Models for the two-phase flow of concentrated suspensions

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behavior of the suspension flow including the appearance and evolution of an unyielded or jammed region

Localized Instabilities and Spinodal Decomposition in Driven Systems in the Presence of Elasticity

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material ux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a at moving front. The second instability is related to the Mullins- Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the ux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.Comment: 8 figures, 19 page

Thin film models for active gels

In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamcs in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Lesli-Erickson-Parodi theory. Analytic expression are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure.Comment: 33 pages, 3 figure

Dewetting rates of thin liquid films

We investigate the dewetting rates of thin liquid films using a lubrication model that describes the dewetting process of polymer melts on hydrophobized substrates. We study the effect of different boundary conditions at the liquid/solid interface, in particular, of the no-slip and the Navier slip boundary condition, and compare our numerical solutions for the no-slip and the slip dominated cases to available results that originate from scaling arguments, simplified flow assumptions and energy balances. We furthermore consider these issues for an extended lubrication model that includes nonlinear curvature

Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion

Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion

Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving exponentially large and small terms and multiple inner layers. In contrast to some results found in the literature, our analysis reveals that the interface motion is driven by a combination of surface diffusion flux proportional to the surface Laplacian of the interface curvature and an additional contribution from nonlinear, porous-medium type bulk diffusion, For higher degenerate mobilities, bulk diffusion is subdominant. The sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model.Comment: 27 pages, 2 figure

Migrant Entrepreneurs in Germany from 2005 to 2014 Their Extent, Economic Impact and Influence in Germany’s Länder. Bertelsmann Stiftung Inclusive Growth for Germany|5

The increasing gaps in income and wealth observed in developed economies around the globe are indicators of problems with inclusive growth. To be sure, the extent of these gaps varies across and within these economies, including Germany. The OECD has found that certain population groups benefit disproportionately from this group, while others are left behind (OECD 2015: 9 and 17). This is not a purely monetary phenomenon, but rather is closely related to the distribution of participation opportunities (e.g., with regard to working life) in a society

Patterns of Force: System Strength, Terrorism and Civil War

We jointly analyze the genesis of terrorism and civil war, providing a simple conceptual framework to explain why violent opposition groups choose distinct forms of violence (i.e., terrorism and open rebellion). We argue that the distinct modes of violent opposition are chosen by violent opposition groups in response to the strengths and weaknesses of the system they challenge. An empirical test of this hypothesis for 103 countries for the period of 1992 to 2004 indeed shows that the socio-economic strength and stability of a system is positively related to the likelihood of terrorism but negatively to incidences of more violent forms of violent opposition. We also show that poor conflict management (as a system weakness) positively impacts the likelihood incidences of more violent modes of violent opposition more likely. Furthermore, we find that system size is positively associated with all analyzed modes of violent opposition.terrorism, civil conflict, system strength

Self-consistent field theory for a polymer brush. Part II: The effective chemical potential

The most successful mean-field model to describe the collective behaviour of the large class of macromolecular polymers is the self-consistent field theory (SCFT). Still, even for the simple system of a grafted dry polymer brush, the mean-field equations have to be solved numerically. As one of very few alternatives that offer some analytical tractability the strong-stretching theory (SST) has led to explicit expressions for the effective chemical potential and consequently the free energy to promote an understanding of the underlying physics. Yet, a direct derivation of these analytical results from the SCFT model is still outstanding. In this study we present a systematic asymptotic theory based on matched asymtptotic expansions to obtain the effective chemical potential from the SCFT model for a dry polymer brush for large but finite stretching