David Halpern: Research Interests and Publications

My research interests include:
Capillary-elastic instabilities with applications to airway closure. The lung is comprised of a network of bifurcating airway tubes which are coated with a thin viscous film. Often times, especially in the case of disease, the liquid film can form a mensicus which fills the whole tube, thus obstructing airflow. The formation of the liquid mensicus is due to capillary driven instabilities which can arise in the lining, causing the lining to close up. In addition, airflow can also be obstructed if the airway tube collapses in on itself. This occurs when the elastic forces of the tube are not large enough to sustain the negative fluid pressures inside the tube, and the tube collapses. More recently, we have been looking at means of preventing closure, for example, the effects of an oscillatory shear stress on the air-fluid interface.
Movies of closure simulations.

 Halpern, D. and Grotberg, J.B. Fluid-elastic instabilities of liquid lined flexible tubes: Airway closure. J. Fluid Mech. 244: 615-632, 1992.

 Halpern, D. and Grotberg, J.B. Surface-tension instabilities of liquid-lined elastic tubes. Contemporary Mathematics 141: 295-316, 1993, edited by A.Y. Cheer and C.P. van Dam.

Halpern, D. and Grotberg, J.B. Surfactant effects on fluid elastic instabilities of liquid lined flexible tubes: a model of airway closure. J. Biomech. Eng. 115: 271-277, 1993.

Cassidy, K.J, Halpern, D., Ressler, B.G. and Grotberg, J.B. Surfactant effects in model airway closure experiments. J. Applied Physiology 87: 415-427,1999. [Abstract] [Full Text] [PDF]

Halpern, D., Moriarty, J.A. and Grotberg, J.B. (1999) Capillary-Elastic Instabilities with an Oscillatory Forcing Function. In IUTAM Symposium on Non-linear Singularities in Deformation and Flow. Editors, Durban, D. and Pearson, J.R.A, pp. 243-255. Publishers: Kluwer Academic, Dordrecht, The Netherlands.

Halpern, D. and Grotberg, J.B. (2000) Oscillatory shear stress induced stabilization of thin film instabilities.In: IUTAM Symposium on Nonlinear Waves in Multiphase Flow.Editor, Chang, H.-C, Volume 57, pp. 33-43. Publishers: Kluwer Academic, Dordrecht, The Netherlands.

Halpern, D. and Grotberg, J.B. Nonlinear Saturation of the Rayleigh instability in a liquid-lined tube due to oscillatory flow.  J. Fluid Mech. 492: 251-270, 2003.

 

Thin film instabilities and pattern formation We recently derived a novel equation describing how the thickness of a viscous film evolves with time, as a by-product of our work on the effects of oscillatory airflow on capillary instabilities related to airway closure. This is a modified Kuramoto-Sivashinsky equation which can also describe the Rayleigh-Taylor instability of a two-fluid system between horizontal plates consisting of a viscous film bounded below by a rigid oscillating plate and above by a heavier fluid. For some parameter values, the growth of waves at the air-liquid interface saturates and capillary instabilities promote chaotic waves. Numerical solutions on extended spatial intervals reveal interesting time-asymptotic regimes in which averaged properties of the extensive spatiotemporal chaos are not steady but oscillate in time. A comprehensive parametric study is being undertaken with the aim of identifying and classifying a wide range of flow patterns that may have biomedical and industrial applications. Extensions to other coating flow problems, including three-dimensional instabilities, are also being considered.

This work is being done in collaboration with A.L. Frenkel.

 Frenkel, A.L. and Halpern, D. (2000) On saturation of Rayleigh-Taylor instability.In: IUTAM Symposium on Nonlinear Waves in Multiphase Flow.Editor, Chang, H.-C, Volume 57, pp. 69-79. Publishers: Kluwer Academic, Dordrecht, The Netherlands.

 Faybishenko, B., Babchin, A.J., Frenkel, A.L., Halpern, D. and Sivashinsky, G.I.  A model of chaotic evolution of an ultrathin film down an inclined plane.  Colloids & Surfaces 192: 377-385, 2001. SummaryPlus | Full Text + Links | PDF.

 Halpern, D. and Frenkel, A.L. Saturated Rayleigh-Taylor instability of an oscillating Couette film flow. J. Fluid Mech. 446: 67-93, 2001. [abstract, full text (PDF)].

Frenkel, A.L. and Halpern, D. Stokes-flow instability due to interfacial surfactant. Phys. Fluids. 14(7), L45-L48, 2002. Abstract Full Text: [PDF (70 kB) GZipped PS ]  Order

Halpern, D. and Frenkel, A.L. Destabilization of a creeping flow by interfacial surfactant: Linear theory extended to all wavenumbers. J. Fluid Mech. 485: 191-220, 2003.

