Abstract Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and, disregarding molecular diffusion, mechanical dispersion. By homogenization, we show that after many cycles, the transport converges to a zero convection, pure nonlinear diffusion problem. The impact of the oscillatory flow requires an adjustment of the dispersion coefficient, where instead of the modulus of the particle velocity, we have to use its time averaged value. Physically, this agrees with a velocity defined by the distance travelled by particles in solution, divided by the time needed for that displacement. The nonlinearity of the sorption reaction is retained in the concentration distribution of the mixing zone, because in the large time limit, this distribution is not Gaussian but asymmetric. With numerical simulations, we show that this convergence may occur relatively fast (say 10 cycles). The implication of the diffusion like large time behaviour is that the transition zone continues to spread beyond the zone of convective oscillation.

中文翻译：

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多孔介质中振荡非线性溶质输运的大时间行为

摘要 由于潮汐、日常或季节性模式，在天然多孔介质中的许多不同情况下都会发生流动振荡。在本文中，我们研究了这种流动的振荡如何影响最初尖锐的溶质前沿的传输，如果溶质经历非线性吸附并且不考虑分子扩散和机械分散。通过均匀化，我们表明经过多次循环后，传输收敛到零对流、纯非线性扩散问题。振荡流的影响需要调整色散系数，其中我们必须使用其时间平均值而不是粒子速度的模量。在物理上，这与由粒子在溶液中行进的距离除以该位移所需的时间所定义的速度一致。吸附反应的非线性保留在混合区的浓度分布中，因为在大的时间限制下，这种分布不是高斯分布而是不对称的。通过数值模拟，我们表明这种收敛可能发生得相对较快（比如 10 个周期）。扩散像大时间行为的含义是过渡区继续扩散到对流振荡区之外。