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Howard Stone

Howard A. Stone

Donald R. Dixon '69 and Elizabeth W. Dixon Professor of Mechanical and Aerospace Engineering

B.S., University of California at Davis, 1982 Ph.D., Caltech, 1988

Room: D326 Engineering Quad
Phone: 609-258-9493
Email: hastone@princeton.edu

Webpage: Stone Fluid Dynamics Group

Honors and Awards

  • Distinguished Engineering Alumni Award, UC Davis, 2009
  • National Academy of Engineering, 2009
  • Southwest Mechanics Lecture, 2009
  • Brooke Benjamin Lecture in Fluid Mechanics, Oxford University, 2008
  • G.K. Batchelor Prize in Fluid Mechanics, 2008
  • Fellow, Division of Fluid Dynamics of the American Physical Society, 2003
  • Midwest Mechanics Lecturer, 2002-3
  • Joseph R. Levenson Memorial Award, 1994
  • Phi Beta Kappa teaching Prize, 1994

Concurrent University Appointments

  • Associated Faculty, Department of Chemical Engineering

Publications

Research Areas

Research Interests

| Fluid Mechanics |

Topic: Imbibition of wetting liquids into media of variable permeability
Area:
Porous media
Researchers: Mathilde Reyssat, Laurent Courbin, Laetitia Sangne, Ernst van Nierop and Howard Stone
Overview:
When surface wetting drives liquids to invade porous media or microstructured materials with uniform channels, the penetration distance is known to increase as the square root of time. We demonstrated, experimentally and theoretically, that shape variations of the channel, in the flow direction, modify this “diffusive” response. We performed experiments with conical tubes which clearly showed the theoretical limits (figure(1)) [1].

We then studied imbibition of a wetting fluid into layers of packed beads and examined how variations of permeability in the flow direction affect the dynamics of imbibition. In the case of systems made of two distinct layers, we showed that the imbibition dynamics exhibit three regimes including diffusive-like imbibition as well as an unusual constant speed imbibition, which can be fine-tuned by adjusting the bead diameters and the length of the initial layer (figure (2)). We also performed experiments with gradients of permeability by ordering layers of beads of increasing (or decreasing) sizes in a tube. We used a continuum description to explain the results from the discrete experimental systems. In all cases, we showed that analytical models based on Darcy's equation are in excellent agreement with the experiments [2].

   
 

(1) In the case of a conical tube of opening angle and opening radius , two different regimes of imbibition are observed [1]. At short time, we recovered the classical diffusive response, whereas at long time, a different power-law occurs, which exponent is uniquely connected to the details of the geometry.

(2) In the case of a systems made of two distinct layers of beads, it is possible to observe a regime of constant speed of imbibition, which can be tuned by choosing the diameters of the small and the large beads d and D, the length of the initial layer and the characteristic of the fluid: its surface tension and its viscosity .

 

Publications:
[1] M. Reyssat, L. Courbin, E. Reyssat, H. A. Stone. "Imbibition in geometries with axial variations". J. Fluid Mech. 615, 335-344 (2008). [pdf]
[2] M. Reyssat, L. Y. Sangne, E. A. van Nierop, H. A. Stone. "Imbibition in layered systems of packed beads". EPL. In Press (2009).

 

| Biophysical Systems |

Publications:

| Colloidal Phenomena |

Topic: Shear-induced diffusion of particles
Area: Colloidal Dispersion
Researchers: Roberto Rusconi and Howard A. Stone
Overview:
Shear-induced diffusion (SID) is a phenomenon which occurs in suspensions undergoing shear when effectively diffusive motions of the particles, due to the hydrodynamic interactions between them, are much greater than Brownian diffusion. Most of the literature on SID over the past 20 years has focused on suspensions of noncolloidal spheres, whereas experimental measurements has been mainly performed in circular Couette flow. We instead exploited the recent developments of microfluidic technologies to investigate the lateral diffusion in dilute suspensions of micron-sized nonspherical particles. In particular, we used an H-sensor, a well-established device typically adopted to make diagnostic determinations of analyte concentrations or diffusion-based extraction, to measure the transverse migration of Montmorillonite clay disk-shaped particles in very long (up to 50 cm) but thin channels (typical height of about 10 microns). Such a microfluidic setup presents several advantages, as, for instance, the possibility to achieve very high and controlled shear rates and avoiding unwanted convection effects, which allow us to obtain quantitative and reproducible results over a wide range of shear rates and concentrations. The results we obtained show high SID values, about 2 orders of magnitude larger than those reported for suspensions of spheres at low fraction (less than 1%). Moreover, we find a linear dependence of the collective diffusion coefficient with the average shear rate and the particle concentration. However, since axisymmetric particles suspended in shear flows undergo tumbling motions, known as Jeffery orbits, with angular velocity proportional to the shear rate, the effective volume spanned by the particles is much larger than the real one. Indeed, these data are in good agreement with previous experimental and theoretical results for spheres when rescaled with the particle number density.

 
a) Schematic of the microfluidic device used in the experiments. (b) Velocity distribution for a pressure-driven flow through a rectangular cross section in the case of an aspect ratio between the height and the width of the channel of 0.1 (not to scale). (c)–(f) Bright-field microscopy images of a 13 micron-high channel (the scale bar is 20 microns) at (c),(e) the inlet and (d),(f ) the outlet, for suspensions of (c),(d) polystyrene spheres and (e),(f ) clay particles: whereas the spheres do not migrate, the platelike particles are dispersed throughout the whole width of the channel. (g) SEM images of the clay particles (the scale bar is 1 micron).
 
Main figure: Linear dependence of the dimensionless SID coefficient on the volume fraction. Each point has been obtained from the linear fit with the shear rate for all the collected data with different channel heights. Upper left-hand inset: Semilogarithmic plot of the same data in comparison with (dotted line) the function used to fit experimental data in dilute dispersions of spheres (Zarraga and Leighton, 2002). Lower right-hand inset: Our data (d) as a function of the particle number density in comparison with experimental (squares - Phillips et al., 1992) and theoretical (triangles - Leshansky et al., 2008) results for collective diffusion in concentrated suspensions of spheres.

Publications:
R. Rusconi and H. A. Stone, "Shear-Induced Diffusion of Platelike Particles in Microchannels," Physical Review Letters 101 (25) (2008). [pdf]


| Applications of Microfluidic Systems |

Publications:

| Other Research |

Publications: