{"product_id":"dynamics-of-complex-fluids-9786207910908","title":"Dynamics of Complex Fluids","description":"\u003cp\u003e • Author(s): Youssef Hairch\u003cbr\u003e • Publisher: Our Knowledge Publishing\u003cbr\u003e • Publisher Imprint: Our Knowledge Publishing\u003cbr\u003e • BISAC: Astronomy - General\u003c\/p\u003e\u003cp\u003eThe coupling of the Navier-Stokes equations with the Allen-Cahn model represents a significant advance in the field of fluid mechanics and interface modeling. This development has its roots in the need to better understand and simulate complex multi-phase fluid dynamics. This book (Complex Fluid Dynamics: Approaches with Allen-Cahn and Navier-Stokes) explores the approximation of dynamics between two fluids of different densities and viscosities. It presents a model that couples the Allen-Cahn equation, describing the evolution of a scalar-order parameter, with the time-dependent Navier-Stokes equations governing fluid motion. This coupling involves a surface tension term, which takes into account the energy required to create an interface between phases, proportional to the curvature of the interface, leading to the formation of a dynamic interface. The two-phase Navier-Stokes\/Allen-Cahn equations simulate several fluid flows, using the Allen-Cahn model for diffuse interfaces and the Navier-Stokes equations for fluid dynamics.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46378713350295,"sku":"9786207910908","price":4106.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9786207910908.webp?v=1768764710","url":"https:\/\/atlanticbooks.com\/products\/dynamics-of-complex-fluids-9786207910908","provider":"Atlantic Books","version":"1.0","type":"link"}