198 research outputs found
Characteristic Angles in the Wetting of an Angular Region: Surface Shape
The shape of a liquid surface bounded by an acute or obtuse planar angular
sector is considered by using classical analysis methods. For acute angular
sectors the two principal curvatures are of the order of the (fixed) mean
curvature. But for obtuse sectors, the principal curvatures both diverge as the
vertex is approached. The power-law divergence becomes stronger with increasing
opening angle. Possible implications of this contrasting behavior are
suggested.Comment: 19 pages, 9 figures, LaTeX; submitted to The European Physics Journal
E; v2: Introduction was revised (a number of references added), minor changes
to the main part (mostly typos), former Implications subsection was almost
entirely rewritten and is now called Experimental Realizations (experimental
results and two figures added); v3: Introduction was slightly modified, four
references added; v4: Title was modified, section Calculation was
significantly modified (subsections Bounary Problem and Horizontal Solution
almost entirely rewritten, minor changes to the other subsections),
subsection Curvature in section Discussion was revised, one reference adde
Deposit Growth in the Wetting of an Angular Region with Uniform Evaporation
Solvent loss due to evaporation in a drying drop can drive capillary flows
and solute migration. The flow is controlled by the evaporation profile and the
geometry of the drop. We predict the flow and solute migration near a sharp
corner of the perimeter under the conditions of uniform evaporation. This
extends the study of Ref. 6, which considered a singular evaporation profile,
characteristic of a dry surrounding surface. We find the rate of the deposit
growth along contact lines in early and intermediate time regimes. Compared to
the dry-surface evaporation profile of Ref. 6, uniform evaporation yields more
singular deposition in the early time regime, and nearly uniform deposition
profile is obtained for a wide range of opening angles in the intermediate time
regime. Uniform evaporation also shows a more pronounced contrast between acute
opening angles and obtuse opening angles.Comment: 12 figures, submitted to Physical Review
Effects of Kinks on DNA Elasticity
We study the elastic response of a worm-like polymer chain with reversible
kink-like structural defects. This is a generic model for (a) the
double-stranded DNA with sharp bends induced by binding of certain proteins,
and (b) effects of trans-gauche rotations in the backbone of the
single-stranded DNA. The problem is solved both analytically and numerically by
generalizing the well-known analogy to the Quantum Rotator. In the small
stretching force regime, we find that the persistence length is renormalized
due to the presence of the kinks. In the opposite regime, the response to the
strong stretching is determined solely by the bare persistence length with
exponential corrections due to the ``ideal gas of kinks''. This high-force
behavior changes significantly in the limit of high bending rigidity of the
chain. In that case, the leading corrections to the mechanical response are
likely to be due to the formation of multi-kink structures, such as kink pairs.Comment: v1: 16 pages, 7 figures, LaTeX; submitted to Physical Review E; v2: a
new subsection on soft kinks added to section Theory, sections Introduction
and Conclusions expanded, references added, other minor changes; v3: a
reference adde
Effects of Sequence Disorder on DNA Looping and Cyclization
Effects of sequence disorder on looping and cyclization of the
double-stranded DNA are studied theoretically. Both random intrinsic curvature
and inhomogeneous bending rigidity are found to result in a remarkably wide
distribution of cyclization probabilities. For short DNA segments, the range of
the distribution reaches several orders of magnitude for even completely random
sequences. The ensemble averaged values of the cyclization probability are also
calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a
substantially revised version; v3: references added, conclusions expanded,
minor editorial corrections to the text; v4: a substantially revised and
expanded version (total number of pages doubled); v5: new Figure 4, captions
expanded, minor editorial improvements to the tex
Characteristic Angles in the Wetting of an Angular Region: Deposit Growth
As was shown in an earlier paper [1], solids dispersed in a drying drop
migrate to the (pinned) contact line. This migration is caused by outward flows
driven by the loss of the solvent due to evaporation and by geometrical
constraint that the drop maintains an equilibrium surface shape with a fixed
boundary. Here, in continuation of our earlier paper [2], we theoretically
investigate the evaporation rate, the flow field and the rate of growth of the
deposit patterns in a drop over an angular sector on a plane substrate.
Asymptotic power laws near the vertex (as distance to the vertex goes to zero)
are obtained. A hydrodynamic model of fluid flow near the singularity of the
vertex is developed and the velocity field is obtained. The rate of the deposit
growth near the contact line is found in two time regimes. The deposited mass
falls off as a weak power Gamma of distance close to the vertex and as a
stronger power Beta of distance further from the vertex. The power Gamma
depends only slightly on the opening angle Alpha and stays between roughly -1/3
and 0. The power Beta varies from -1 to 0 as the opening angle increases from 0
to 180 degrees. At a given distance from the vertex, the deposited mass grows
faster and faster with time, with the greatest increase in the growth rate
occurring at the early stages of the drying process.Comment: v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2:
minor additions to Abstract and Introductio
Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit
A model accounting for finite spatial dimensions of the deposit patterns in
the evaporating sessile drops of colloidal solution on a plane substrate is
proposed. The model is based on the assumption that the solute particles occupy
finite volume and hence these dimensions are of the steric origin. Within this
model, the geometrical characteristics of the deposition patterns are found as
functions of the initial concentration of the solute, the initial geometry of
the drop, and the time elapsed from the beginning of the drying process. The
model is solved analytically for small initial concentrations of the solute and
numerically for arbitrary initial concentrations of the solute. The agreement
between our theoretical results and the experimental data is demonstrated, and
it is shown that the observed dependence of the deposit dimensions on the
experimental parameters can indeed be attributed to the finite dimensions of
the solute particles. These results are universal and do not depend on any free
or fitting parameters; they are important for understanding the evaporative
deposition and may be useful for creating controlled deposition patterns.Comment: 34 pages, 14 figures, LaTeX; submitted to Physical Review
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