Browsing by Author "Cristini, Vittorio"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence
    (2001-06) Cristini, Vittorio; Blawzdziewicz, Jerzy; Loewenberg, Michael
    An algorithm is presented for the adaptive restructuring of meshes on evolving surfaces. The resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations.
  • Thumbnail Image
    Item
    Critical behavior of drops in linear flows: I. Phenomenological theory for drop dynamics near critical stationary states
    (2001-06) Blawzdziewicz, Jerzy; Cristini, Vittorio; Loewenberg, Michael
    The dynamics of viscous drops in linear creeping flows are investigated near the critical flow strength at which stationary drop shapes cease to exist. It is shown that the near-critical drop behavior is dominated by a single slow mode that evolves on the time scale diverging at the critical point with the exponent 1/2.
  • Thumbnail Image
    Item
    Effect of inertia on drop breakup under shear
    (2001-06) Renardy, Yuriko Y.; Cristini, Vittorio
    A spherical drop, placed in a second liquid of the same density and viscosity, is subjected to shear between parallel walls. The subsequent flow is investigated numerically with a volume-of-fluid continuous-surface-force algorithm. Inertially driven breakup is examined. The critical Reynolds numbers are examined for capillary numbers in the range where the drop does not break up in Stokes flow.
  • Thumbnail Image
    Item
    Modeling multiphase flows using a novel 3D adaptive remeshing algorithm
    (2001-06) Hooper, Russell; Cristini, Vittorio; Shakya, Sundeep; Lowengrub, John S.; Derby, Jeffrey J.; Macosko, Christopher W.
    A novel three-dimensional adaptive remeshing algorithm is presented and applied to finite-element simulations of multiphase fluid flows. A three-dimensional domain enclosing another phase is discretized by an unstructured mesh of tetrahedra constructed from a triangulated surface of the phase boundaries. Complete remeshing is performed after each time step. The boundary mesh is reconstructed using an existing algorithm employing element addition/subtraction, edge swapping based on Delaunay triangulation and spring-like dynamical relaxation. The volume mesh is then generated from the boundary using the commercial software Hypermesh. The resulting adaptive discretization maintains resolution of prescribed local length scales.
  • Thumbnail Image
    Item
    Nonnecrotic tumor growth and the effect of vascularization. I. Linear analysis and self-similar evolution
    (2001-06) Cristini, Vittorio; Lowengrub, John; Nie, Qing
    In this paper, we revisit the linear analysis of the transient evolution of a perturbed tumor interface in two and three dimensions. In Part II, we will study the full nonlinear problem using boundary-integral simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A new formulation is developed that demonstrates that tumor evolution is described by a reduced set of two parameters and is qualitatively unaffected by the number of spatial dimensions. One parameter is related to the rate of mitosis. The other describes the balance between vascularization and apoptosis (programmed cell-death). Three regimes of growth are identified with increasing degrees of vascularization: low (diffusion dominated), moderate and high vascularization. We demonstrate that parameter ranges exist for which the tumor evolves self-similarly (i.e., shape invariant) in the first two regimes. In the diffusion-dominated regime, vascularization is weak or absent and self-similar evolution leads to a nontrivial dormant state. In the second regime vascularization becomes significant with respect to apoptosis; self-similar growth is unbounded and is associated with critical conditions of vascularization. Away from these critical conditions, perturbations may either grow with respect to the unperturbed shape, and thus lead to invasive fingering into the external tissues and metastasization, or decay to zero. In the high-vascularization regime, we find that during unbounded growth the tumor shape always tends to the unperturbed shape and neither self-similar nor fingering evolution occur. This last result is in agreement with recent experimental observations of in vivo tumor growth and angiogenesis, and suggests that the metastatic growth of highly-vascularized tumors is associated to vascular and elastic anisotropies, which are not included in our model.
  • Thumbnail Image
    Item
    Scalings for fragments produced from drop breakup in shear flow with inertia
    (2001-06) Renardy, Yuriko Y.; Cristini, Vittorio
    When a drop is sheared in a matrix liquid, the largest daughter drops are produced by elongative end-pinching. The daughter drop size is found to scale with the critical drop size that would occur under the same flow conditions and fluid properties.