Ronald Suryo

Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid

Dynamics of formation of a drop of an incompressible Newtonian fluid of viscosity μ1 and density ρ1 from the tip of a tube of radius R1 into a co-flowing immiscible, incompressible Newtonian fluid of viscosity μ2 and density ρ2 that is enclosed in a concentric cylindrical tube of radius R2 are investigated under creeping flow conditions. Transient drop shapes, and fluid velocities and pressures, are calculated numerically by solving the governing Stokes equations with the appropriate boundary and initial conditions using the Galerkin/finite element method for spatial discretization and an adaptive finite difference method for time integration. In accord with previous studies, the primary effect of increasing the ratio of the volumetric injection rate Q2 of the outer fluid to that of the inner fluid Q1, Qr≡Q2∕Q1, is shown to be a reduction in the volume of primary drops that are formed. When Qr is small, calculations show that drop formation occurs in a slug flow regime where the primary drops that are...

Scaling in pinch-off of generalized Newtonian fluids

Abstract Pinch-off dynamics of slender liquid bridges of generalized Newtonian fluids without and with inertia are studied using asymptotic analysis and numerical computation. The deformation-rate-dependent rheology is described by power law and Carreau models. Because the bridges are slender, their dynamics are governed by a pair of spatially one-dimensional (1D), non-linear evolution equations for the bridge shape and axial velocity. A bridge of a power law fluid under creeping flow conditions exhibits self-similar dynamics in the vicinity of the axial location where the bridge radius is a minimum. The scaling exponents that determine the variation with time remaining to breakup of the bridge radius or radial length scale, axial length scale, and axial velocity are evaluated by a combined analytical and numerical approach. Similarity solutions are obtained by collapsing numerically computed profiles of both the bridge shape and the axial velocity in the vicinity of the axial location where the bridge radius is minimum by rescaling of the transient profiles with radial and axial scalings deduced from theory. This scaling behavior is transitory and inertial effects become significant as pinch-off is approached. Thereafter, a new balance is established between viscous, capillary, and inertial forces that leads to a new self-similar regime which persists until pinch-off. The scaling exponents appropriate to this regime are also determined. Moreover, it is shown theoretically that interface shapes in the vicinity of the singularity are non-slender for values of the power law exponent below 2/3. Similarity solutions are once again obtained in the same manner as that used in the creeping flow limit. Low-viscosity bridges of Carreau fluids are known to exhibit a transition from potential flow (PF) scaling to Newtonian scaling. Here it is demonstrated that high-viscosity bridges of Carreau fluids exhibit a transition from power law scaling to Newtonian scaling. The point of transition between the latter two regimes is predicted in terms of parameters of the Carreau model.

Simplicity and complexity in a dripping faucet

Continuous emission of drops of an incompressible Newtonian liquid from a tube–dripping–is a much studied problem because it is important in applications as diverse as inkjet printing, microarraying, and microencapsulation, and recognized as the prototypical nonlinear dynamical system, viz., the leaky faucet. The faucet’s dynamics are studied in this paper by a combination of experiment, using high-speed imaging, and computation, in which the one-dimensional slender-jet equations are solved numerically by finite element analysis, over ranges of the governing parameters that have heretofore been unexplored. Previous studies when the Bond number G that measures the relative importance of gravitational to surface tension force is moderate, G≈0.5, and the Ohnesorge number Oh that measures the relative importance of viscous to surface tension force is low, Oh≈0.1, have shown that the dynamics changes from (a) simple dripping, i.e., period-1 dripping with or without satellites, to (b) complex dripping, where th...

Nonlinear dynamics and breakup of compound jets

Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase (ω=0) or π radians out phase (ω=π), where ω is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory [Chauhan et al., J. Fluid Mech. 420, 1 (2000)]. Computations reveal that recirculating flows occur commonly during the deformation and pinch...

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

Based on an experimental and computational study of the breakup of a drop (jet) of small viscosity in an ambient fluid of large viscosity, Doshi et al. [Science 302, 1185 (2003)] have shown that the breakup of a drop (jet) of zero viscosity in a very viscous ambient fluid gives rise to an unexpected, nonuniversal form of singularity. Doshi et al. conjectured that the nonuniversal dynamics result from the fact that stresses exerted by the inner fluid are negligible. To verify this conjecture and overcome computational difficulties associated with simulating systems in which the disparity between the viscosities of the inner and the outer fluids is large, the breakup of an annular jet whose core is a gas of negligible viscosity is analyzed. Calculations show that as the jet’s minimum radius hmin→0, both core- and shell-side pressures remain bounded while surface tension pressure, which diverges as 1/hmin, is balanced by viscous normal stress exerted by the shell fluid. Simulations show that interfacial poin...