稳定平移抛物线溶解指
Steadily translating parabolic dissolution fingers
摘要：
溶蚀指（或虫孔）是多孔岩石在溶蚀过程中由于流动、运移和孔隙表面化学反应之间的非线性反馈而形成的。我们分析的形状和增长速度的薄前近似，其中反应被假定为瞬间发生的反应物完全消耗在溶解前内的手指。我们集中在的情况下，当主流是由恒定的压力梯度远离手指，和手指的内部和外部之间的渗透率差是有限的。使用Ivantsov变换和保角变换，我们发现家庭的稳定平移手指的特点是由一个抛物线形状。我们推导出的反应物浓度场和压力场的内部和外部的手指，并表明，他们内的流动是均匀的。手指的前进速度被证明是成反比的曲率半径在小的Péclet数限制和常数为大的Péclet数。
英文摘要：
Dissolution fingers (or wormholes) are formed during the dissolution of a porous rock as a result of nonlinear feedbacks between the flow, transport and chemical reactions at pore surfaces. We analyze the shapes and growth velocities of such fingers within the thin-front approximation, in which the reaction is assumed to take place instantaneously with the reactants fully consumed at the dissolution front. We concentrate on the case when the main flow is driven by the constant pressure gradient far from the finger, and the permeability contrast between the inside and the outside of the finger is finite. Using Ivantsov ansatz and conformal transformations we find the family of steadily translating fingers characterized by a parabolic shape. We derive the reactant concentration field and the pressure field inside and outside of the fingers and show that the flow within them is uniform. The advancement velocity of the finger is shown to be inversely proportional to its radius of curvature in the small Péclet number limit and constant for large Péclet numbers.
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