Browsing by Author "Zhang, Jiaqi"

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    An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid
    Li, Lei; Zhang, Jiaqi; Xu, Zelai; Young, Y. -N.; Feng, James J.; Yue, Pengtao (Academic Press/Elsevier, 2022-02-15)
    Hydrogels are crosslinked polymer networks swollen with an aqueous solvent, and play central roles in biomicrofluidic devices. In such applications, the gel is often in contact with a flowing fluid, thus setting up a fluid-hydrogel two-phase system. Using a recently proposed model (Young et al. [41] 2019), we treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian viscous solvent, and develop a finite-element method for computing flows involving a fluid-hydrogel interface. The interface is tracked by using a fixed-mesh arbitrary Lagrangian-Eulerian method that maps the interface to a reference configuration. The interfacial deformation is coupled with the fluid and solid governing equations into a monolithic algorithm using the finite-element library deal.II. The code is validated against available analytical solutions in several non-trivial flow problems: one-dimensional compression of a gel layer by a uniform flow, two-layer shear flow, and the deformation of a Darcy gel particle in a planar extensional flow. In all cases, the numerical solutions are in excellent agreement with the analytical solutions. Numerical tests show second-order convergence with respect to mesh refinement, and first-order convergence with respect to time-step refinement.
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    Comparison of four boundary conditions for the fluid-hydrogel interface
    Xu, Zelai; Zhang, Jiaqi; Young, Yuan-Nan; Yue, Pengtao; Feng, James J. (American Physical Society, 2022-09-01)
    In adopting a poroelastic model for a hydrogel, one views its constituent fluid and solid phases as interpenetrating continua, thereby erasing the pore-scale geometry. This gives rise to the need for additional boundary conditions (BCs) at the interface between a hydrogel and a clear fluid to supplement the momentum equations for the fluid and solid phases in the hydrogel. Using a thermodynamic argument on energy dissipation, we propose three sets of BCs for the gel-fluid interface that link the normal and tangential velocity jumps across the interface to the normal and tangential stresses on either side of the interface. Using several flow problems - one-dimensional compression, two-layer Couette and Poiseuille shear flows, and deformation of a gel particle by a planar extension flow - as tests, we compare the predictions of these three BCs with that of a previously proposed BC. Some differences are stark and reveal flaws in certain BCs. Others are subtler and will require quantitative experimental data for validation. Based on these results, we recommend one set of BCs over the other three for computing the flow and deformation of hydrogels in contact with a clear fluid. In addition, we suggest benchmark experiments to validate the BCs and our recommendation.
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    Finite-element simulations of interfacial flows with moving contact lines
    Zhang, Jiaqi (Virginia Tech, 2020-06-19)
    In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results.
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    A fluid mechanical study of rotation-induced traumatic brain injury
    Wang, Qifu; Zhang, Jiaqi; Bates, David; Feng, James J.; Yue, Pengtao; Wu, Qianhong (2025)
    Traumatic brain injury (TBI) is a serious health issue. Studies have highlighted the severity of rotation induced TBI. However, the role of cerebrospinal fluid (CSF) in transmitting the impact from the skull to the soft brain matter remains unclear. Herein, we use experiments and computations to define and probe this role in a simplified setup. A spherical hydrogel ball, serving as a soft brain model, was subjected to controlled rotation within a water bath, emulating the CSF, filling a transparent cylinder. The cylinder and ball velocities, as well as the ball’s deformation over time, were measured. We found that the soft hydrogel ball is very sensitive to decelerating rotational impacts, experiencing significant deformation during the process. A finite-element code is written to simulate the process. The hydrogel ball is modelled as a poroelastic material infused with fluid and its coupling with the suspending fluid is handled by an arbitrary Lagrangian-Eulerian method. The results indicate that the density contrast, as well as the rotational velocity difference, between the hydrogel ball and the suspending fluid play a central role in the ball’s deformation due to centrifugal forces. This approach contributes a deeper understanding of brain injuries and may portend the development of preventive measures and improved treatment strategies.
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    A level-set method for moving contact lines with contact angle hysteresis
    Zhang, Jiaqi; Yue, Pengtao (Academic Press/Elsevier, 2020-10-01)
    We develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E (2007) [6], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN,βCL), based on which we come up with a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method.
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    The Regulation of Micro-Organisms' Extra-Cellular Polysaccharides on Immunity: A Meta-Analysis
    Zhang, Jin; Chen, Yirui; Zhang, Jiaqi; Wang, Yitong; Liu, Yanan (MDPI, 2022-06-30)
    Extra-cellular polysaccharides (EPSs) have excellent immunomodulatory functions. In order to further promote their application, we studied the ability of extra-cellular polysaccharides from different sources to regulate immunity. We studied the association of extra-cellular polysaccharides with immune factors (Interleukin (IL-2, IL-4, IL-10), Interferon γ (IFN-γ), tumor necrosis factor-α (TNF-α), Immunoglobulin A (IgA), and Immunoglobulin G (IgG)) and different concentrations of EPSs and interfering media on experimental results by using a forest plot under fixed-effect or random-effects models. Through Google, PubMed, Embase, ScienceDirect, and Medline, from 2000 to 2021, 12 articles were included. We found that exopolysaccharides (from bacteria or fungi) could significantly increase the immune index of spleen and thymus, spleen index (SMD: 2.11, ‘95%CI: [1.15, 3.08]’; p < 0.01), and thymus index (SMD: 1.62, ‘95%CI: [0.93, 2.32]’; p = 0.01 < 0.05). In addition, exopolysaccharides had a significant effect on TNF-α (SMD: 0.94, ‘95%CI: [0.29, 1.59]’; p = 0.01 < 0.05). For IL-4 (SMD: 0.49, ‘95%CI: [0.01, 0.98]’; p = 0.046 < 0.05), extra-cellular polysaccharides had a statistically significant effect on immunity. Although the data of other immune factors were not ideal, the comprehensive analysis showed that exopolysaccharides also had an effect on the release of these five immune factors. In the sub-group analysis, different concentrations of EPSs affected the results of experiments on the spleen and thymus, and the CY intervention had a relatively significant effect on immune regulation. Taken together, our study highlighted that EPSs have a significant impact on immune regulation.