Dendrites in the Small Undercooling Limit

Pelcé, Pierre

doi:10.1016/b978-0-08-092523-3.50035-6

Cited by 59 publications

(85 citation statements)

References 7 publications

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“…We have shown that the binder diffusion-mediated front motion is unstable to perturbations in its shape. It is interesting to note that, from a mathematical perspective, the instability studied in the present work is similar to other instabilities studied in nonequilibrium physics (22,23), where the interface motion is determined by solution of a partial differential equation (e.g., Euler or NavierStokes equation, Laplace equation, and heat equation). Examples include viscous fingering, crystal growth from a supercooled liquid, and propagation of flames.…”

Section: Concluding Observationsmentioning

confidence: 72%

“…Similarities and differences between dendritic, fingering, and tip-splitting instabilities observed in different physical systems are discussed in ref. 22 along with a large collection of preprints in each area. Most of the experimental and theoretical work in these systems focuses on instabilities during the propagation of elongated fronts (usually parabolic), in contrast to the instabilities of a circular front studied here.…”

Section: Concluding Observationsmentioning

confidence: 99%

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Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime

Shenoy

Freund

2005

Proc. Natl. Acad. Sci. U.S.A.

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We examine the process of expansion of a focal adhesion complex by which a biological membrane containing mobile binders adheres to a substrate with complementary binders. Attention is focused on the situation, common among living cells, in which the mean mobile binder density is insufficient to overcome generic resistance to close approach of the membrane to its substrate. For the membrane to adhere, binders must be recruited from adjacent regions to join an adhesion patch of density adequate for adhesion, thereby expanding the size of the patch. The specific configuration examined is the expansion of a circular adhesion zone for which diffusive binder transport driven by a chemical potential gradient is the mechanism of binder recruitment. An aspect of the process of particular interest is the stability of the circular shape of the expanding front. It is found that the adhesion front radius increases as ͌ t, where t is the time elapsed since nucleation, and that the circular shape becomes unstable under sinusoidal perturbations for radii large compared with the nucleation size, as observed in recent experiments.adhesion receptors ͉ biomembrane ͉ cell adhesion A dhesion of cells with other cells and surfaces plays an important role in processes such as cell migration, spreading, differentiation, and growth. The interactions that are responsible for cell adhesion include nonspecific electrostatic and repulsive steric forces as well as specific binding between receptors and ligands. In a series of early and important papers, Bell and coworkers (1-3) have developed quantitative models for cell adhesion based on equilibrium thermodynamics; their work shows that adhesion of cells involves a competition between the nonspecific repulsive forces due to the presence of glycocalyx and the specific bonding interactions between ligand-receptor pairs. The changes in shapes of adhered cells due to the deformation of the cell membrane and the role of ligand-receptor bond kinetics on attachment and separation of cells has been considered by Evans (4, 5) and Dembo and coworkers (6). Advances in experimental techniques based on atomic force microscopes, optical tweezers, and flexible transducers has led to considerable improvement in the understanding of ligand-receptor interactions that are responsible for cell adhesion (7-9).Recent experiments have shown that cell adhesion to surfaces which carry a large concentration of receptors that are complementary to the binders in the cell membrane results in the formation of localized regions of tight adhesion (sometimes referred to as focal adhesion complexes). Examples include spreading of blood platelets (10), vesicles (11,12), and different types of cells including fibroblasts, melanocytes, osteoblasts, lymphoblasts, and red blood cells (13-16) on substrates functionalized with receptors. On the basis of experiments on adhesion of a variety of cultured cells on arrays of patterned gold nanodots with a single bound integrin per dot, Arnold and coworkers (16) have proposed that the c...

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Section: Concluding Observationsmentioning

confidence: 72%

Section: Concluding Observationsmentioning

confidence: 99%

Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime

Shenoy

Freund

2005

Proc. Natl. Acad. Sci. U.S.A.

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“…Reviews by Saffman [38], Bensimon, Kadanoff, Liang, Shraiman, & Tang [.5], and Homsy [16] summarize the state of affairs as of the mid-eighties, while_some of the the more recent developments are reviewed by Pelce [31], Kessler, Koplik, & Levine [22], nowison [21], and Tanveer [42] from a range of different perspectives.…”

Section: Introductionmentioning

confidence: 99%

A Well-Posed Numerical Method to Track Isolated Conformal Map Singularities in Hele-Shaw Flow

Baker

Siegel

Tanveer

1995

Journal of Computational Physics

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“…[4][5][6][7][8] In particular, all the theoretical efforts to prescribe appropriate boundary conditions at the interface have considered the less viscous fluid as the invader. 9 In the opposite scenario, studied here, a more viscous fluid displaces a less viscous fluid, and the interfacial instability is driven by the density contrast between the two fluids in the presence of gravity 1,10 or a centrifugal force.…”

Section: Introductionmentioning

confidence: 99%

Radial displacement of a fluid annulus in a rotating Hele–Shaw cell

1999

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The radial displacement of a fluid annulus in a rotating circular Hele-Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy's law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interface motion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface, ␣ i , is obtained as a function of Ca.

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Dendrites in the Small Undercooling Limit

Cited by 59 publications

References 7 publications

Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime

Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime

A Well-Posed Numerical Method to Track Isolated Conformal Map Singularities in Hele-Shaw Flow

Radial displacement of a fluid annulus in a rotating Hele–Shaw cell

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