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Lipeng Lai

Screen Name: Lipeng
Email: lplai@uchicago.edu
ICAM Affiliation:
Branch Affiliation: University of Chicago
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Research Area: My current research is supervised by Professor Wendy Zhang. Our study focuses on how the formation of finite time singularities in free surface flows is affected by initial/boundary conditions. Experimental examples include the breakup of an underwater air bubble and the collapse of an impact-created air cavity in water. This problem represents a wide range of natural and industrial processes: whenever a stone is thrown into a pond, rain drops hit the ocean’s surface, or a propeller is running with its maximum power, gas cavities are produced. Those cavities often break up into smaller pieces subsequently. We have studied this problem both analytically and numerically. When one bulk of fluid breaks up into smaller pieces, the part where the fluid pinches off shrinks towards zero. In the process, the local stress and velocity diverge, forming a finite time singularity. In many cases (like water drop breaking up in air), the singularity is known to be universal (independent of initial/boundary conditions). Conversely, underwater air bubble breakup is very sensitive to initial perturbations. Various forms of breakup are observed experimentally. What makes this problem challenging and interesting is that previous studies using linear stability analysis show that underwater bubble breakup inevitably evolves into a nonlinear region. Our work emphasizing the nonlinear part is thus essential to provide a fundamental understanding to this problem. To address the nonlinear effects, I wrote a simulation code using standard boundary integral method with adaptive mesh and time-stepping, which now allows us to classify the ostensibly complex form of breakup into two categories (paper in preparation). In one category, the interface evolves into smooth contact. The dynamics is well approximated by linear dynamics (after conformal mapping and sets of nonlinear transformation adopted from literature (work together with Dr. Konstantin S. Turitsyn)). In the other, the nonlinear effects are significant and the interface evolves into a “near singular” surface with highly curved regions. Furthermore, we carefully analyzed the possible curvature singularity related to the “near singular” surface and the resulting high-speed water jets (thesis in preparation).
Research Description:
Thrust Area: Soft Matter Biological Matter

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