The identification of isomorphism in epicyclic gear trains has been found a lot of attention by researchers for the last few years. Various methods have been suggested by different authors for the detection of isomorphism in planer kinematic chains and epicyclic gear trains (EGTs), but everyone has found some difficulties to address new issues. In this paper, a modified path matrix approach was presented in order to compare all the distinct geared kinematic mechanisms. A new method based on the matrix approach and corresponding train values is required to identify isomorphism among epicyclic gear trains and their mechanisms. The proposed method was examined on the basis of various examples from four-link, five-link, six links, and eight-link one-degree-of-freedom EGTs and six links two-degree-of-freedom EGTs. All the examples have been found satisfactory results with existing literature.
As one of the flow-based passive sorting, the hydrodynamic filtration using a microfluidic-chip has shown to effectively separate into different sizes of subpopulations from cell or particle suspensions. Its model framework involving two-phase Newtonian or generalized Newtonian fluid (GNF) was developed, by performing the complete analysis of laminar flow and complicated networks of main and multiple branch channels. To predict rigorously what occurs in flow fields, we estimated pressure drop, velocity profile, and the ratio of the flow fraction at each branch point, in which the analytical model was validated with numerical flow simulations. As a model fluid of the GNF, polysaccharide solution based on Carreau type was examined. The objective parameters aiming practical channel design include the number of the branches and the length of narrow section of each branch for arbitrary conditions. The flow fraction and the number of branches are distinctly affected by the viscosity ratio between feed and side flows. As the side flow becomes more viscous, the flow fraction increases but the number of branches decreases, which enables a compact chip designed with fewer branches being operated under the same throughput. Hence, our rational design analysis indicates the significance of constitutive properties of each stream.
Human bone marrow-derived mesenchymal stem cells (hMSCs) consist of heterogeneous subpopulations with different multipotent properties: small and large cells with high and low multipotency, respectively. Accordingly, sorting out a target subpopulation from the others is very important to increase the effectiveness of cell-based therapy. We performed flow-based sorting of hMSCs by using optimally designed microfluidic chips based on the hydrodynamic filtration (HDF) principle. The chip was designed with the parameters rigorously determined by the complete analysis of laminar flow for flow fraction and complicated networks of main and multi-branched channels for hMSCs sorting into three subpopulations: small (<25>40 μm) cells. By focusing with a proper ratio between main and side flows, cells migrate toward the sidewall due to a virtual boundary of fluid layers and enter the branch channels. This opens the possibility of sorting stem cells rapidly without damage. Over 86% recovery was achieved for each population of cells with complete purity in small cells, but the sorting efficiency of cells is slightly lower than that of rigid model particles, due to the effect of cell deformation. Finally, we confirmed that our method could successfully fractionate the three subpopulations of hMSCs by analyzing the surface marker expressions of cells from each outlet.