been characterized by a wide range of spectroscopic and electrochemical methods. In particular, the pyrene‐fused phthalocyanine structure was unambiguously revealed on the basis of single crystal X‐ray diffraction analysis of 1 , representing the first structurally characterized phthalocyanine derivative fused with an aromatic moiety larger than benzene.     

Strategies for Improving the Catalytic Performance of 2D Covalent Organic Frameworks for Hydrogen Evolution and Oxygen Evolution Reactions

Hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) have been deemed as clean and sustainable strategies to solve the energy crisis and environmental problems. Various catalysts have been developed to promote the process of HER and OER. Among them, two-dimensional covalent organic frameworks (2D COFs) have received great attention due to their diverse and designable structure. In this minireview, we mainly summarize the diverse linkages of 2D COFs and strategies for enhancing the catalytic performance of 2D COFs for HER and OER, such as introducing active building blocks, metal ions and tailored linkages. Furthermore, a brief outlook for the development directions of COFs in the field of HER and OER is provided, expecting to stimulate new opportunities in future research.