Study of flow of crystals and deformable particles in a channel and the effective segregation of soft and hard particles

Abstract

Soft matters whose constituents are deformable are ubiquitous in nature especially in biological systems-including cells and their organelles-as well as in foams and emulsions. The capacity for deformation in these soft materials gives rise to a range of intriguing phenomena, such as glassy behavior without any size dispersity, cluster crystal formation, and re-entrant melting. Deformability also plays a crucial role in facilitating essential biological processes, such as the flow of blood through veins and arteries. In this work, we investigate assemblies of two-dimensional (2D) polymeric, non-overlapping rings, which mimic deformable particulates in 2D using extensive molecular dynamics simulations. The rings are confined in a rectangular channel with hard walls perpendicular to the flow direction, mimicking natural flow conditions. We analyze the flow properties of these deformable particle assemblies at two different stiffness values. To further asses the impact of deformability, we examine the same monodisperse system at higher densities for the stiffer rings, where deformation is necessary and a fluid layer emerges at the channel edges. Finally, we explore a mixture of rings with two distinct stiffnesses and observe effective segregation of soft and hard particles at small channel widths.

Figures (5)

• Figure 1: Flow characteristics in the hexatic phase at large stiffness, $k_\theta=150.0$.(a) A typical configuration of the rings placed in a crystalline order in two dimensions. The red rings are the mobile rings, while the blue ones are the immobile ones, forming the channel walls. We show only a part of the whole channel in y direction. (b) The velocity profile of the ring CoMs along the transverse direction to flow for different values of applied-stress. For large stresses a plug-like velocity profile emerges. (c) The standard-deviation of the velocities of the ring CoMs for each bin in transverse direction to flow for same value of applied stress (d) The magnitude of hexatic-order parameter across the channel for both flowing (red) and non-flowing (black) cases. Near unity value of the hexatic order parameter at the centre of the flow signifies strong hexatic ordering even during a flow at the centre during plug-flows. Inset shows the standard deviation of the same quantity across bins and there is a strong variation in ordering near walls signifying higher strain. (e) The plug-like and parabolic flow profiles for two different widths of channel at two different applied stresses. The axes are scaled appropriately. (f) The flow of mass with forcing for different values of channel widths
• Figure 2: The rotational characteristics in the hexatic phase.(a) A snippet of the channel when there is no flow through the channel with the Ring CoMs represented by points. The inset shows the averaged variation of $\omega_z$ in the transverse direction. (b) The same snippet when there is a flow through the channel. The inset clearly represents the change of rotational direction across the channel due to the flow. (c) The absolute value of $\omega_z$ variation across channel with ($\sigma_w\le0.0828$) and without flow ($\sigma_w\ge0.1036$). The inset shows the standard deviation of $\omega_z$ across the channel (d) $|\omega_z|$ across the channel for three different values of forcing are shown. For $\sigma_w\le0.0828$, the system does not flow, and one can clearly see the indication of jamming as $|\omega_z|$ decreases with increase in $\sigma_w$ which indicates less rotation of the rings with increase in forcing which indicates a more jammed state. The inset shows the standard deviation of $|\omega_z|$ across the channel width.
• Figure 3: The velocity profiles and jamming-unjamming transitions on application of stress(a) Typical velocity distribution along the flow direction with humps appearing at a +ve $v_y$ in flowing states, (b) Velocity distribution for $\sigma_w=0.104$. The mean of the distribution is greater than 0, and the distribution is skewed towards $+v_y$, (c) The phase-portrait of $\sigma_w$ vs w for $k_\theta=150.0$, the red dots represent jammed states and the green dots represent flowing states (d) The same portrait for ring-stiffness, $k_\theta=20.0$, at the same density. Note the reduction of stress-values in this case for the same channel widths.
• Figure 4: Travelling-waves in a dense system of mono-disperse ring polymers(a) Snapshot of a section containing mono-disperse stiff ($k_\theta=150.0$) rings in a channel. The red rings in the central region represent mobile rings, and the blue rings form the channel walls. (b) Variation in the asphericity of the rings across the channel. The system flows for $\sigma_w\ge0.6025$. For stresses larger than the flowing stress, the asphericity parameter starts to develop a U-shape characteristic with channel width, $\Delta x$ (see text). (c) The temporal velocity variation in a fixed-square patch. Note the near-periodic spikes in the y-velocity of the rings. (d) The fast Fourier Transform (FFT) of the time signals for three different values of $\sigma_w$ at which the periodic spikes (travelling waves) appear. The inset shows the near-linear increase in the frequency of the waves (taken from the dominant peak position in the FFT of the signals) with an increase in $\sigma_w$.
• Figure 5: Separation of soft and hard rings based on channel width(a) Snapshot of a section containing bi-disperse stiff ($k_\theta=20.0$ and $150.0$) rings with a channel width of $\approx130$. Hard rings are coloured red, and softer ones are coloured blue. The wall is represented as black rings. (b),(c) The soft rings get pushed towards the walls while the hard rings move towards the centre of the flow (blue curve). For comparison, without flow, the variation of the hard and soft ring density is almost constant (black curve). (d) Snapshot of the channel with wider width $\approx210$, (e),(f) Margination effect observed with softer rings clumping at the centre and harder rings clumping near the walls due to hydrodynamic lift effect (blue curves). The variation of the density of the soft and hard rings shows no such effect in the absence of flow. One point to note is that increased forcing ($\sigma_w$) doesn't change the intensity of this separation in a significant way in both these cases.