A mesoscopic model for microscale hydrodynamics and interfacial phenomena: Slip, films, and contact angle hysteresis

We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo- potentials employed for fluid-solid interactions are composed of a repulsive core and an attractive tail that can be independently adjusted. This enables effective modification of the functional form of the disjoining pressure so that one can vary the static and dynamic hysteresis on surfaces that exhibit the same equilibrium contact angle. The modeled solid-fluid interface is diffuse, represented by a wall probability function which ultimately controls the momentum exchange between solid and fluid phases. This approach allows us to effectively vary the slip length for a given wettability (i.e. the static contact angle) of the solid substrate

Effect of Intrinsic Noise on the Phenotype of Cell Populations Featuring Solution Multiplicity: An Artificial lac Operon Network Paradigm.

Heterogeneity in cell populations originates from two fundamentally different sources: the uneven distribution of intracellular content during cell division, and the stochastic fluctuations of regulatory molecules existing in small amounts. Discrete stochastic models can incorporate both sources of cell heterogeneity with sufficient accuracy in the description of an isogenic cell population; however, they lack efficiency when a systems level analysis is required, due to substantial computational requirements. In this work, we study the effect of cell heterogeneity in the behaviour of isogenic cell populations carrying the genetic network of lac operon, which exhibits solution multiplicity over a wide range of extracellular conditions. For such systems, the strategy of performing solely direct temporal solutions is a prohibitive task, since a large ensemble of initial states needs to be tested in order to drive the system--through long time simulations--to possible co-existing steady state solutions. We implement a multiscale computational framework, the so-called "equation-free" methodology, which enables the performance of numerical tasks, such as the computation of coarse steady state solutions and coarse bifurcation analysis. Dynamically stable and unstable solutions are computed and the effect of intrinsic noise on the range of bistability is efficiently investigated. The results are compared with the homogeneous model, which neglects all sources of heterogeneity, with the deterministic cell population balance model, as well as with a stochastic model neglecting the heterogeneity originating from intrinsic noise effects. We show that when the effect of intrinsic source of heterogeneity is intensified, the bistability range shifts towards higher extracellular inducer concentration values

Mesoscopic model for microscale hydrodynamics and interfacial phenomena: slip, films, and contact-angle hysteresis.

We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo-potentials employed for fluid-solid interactions are composed of a repulsive core and an attractive tail that can be independently adjusted. This enables effective modification of the functional form of the disjoining pressure so that one can vary the static and dynamic hysteresis on surfaces that exhibit the same equilibrium contact angle. The modeled fluid-solid interface is diffuse, represented by a wall probability function that ultimately controls the momentum exchange between solid and fluid phases. This approach allows us to effectively vary the slip length for a given wettability (i.e., a given static contact angle) of the solid substrate

Effect of the sharpness division parameter.

<p>Effect of the sharpness division parameter, <i>m</i>, on the average expression of <i>lacY</i> gene steady state. (a) CNMC simulations of 10,000 cells with <i>K</i> = 500 and <i>y</i>* = 50. <i>Lines with full squares</i> correspond to <i>m</i> = 1, <i>lines with full circles</i> to <i>m</i> = 2 and <i>lines with full triangles</i> to the largest division rate, <i>m</i> = 3. (b) Comparison between the CNMC model with <i>m</i> = 3 (<i>lines with full triangles</i>) with the DCPB model (<i>black lines (solid and dashed)</i>) and the CNMC model neglecting intrinsic noise effects (<i>lines with open circles</i>). Parameter set values: <i>f</i> = 0.5, <i>π</i> = 0.03 and <i>κ</i> = 0.05.</p

The coarse time-stepper.

<p>A schematic of the coarse time-stepper for the model of an isogenic cell population simulated by the CNMC algorithm.</p