In the process of filtration, fluid impurities precipitate/accumulate; this results in an uneven inner wall of the filter, consequently leading to non-uniform suction/injection. The Riemannian–Liouville fractional derivative model is used to investigate viscoelastic incompressible liquid food flowing through a permeable plate and to generalize Fick’s law. Moreover, we consider steady-state mass balance during ultrafiltration on a plate surface, and a fractional-order concentration boundary condition is established, thereby rendering the problem real and complex. The governing equation is numerically solved using the finite difference algorithm. The effects of the fractional constitutive models, generalized Reynolds number, generalized Schmidt number, and permeability parameter on the velocity and concentration fields are compared. The results show that an increase in fractional-order α in the momentum equation leads to a decrease in the horizontal velocity. Anomalous diffusion described by the fractional derivative model weakens the mass transfer; therefore, the concentration decreases with increasing fractional derivative γ in the concentration equation.

在过滤过程中，流体杂质沉淀/积累；这导致过滤器的内壁不均匀，从而导致不均匀的抽吸/注入。黎曼－利维尔分数阶导数模型用于研究流过可渗透板的粘弹性不可压缩液体食物，并推广菲克定律。此外，我们考虑了板表面超滤过程中的稳态质量平衡，并建立了分数阶浓度边界条件，从而使问题变得真实而复杂。使用有限差分算法对控制方程进行数值求解。比较了分数本构模型，广义雷诺数，广义施密特数和渗透率参数对速度场和浓度场的影响。结果表明，动量方程中分数阶α的增加导致水平速度的减小。分数导数模型描述的反常扩散会削弱传质；因此，浓度随分数导数的增加而降低浓度方程中的γ。