A novel numerical model to predict the morphological behavior of magnetic liquid marbles using coarse grained molecular dynamics concepts

© 2018 Author(s). Liquid marbles are liquid droplets coated with superhydrophobic powders whose morphology is governed by the gravitational and surface tension forces. Small liquid marbles take spherical shapes, while larger liquid marbles exhibit puddle shapes due to the dominance of gravitational forces. Liquid marbles coated with hydrophobic magnetic powders respond to an external magnetic field. This unique feature of magnetic liquid marbles is very attractive for digital microfluidics and drug delivery systems. Several experimental studies have reported the behavior of the liquid marbles. However, the complete behavior of liquid marbles under various environmental conditions is yet to be understood. Modeling techniques can be used to predict the properties and the behavior of the liquid marbles effectively and efficiently. A robust liquid marble model will inspire new experiments and provide new insights. This paper presents a novel numerical modeling technique to predict the morphology of magnetic liquid marbles based on coarse grained molecular dynamics concepts. The proposed model is employed to predict the changes in height of a magnetic liquid marble against its width and compared with the experimental data. The model predictions agree well with the experimental findings. Subsequently, the relationship between the morphology of a liquid marble with the properties of the liquid is investigated. Furthermore, the developed model is capable of simulating the reversible process of opening and closing of the magnetic liquid marble under the action of a magnetic force. The scaling analysis shows that the model predictions are consistent with the scaling laws. Finally, the proposed model is used to assess the compressibility of the liquid marbles. The proposed modeling approach has the potential to be a powerful tool to predict the behavior of magnetic liquid marbles serving as bioreactors

SPH-DEM approach to numerically simulate the deformation of three-dimensional RBCs in non-uniform capillaries

© 2016 The Author(s). Background: Blood continuously flows through the blood vessels in the human body. When blood flows through the smallest blood vessels, red blood cells (RBCs) in the blood exhibit various types of motion and deformed shapes. Computational modelling techniques can be used to successfully predict the behaviour of the RBCs in capillaries. In this study, we report the application of a meshfree particle approach to model and predict the motion and deformation of three-dimensional RBCs in capillaries. Methods: An elastic spring network based on the discrete element method (DEM) is employed to model the three-dimensional RBC membrane. The haemoglobin in the RBC and the plasma in the blood are modelled as smoothed particle hydrodynamics (SPH) particles. For validation purposes, the behaviour of a single RBC in a simple shear flow is examined and compared against experimental results. Then simulations are carried out to predict the behaviour of RBCs in a capillary; (i) the motion of five identical RBCs in a uniform capillary, (ii) the motion of five identical RBCs with different bending stiffness (K b ) values in a stenosed capillary, (iii) the motion of three RBCs in a narrow capillary. Finally five identical RBCs are employed to determine the critical diameter of a stenosed capillary. Results: Validation results showed a good agreement with less than 10% difference. From the above simulations, the following results are obtained; (i) RBCs exhibit different deformation behaviours due to the hydrodynamic interaction between them. (ii) Asymmetrical deformation behaviours of the RBCs are clearly observed when the bending stiffness (K b ) of the RBCs is changed. (iii) The model predicts the ability of the RBCs to squeeze through smaller blood vessels. Finally, from the simulations, the critical diameter of the stenosed section to stop the motion of blood flow is predicted. Conclusions: A three-dimensional spring network model based on DEM in combination with the SPH method is successfully used to model the motion and deformation of RBCs in capillaries. Simulation results reveal that the condition of blood flow stopping depends on the pressure gradient of the capillary and the severity of stenosis of the capillary. In addition, this model is capable of predicting the critical diameter which prevents motion of RBCs for different blood pressures

A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries

Red blood cells (RBCs) are the most common type of blood cells in the blood and 99 % of the blood cells are RBCs. During the circulation of blood in the cardiovascular network, RBCs squeeze through the tiny blood vessels (capillaries). They exhibit various types of motions and deformed shapes, when flowing through these capillaries with diameters varying between 5 and 10 µm. RBCs occupy about 45 % of the whole blood volume and the interaction between the RBCs directly influences on the motion and the deformation of the RBCs. However, most of the previous numerical studies have explored the motion and deformation of a single RBC when the interaction between RBCs has been neglected. In this study, motion and deformation of two 2D (two-dimensional) RBCs in capillaries are comprehensively explored using a coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM) model. In order to clearly model the interactions between RBCs, only two RBCs are considered in this study even though blood with RBCs is continuously flowing through the blood vessels. A spring network based on the DEM is employed to model the viscoelastic membrane of the RBC while the inside and outside fluid of RBC is modelled by SPH. The effect of the initial distance between two RBCs, membrane bending stiffness (Kb) of one RBC and undeformed diameter of one RBC on the motion and deformation of both RBCs in a uniform capillary is studied. Finally, the deformation behavior of two RBCs in a stenosed capillary is also examined. Simulation results reveal that the interaction between RBCs has significant influence on their motion and deformation

On the physics underlying longitudinal capillary recruitment

\u3cp\u3eNumerous researchers have found that capillary vessel haematocrit depends on the vasodilatory state of the arterioles. At rest, vessel haematocrit is down to 15 %, suggesting a red blood cell velocity three times higher than the plasma velocity. This finding is analysed in the context of present understanding of propulsion of red blood cells (RBCs) and plasma by means of the arteriovenous pressure gradient. Interfacial forces between the red blood cells and the plasma are proposed as a rational explanation of the observed red blood cell velocities. While the arteriovenous pressure gradient across the capillaries propels the red blood cell and the plasma jointly, interfacial forces along the red blood cell membrane can propel RBCs at the cost of the plasma. Different options are explored for the physical origin of these interfacial forces and oxygen gradients are found to be the most probable source.\u3c/p\u3

An Improved Coarse-Grained Model to Accurately Predict Red Blood Cell Morphology and Deformability

Accurate modelling of red blood cells (RBCs) has greater potential over experiments, as it can be more robust and significantly cheaper than equivalent experimental procedures to investigate the mechanical properties, rheology and dynamics of RBCs. The recent advances in numerical modelling techniques for RBC studies are reviewed in this study, and in particular, the discrete models for a triangulated surface to represent the in-plane stretching energy and out-of-plane bending energy of the RBC membrane are discussed. In addition, an improved RBC membrane model is presented based on coarse-grained (CG) technique that accurately and efficiently predicts the morphology and deformability of a RBC. The CG-RBC membrane model predicts the minimum energy configuration of the RBC from the competition between the in-plane stretching energy of the cytoskeleton and the out-of-plane bending energy of the lipid-bilayer under the given reference states of the cell surface area and volume. A quantitative evaluation of several cellular measurements including length, thickness and shape factor, is presented between the CG-RBC membrane model and three-dimensional (3D) confocal microscopy imaging generated RBC shapes at equivalent reference states. The CG-RBC membrane model predicts agreeable deformation characteristics of a healthy RBC with the analogous experimental observations corresponding to optical tweezers stretching deformations. The numerical approach presented here forms the foundation for investigations into RBC morphology and deformability under diverse shape-transforming scenarios, in vitro RBC storage, microvascular circulation and flow through microfluidic devices