Frenkel, A.L and Halpern, D. Effect of inertia on the insoluble-surfactant instability of a shear flow. Phys. Rev. E 71, 016302, 2005.  Abstract   Full Text: [ PDF (117 kB)  GZipped PS 

Frenkel, A.L and Halpern, D. Strongly nonlinear nature of interfacial-surfactant instability of Couette flow. Int. J. Pure Appl. Math, 29(2), 205-224, 2006 or arXiv:nlin/0601025

Surfactant spreading on thin liquid layers. Pulmonary surfactant is a vital component of the liquid layer that lines lung airways and alveoli because, by reducing the surface tension at the air-liquid interface, it helps to maintain high lung compliance and to retard the surface-tension-driven instabilities that lead to airway closure. Since the lungs of prematurely born infants may not produce sufficient quantities of natural surfactant, a substitute may be delivered to them, either by inhalation of an aerosol or by direct intratracheal instillation. The delivered surfactant spreads throughout the lung under the action of gravity, surface-tension gradients and surface diffusion.

Halpern, D. and Grotberg, J.B. Dynamics and transport of a localized soluble surfactant on a thin film. J. Fluid Mech. 237: 1-11, 1992.
Jensen, O.E., Halpern, D. and Grotberg, J.B. Transport of a passive solute by surfactant-driven flows. Chem. Eng. Sci. 49(8): 1107-1117, 1994.
Grotberg, J.B., Halpern, D. and Jensen, O.E. The interaction of exogenous and endogenous surfactant: spreading-rate effects. J. Applied Physiology 78: 750-756, 1995. [Abstract] [PDF]
 Halpern, D., Jensen, O.E. and Grotberg, J.B. A theoretical study of surfactant and liquid delivery into the lung. J. Applied Physiology 85: 333-352, 1998. [Abstract] [Full Text] [PDF]
Jensen, O.E. and Halpern, D. The stress singularity in surfactant-driven-film flows. Part 1. Viscous effects. J. Fluid Mech. 372: 273-300, 1998.

Halpern, D., Bull, J.L. and Grotberg The effect of Airway Wall Motion on Surfactant Delivery.   J. Biomech.l Eng. 126(4): 410-419, 2004.

 

 

Airway reopening mechanics. The reopening of collapsed small airways is modeled by the convection of a finger of air through a viscous fluid contained between two narrowly spaced compliant plates.

 Halpern, D. and Gaver, D.P. Boundary element analysis of two-phase displacement in a Hele-Shaw cell. J. Comp. Phys. 115(2): 366-375, 1994. Abstract Article (PDF 466K)

 Gaver, D.P. III, Halpern, D., Jensen, O.E. & Grotberg, J.B. The Steady motion of a Semi-Infinite Bubble Through a Flexible-Walled Channel. J. Fluid Mech. 319: 25-45, 1996. (Abstract).

 Ghadiali, S.N. , Halpern, D. and Gaver, D.P.  A dual-reciprocity boundary element method for evaluating bulk convective transport of surfactant in free surface flows. J. Comp. Phys. 171: 534-559, 2001.  Abstract | References  Article (PDF 373K)

 Halpern, D. and Jensen, O.E. A semi-infinite bubble advancing into a planar tapered channel.  Phys. Fluids. 14(2), 431-442, 2002.  PDF (168 kB) GZipped PS   Order.

 Jensen, O.E., Horsburgh, M.K., Halpern, D. & Gaver, D.P. III The steady propagation of a bubble in a flexible-walled channel: asymptotic and computational models. Phys. Fluids. 14(2), 443-457, 2002.  PDF (217 kB)   GZipped PS   Order.

Halpern, D., Naire, S., Jensen, O.E. & Gaver, D.P. III Unsteady bubble propagation in a flexible-walled channel: predictions of a viscous stick-slip instability.J. Fluid Mech. 528, 53-86,2005. [abstract] [PDF] 

Evolution of gas bubbles in the circulation with application to the bends. Deep sea divers suffer from decompression sickness (DCS) when their rate of ascent to the surface is too quick. When the ambient pressure drops, inert gas bubbles are usually formed in blood vessels and tissues of divers. The evolution of a gas bubble in a straight tube filled with slowly moving fluid is studied by solving a coupled system of fluid-flow and gas transport equations.
 

Halpern, D., Jiang, Y. and Himm, J.F. Mathematical modeling of gas bubble evolution in a straight tube. J. Biomech. Eng. 121(5): 505, 1999.

Motion of red blood cells in the microcirculation


Halpern, D. and Secomb, T.W. The squeezing of red blood cells through capillaries with near-minimal diameters. J. Fluid Mech. 203: 381-400, 1989.
Halpern, D. and Secomb, T.W. Viscous motion of disc-shaped particles through parallel-sided channels with near-minimal widths. J. Fluid Mech. 231: 545-560, 1991.
Halpern, D. and Secomb, T.W. The squeezing of red blood cells through parallel-sided channels with near-minimal widths. J. Fluid Mech. 244: 307-322, 1992.

Gas dispersion

Elad, D., Halpern, D. and Grotberg, J.B. Gas bolus dispersion in volume-cycled tube flow. Part I: Theory. J. Applied Physiology 72: 312-320, 1992. [Abstract] [PDF]