AI 中文总结
本研究通过耦合微极速度场与广义弥散框架，解析了插管动脉环形流动中瞬态溶质弥散，揭示了导管接近壁面时剪切弥散的六次方抑制及壁面动力学与微旋转效应的区分。
AI 中文摘要
我们研究了压力驱动下通过同心环形管（代表插管动脉）的微极流动中的瞬态溶质弥散。导管对溶质不可渗透，而动脉壁结合了不可逆清除与可逆表面滞留。精确的稳态微极速度场与Gill-Sankarasubramanian广义弥散框架耦合；由此产生的体相-表面层级通过Rannacher阻尼Crank-Nicolson时间步进推进，以确定$K_0(t)$、$K_1(t)$和$K_2(t)$。交换系数与微极参数无关，并满足$-K_0(0^+)=2(\beta+\theta Da)/(1-\lambda^2)$，而$K_2-Pe^{-2}\sim\sigma_v^2t$在初始时成立，因此短时主导弥散是流体动力学的，且与壁动力学无关。在弱反应状态下，微极性通过速度振幅因子近似线性地修改对流，并二次地修改剪切弥散。窄间隙分析取$\varepsilon=1-\lambda$，在固定压力梯度下给出$\bar v\sim(2-N_c)\varepsilon^2/6$和$K_2-Pe^{-2}\sim(2-N_c)^2\varepsilon^6/7560$，揭示了当导管接近动脉壁时剪切弥散的六次方抑制。将$\lambda$从$0.01$增加到$0.30$会使有效对流减少约$2.45$倍，而化学惰性的剪切诱导弥散减少$24$倍。耦合公式还产生了精确的分配$\Phi_m+\Phi_s+\Phi_a=1$，将移动、可逆滞留和不可逆吸收的溶质分开。重建的场量化了反应调制的横向非均匀性，而结果将限制和微旋转的水动力学效应与壁动力学效应区分开来。
英文摘要
We study transient solute dispersion in pressure-driven micropolar flow through a concentric annulus representing a catheterized artery. The catheter is impermeable to solute, whereas the arterial wall combines irreversible removal with reversible surface retention. The exact steady micropolar velocity field is coupled to the Gill-Sankarasubramanian generalized-dispersion framework; the resulting bulk-surface hierarchy is advanced with Rannacher-damped Crank-Nicolson time stepping to determine $K_0(t)$, $K_1(t)$ and $K_2(t)$. The exchange coefficient is independent of the micropolar parameters and satisfies $-K_0(0^+)=2(β+θDa)/(1-λ^2)$, whereas $K_2-Pe^{-2}\simσ_v^2t$ initially, so the leading short-time dispersion is hydrodynamic and independent of wall kinetics. In the weak-reaction regime, micropolarity modifies convection approximately linearly and shear dispersion quadratically through the velocity-amplitude factor. A narrow-gap analysis with $\varepsilon=1-λ$ gives $\bar v\sim(2-N_c)\varepsilon^2/6$ and $K_2-Pe^{-2}\sim(2-N_c)^2\varepsilon^6/7560$ for a fixed pressure gradient, revealing a sixth-power suppression of shear dispersion as the catheter approaches the arterial wall. Increasing $λ$ from $0.01$ to $0.30$ reduces effective convection by about a factor of $2.45$, while chemically passive shear-induced dispersion falls by a factor of $24$. The coupled formulation also yields the exact partition $Φ_m+Φ_s+Φ_a=1$, separating mobile, reversibly retained and irreversibly absorbed solute. The reconstructed field quantifies reaction-modulated transverse non-uniformity, while the results distinguish hydrodynamic effects of confinement and microrotation from kinetic wall effects.
