We study the shape evolution of pores with calcite surfaces that dissolve with rates linearly varying along the pore length due to saturation gradients. A reaction–diffusion equation predicts that the walls have uniform slope along the pore length, which corresponds to walls with equally separated monolayer steps in a microscopic scale. We also study a nanoscale model that represents the detachment of individual molecules from the pore surface with rates obeying the same linear dependence on the position. Kinetic Monte Carlo simulations performed with two different conditions of the crystal surfaces at the pore ends show wall profiles very different from those of the reaction–diffusion equation. These profiles are controlled by the formation of surface steps at points of low saturation and by dominant step propagation to the saturated region. When crystal edges are present at the pore ends, there is fast widening at the unsaturated side, formation of step trains, and their propagation along the inner and outer surfaces. The hydrodynamic interpretation of the process in the light of the Kardar–Parisi–Zhang theory explains why the initially sharp edges acquire an approximately circular shape in a few seconds of dissolution. Instead, when a flat wall condition is imposed at the pore ends, surface steps are slowly formed at the unsaturated side, propagate to the saturated region, and accumulate there in a phenomenon of step bunching. A stationary shape with flat (rough) walls at the unsaturated (saturated) side is attained typically after some tens of minutes and is approximately predicted by a hydrodynamic approach assuming an inverse proportionality between step density and local dissolution rate. Thus, the consequences of the molecular scale model can be explained by upscaled treatments of the kinetics of step generation and propagation and have a potential to improve multiscale approaches.

中文翻译：

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当矿物壁在饱和梯度下溶解时，阶梯传播控制孔隙形状演化


我们研究了方解石表面孔隙的形状演化，由于饱和梯度，方解石表面的溶解速率沿孔隙长度线性变化。反应扩散方程预测壁沿孔隙长度具有均匀的斜率，这对应于微观尺度上具有均匀分离的单层台阶的壁。我们还研究了一个纳米级模型，该模型表示单个分子从孔表面的脱离，其速率服从与位置相同的线性依赖性。在孔端晶体表面的两种不同条件下进行的动力学蒙特卡罗模拟显示，壁面轮廓与反应扩散方程的壁面轮廓非常不同。这些轮廓由低饱和点处表面台阶的形成以及向饱和区域的主要台阶传播控制。当晶体边缘出现在孔隙末端时，不饱和侧会快速加宽，形成阶梯序列，并沿着内表面和外表面传播。根据卡达尔-帕里西-张理论对该过程的流体动力学解释解释了为什么最初尖锐的边缘在溶解的几秒钟内获得近似圆形的形状。相反，当在孔端施加平壁条件时，表面台阶在不饱和侧缓慢形成，传播到饱和区域，并在那里累积，形成台阶聚束现象。通常在数十分钟后获得在不饱和（饱和）侧具有平坦（粗糙）壁的固定形状，并且通过假设阶梯密度和局部溶解速率之间成反比的流体动力学方法来近似预测。 因此，分子尺度模型的结果可以通过对步骤生成和传播动力学的放大处理来解释，并且有可能改进多尺度方法。