Electromigration affected sublimation is a complicated phenomenon, involving surface transport coupled to a process of atom exchange between the two-dimensional gas of adatoms and the crystal phase. The case of intensive exchange is theoretically treated and equations of step motion are derived for the case of “nontransparent” steps (kinetics with local conservation of adatoms). The numerical integration of these equations manifests step bunching (a formation of step density waves) at step-down direction of the electromigration of adatoms. We studied some properties of the step density waves: the amplitude (the maximum slope of the bunch) and its dependence on the number of steps in the bunch, the kinematic wave velocity and the dynamic interaction of waves of different amplitudes. The central result of this work is the dependence of the minimum interstep distance (in the steady state shape of the bunch) on the model parameters. This dependence, extracted from numerical study, is presented in terms of scaling laws $l_{\min }\sim N^{-r}{\mathrm{}(A/F)\mathrm{}}^q$, where $N$ is the number of steps in the bunch, $A$ is the magnitude of step-step repulsion, and $F$ is the force, inducing electromigration of the adatoms. Both scaling exponents $r$ and $q$ depend on the power $n$ in the step-step repulsion dependence on the interstep distance ${(U=A/l}^n)$ and, therefore, they are a key to the problem of experimental evaluation of $n$. A striking result of this model is the constant value of $l_{\min }$ in a wide range of values of the average diffusion distance ${\lambda }_s.$ Thus one cannot relate the temperature dependence of $l_{\min }$ to the temperature dependence of ${\lambda }_s.$ Numerical analysis of the dynamics of steps at a crystal surface of small misorientation angle reveals two types of dynamic interaction of bunches of steps: “bunch size exchange” and “effective coalescence.” The former type of interaction is rather interesting — a smaller (and faster) bunch approaches a larger one and they travel together until the initially larger bunch achieves (by losing steps) a size, smaller than the size of its partner, and runs away of it.

We propose a unified treatment of the step bunching instability during epitaxial growth. The scaling properties of the self-organized surface pattern are shown to depend on a single parameter, the leading power in the expansion of the biased diffusion current in powers of the local surface slope. We demonstrate the existence of universality classes for the self-organized patterning appearing in models and experiments.

The surface properties of human meibomian lipids (MGS), the major constituent of the tear film (TF) lipid layer, are of key importance for TF stability. The dynamic interfacial properties of films by MGS from normal eyes (nMGS) and eyes with meibomian gland dysfunction (dMGS) were studied using a Langmuir surface balance. The behavior of the samples during dynamic area changes was evaluated by surface pressure–area isotherms and isocycles. The surface dilatational rheology of the films was examined in the frequency range 10⁻⁵ to 1 Hz by the stress-relaxation method. A significant difference was found, with dMGS showing slow viscosity-dominated relaxation at 10⁻⁴ to 10⁻³ Hz, whereas nMGS remained predominantly elastic over the whole range. A Cole–Cole plot revealed two characteristic processes contributing to the relaxation, fast (on the scale of characteristic time τ < 5 s) and slow (τ > 100 s), the latter prevailing in dMGS films. Brewster angle microscopy revealed better spreading of nMGS at the air–water interface, whereas dMGS layers were non-uniform and patchy. The distinctions in the interfacial properties of the films in vitro correlated with the accelerated degradation of meibum layer pattern at the air–tear interface and with the decreased stability of TF in vivo. These results, and also recent findings on the modest capability of meibum to suppress the evaporation of the aqueous subphase, suggest the need for a re-evaluation of the role of MGS. The probable key function of meibomian lipids might be to form viscoelastic films capable of opposing dilation of the air–tear interface. The impact of temperature on the meibum surface properties is discussed in terms of its possible effect on the normal structure of the film.

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length $d_{+}=D_s∕K_{+}$ is larger than the average distance $l$ between the steps on the vicinal surface; here $D_s$ is the surface diffusion coefficient and $K_{+}$ is the step kinetic coefficient. In the opposite limit $d_{+}⪡l$ the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the form $L\sim H^{\alpha }$, $l_{\min }\sim H^{-\gamma }$ between the width $L$, the height $H$, and the minimum interstep distance $l_{\min }$ of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for the case $d_{+}⪢l$. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through comparison with numerical simulations of the discrete step equations, we establish the value $\gamma =2∕(n+1)$ for the scaling exponent of $l_{\min }$ in terms of the exponent $n$ of the repulsive step-step interaction, and provide an exact expression for the prefactor in terms of the energetic and kinetic parameters of the system. For the bunch width $L$ we observe significant deviations from the expected scaling with exponent $\gamma =1-1∕\alpha$, which are attributed to the pronounced asymmetry between the leading and the trailing edges of the bunch, and the fact that bunches move. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment∕detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

Squalene (SQ) possesses a wide range of pharmacological activities (antioxidant, drug carrier, detoxifier, hydrating, emollient) that can be of benefit to the ocular surface. It can come in contact with human meibum (hMGS; the most abundant component of the tear film lipid layer) as an endogenous tear lipid or from exogenous sources as eyelid sebum or pharmaceuticals. The aims of this study were to determine (i) if SQ is in tear lipids and (ii) its influence on the surface properties of hMGS films. Heteronuclear single quantum correlation NMR confirmed 7 mol % SQ in Schirmer’s strips extracts. The properties of SQ/hMGS pseudo-binary films at the air/water interface were studied with Langmuir surface balance, stress-relaxation dilatational rheology and Brewster angle microscopy. SQ does not possess surfactant properties. When mixed with hMGS squalene (i) localized over the layers’ thinner regions and (ii) did not affect the film pressure at high compression. Therefore, tear SQ is unlikely to instigate dry eye, and SQ can be used as a safe and “inert” ingredient in formulations to protect against dry eye. The layering of SQ over the thinner film regions in addition to its pharmacological properties could contribute to the protection of the ocular surface.