各向异性的双孔隙多孔介质中Oldroyd-B流体双扩散对流不稳定性

The Double-Diffusive Convection Instability in an Anisotropic Bidispersive Layer of an Oldroyd-B Fluid

摘要: 本文研究了饱和Oldroyd-B流体的各向异性双孔隙多孔层内的双扩散对流不稳定性。建立了相关控制方程和边界条件的理论模型。通过小扰动法和常规展开法推导了Orr-Sommerfeld方程。此外，通过理论分析和数值模拟，得到了中性稳定曲线。结果表明，体系稳定性受到Lewis数Le、浮力比N、大孔与微孔渗透率比K_r、大孔隙各向异性参数K_fr、微孔隙各向异性参数K_pr以及弛豫时间λ₁和滞后时间λ₂的综合影响。各参数在临界Darcy-Rayleigh数与中性稳定曲线的变化中均起关键作用。具体而言，增大λ₁提高流体的弹性储能能力，从而削弱扰动增长、延迟失稳发生；增大λ₂使应力响应具有更强的时间滞后性，进一步提高系统稳定阈值。随着浮力比N的增加，溶质浮力削弱热浮力的驱动作用，导致体系更难发生对流。大孔与微孔隙各向异性参数K_fr、K_pr的增大均会使临界Darcy-Rayleigh数上升，表明孔隙各向异性对系统具有稳定化效应。总体而言，Oldroyd-B流体的粘弹性效应与孔隙结构各向异性共同主导了双扩散对流的不稳定性行为，增强任一因素均能有效推迟失稳的发生，为非牛顿流体在复杂多孔介质中的传热传质调控提供了理论依据。

Abstract: This paper investigates the double-diffusive convection instability in an anisotropic bidispersive layer of an Oldroyd-B fluid. A theoretical model with the relevant control equations and boundary conditions was established. The Orr-Sommerfeld equation was derived using the method of small perturbations and regular expansion. Further, through theoretical analysis and numerical simulation, the neutral stability curve was obtained. The results show that the system stability is jointly influenced by the Lewis number Le, buoyancy ratio N, permeability ratio between macropores and micropores K_r, anisotropy parameters of the macroporous and microporous structures K_fr and K_pr, as well as the relaxation time λ₁ and retardation time λ₂. All these parameters play crucial roles in determining the critical Darcy-Rayleigh number and the shape of the neutral stability curves. Specifically, increasing λ₁ enhances the elastic energy storage capacity of the fluid, suppressing disturbance growth and delaying the onset of convection. A larger λ₂ introduces stronger temporal lag in the stress response, further raising the stability threshold. With the increase of N, the solutal buoyancy counteracts the thermal buoyancy, making the system more resistant to convection. In addition, higher anisotropy parameters K_fr and K_pr of the macro- and micropores lead to an increase in the critical Darcy-Rayleigh number, indicating that pore anisotropy exerts a stabilizing influence on the system. Overall, the viscoelastic effects of the Oldroyd-B fluid and the anisotropic pore structure jointly govern the double-diffusive convection instability, and the enhancement of either factor effectively delays the onset of instability, providing theoretical insights for the control of heat and mass transfer of non-Newtonian fluids in complex porous media.