It's Harder to Splash on Soft Solids.

Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses, we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young's moduli ≲100 kPa reduce splashing, in agreement with simple scaling arguments. Thus, materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.

A multiphase model for chemically- and mechanically- induced cell differentiation in a hollow fibre membrane bioreactor: minimising growth factor consumption.

We present a simplified two-dimensional model of fluid flow, solute transport, and cell distribution in a hollow fibre membrane bioreactor. We consider two cell populations, one undifferentiated and one differentiated, with differentiation stimulated either by growth factor alone, or by both growth factor and fluid shear stress. Two experimental configurations are considered, a 3-layer model in which the cells are seeded in a scaffold throughout the extracapillary space (ECS), and a 4-layer model in which the cell-scaffold construct occupies a layer surrounding the outside of the hollow fibre, only partially filling the ECS. Above this is a region of free-flowing fluid, referred to as the upper fluid layer. Following previous models by the authors (Pearson et al. in Math Med Biol, 2013, Biomech Model Mechanbiol 1-16, 2014a, we employ porous mixture theory to model the dynamics of, and interactions between, the cells, scaffold, and fluid in the cell-scaffold construct. We use this model to determine operating conditions (experiment end time, growth factor inlet concentration, and inlet fluid fluxes) which result in a required percentage of differentiated cells, as well as maximising the differentiated cell yield and minimising the consumption of expensive growth factor.

Global contraction or local growth, bleb shape depends on more than just cell structure.

When the plasma membrane of a cell locally delaminates from its actin cortex the membrane is pushed outwards due to the cell׳s internal fluid pressure. The resulting spherical protrusion is known as a bleb. A cell׳s ability to function correctly is highly dependent on the production of such protrusions with the correct size and shape. Here, we investigate the nucleation of large blebs from small, local neck regions. A mathematical model of a cell׳s membrane, cortex and interconnecting adhesions demonstrates that these three components are unable to capture experimentally observed bleb shapes without the addition of further assumptions. We have identified that combinations of global cortex contraction and localised membrane growth are the most promising methods for generating prototypical blebs. Currently, neither proposed mechanism has been fully tested experimentally and, thus, we propose experiments that will distinguish between the two methods of bleb production.

Multiphase modelling of the effect of fluid shear stress on cell yield and distribution in a hollow fibre membrane bioreactor.

We present a simplified two-dimensional model of fluid flow, nutrient transport and cell distribution in a hollow fibre membrane bioreactor, with the aim of exploring how fluid flow can be used to control the distribution and yield of a cell population which is sensitive to both fluid shear stress and nutrient concentration. The cells are seeded in a scaffold in a layer on top of the hollow fibre, only partially occupying the extracapillary space. Above this layer is a region of free-flowing fluid which we refer to as the upper fluid layer. The flow in the lumen and upper fluid layer is described by the Stokes equations, whilst the flow in the porous fibre membrane is assumed to follow Darcy's law. Porous mixture theory is used to model the dynamics of and interactions between the cells, scaffold and fluid in the cell-scaffold construct. The concentration of a limiting nutrient (e.g. oxygen) is governed by an advection-reaction-diffusion equation in each region. Through exploitation of the small aspect ratio of each region and asymptotic analysis, we derive a coupled system of partial differential equations for the cell volume fraction and nutrient concentration. We use this model to investigate the effect of mechanotransduction on the distribution and yield of the cell population, by considering cases in which cell proliferation is either enhanced or limited by fluid shear stress and by varying experimentally controllable parameters such as flow rate and cell-scaffold construct thickness.

Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in a hollow fibre membrane bioreactor.

A 2D model is developed for fluid flow, mass transport and cell distribution in a hollow fibre membrane bioreactor. The geometry of the modelling region is simplified by excluding the exit ports at either end and focusing on the upper half of the central section of the bioreactor. Cells are seeded on a porous scaffold throughout the extracapillary space (ECS), and fluid pumped through the bioreactor via the lumen inlet and/or exit ports. In the fibre lumen and porous fibre wall, flow is described using Stokes and Darcy governing equations, respectively, while in the ECS porous mixture theory is used to model the cells, culture medium and scaffold. Reaction-advection-diffusion equations govern the concentration of a solute of interest in each region. The governing equations are reduced by exploiting the small aspect ratio of the bioreactor. This yields a coupled system for the cell volume fraction, solute concentration and ECS water pressure which is solved numerically for a variety of experimentally relevant case studies. The model is used to identify different regimes of cell behaviour, and results indicate how the flow rate can be controlled experimentally to generate a uniform cell distribution under regimes relevant to nutrient- and/or chemotactic-driven behaviours.

Cellular blebs: pressure-driven, axisymmetric, membrane protrusions.

Blebs are cellular protrusions that are used by cells for multiple purposes including locomotion. A mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell model is proposed. The formation of a bleb is initiated by weakening the shell over a small region, and the deformation of the cellular membrane from the cortex is obtained during inflation. However, simply weakening the shell leads to an area increase of more than 4%, which is physically unrealistic. Thus, the model is extended to include a reconfiguration process that allows large blebs to form with small increases in area. It is observed that both geometric and biomechanical constraints are important in this process. In particular, it is shown that although blebs are driven by a pressure difference across the cellular membrane, it is not the limiting factor in determining bleb size.

Comparison of environmental scanning electron microscopy with high vacuum scanning electron microscopy as applied to the assessment of cell morphology.

The efficacy of conventional high vacuum scanning electron microscopy (SEM), environmental SEM (ESEM), and confocal laser scanning microscopy techniques in the assessment of cell-material interactions is compared. Specific attention is given to the application of these techniques in the assessment of the early morphological response of human osteoblast-like cells cultured on titanium dioxide. The processing of cells cultured for conventional high vacuum SEM leads to the loss of morphological features that are retained when using ESEM. The use of cytoskeletal labeling, viewed with confocal laser scanning microscopy, in conjunction with ESEM gives an indication of the changes to cell morphology as a consequence of incubation time in response to interactions at the biological/material interface.