title: Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow.
abstract: Cracks filled with fluid propagation when the pressurized fluid is injected into the crack. Subsequently, when the fluid inlet is exposed to a lower pressure, the fluid flows backwards (backflow) and the crack closes due to the elastic relaxation of the solid. Here we study the dynamics of the crack closure during the backflow. We find that the crack radius remains constant and the fluid volume in the crack decreases with time in a power-law manner at late times. The balance between the viscous stresses in the fluid and elastic stresses in the fluid and the elastic stresses in the solid yields a scaling law that agrees with the experimental results for different fluid viscosities, Young's moduli of the solid, and initial radii of the cracks. Furthermore, we visualize the time-dependent crack shapes, and the convergence to a universal dimensionless shape demonstrates the self-similarity of the crack shapes during the backflow process.
authors.affiliation: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Ching-Yao
authors.initials: CY
authors.lastname: Lai
authors.affiliation: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.|Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
authors.forename: Zhong
authors.initials: Z
authors.lastname: Zheng
authors.affiliation: Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, New York 11201, USA.
authors.forename: Emilie
authors.initials: E
authors.lastname: Dressaire
authors.affiliation: Department of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Guy Z
authors.initials: GZ
authors.lastname: Ramon
authors.affiliation: Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.|School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia.
authors.forename: Herbert E
authors.initials: HE
authors.lastname: Huppert
authors.affiliation: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Howard A
authors.initials: HA
authors.lastname: Stone