BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrea Papini (Chalmers and GU) DTSTART:20240304T121500Z DTEND:20240304T130000Z DTSTAMP:20260417T004449Z UID:cam/20 DESCRIPTION:Title: Tur bulence enhancement of coagulating processes\nby Andrea Papini (Chalme rs and GU) as part of CAM seminar\n\nLecture held in MV:L14.\n\nAbstract\n We present and investigate the collision-coalescence process of particles in the presence of a fluid velocity field\, examining the relationship bet ween flow properties and enhanced coagulation. Our research focuses on two main aspects. Firstly\, we propose a novel modeling approach for turbulen t fluid at small scales\, employing a Gaussian random field with non-trivi al spatial covariance. Secondly\, we derive rigorous partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) fro m this model\, capturing the physical characteristics of particles suspend ed in the fluid. From an Eulerian perspective\, we analyze a kinetic parti cle system subjected to environmental transport noise. Specifically\, we r igorously study a modified version of Smoluchowski’s coagulation equatio n\, which incorporates velocity dependence akin to the Boltzmann equation. By utilizing techniques rooted in unbounded elliptic semigroup theory and weighted Sobolev space inequalities\, we establish the existence and uniq ueness of classical solutions for the case of a spatially homogeneous init ial distribution. Moreover\, from a Lagrangian viewpoint\, we employ this particle system to gain insights into the collision rate at a steady state for particles uniformly distributed within a medium. Considering a partic le-fluid model\, we perform two scaling limits. The first limit\, involvin g the number of particles\, yields a stochastic Smoluchowski-type system\, with the turbulent velocity field still governed by a noise stochastic pr ocess. The second scaling limit pertains to the parameters of the noise\, specifically targeting the direction associated with small-scale turbulenc e. This limit leads to a deterministic equation with eddy dissipation in t he velocity variable. We conduct numerical simulations of this equation sy stem and demonstrate the influence of turbulence on rain formation. Our qu alitative findings reveal a steady increase in coagulation efficiency with escalating turbulent kinetic energy of the fluid. Additionally\, we obser ve a power-law decay over time and in relation to the turbulence parameter . Furthermore\, we recover fundamental laws governing the collision rate a nd relative velocity of moving particles in the high Stokes number regime. \n LOCATION:https://researchseminars.org/talk/cam/20/ END:VEVENT END:VCALENDAR