R.J.J. Jongschaap

Bio: R.J.J. Jongschaap is an academic researcher. The author has contributed to research in topics: Transient (oscillation). The author has an hindex of 1, co-authored 1 publications receiving 16 citations.

Derivation of the Marrucci model from transient-network theory

Abstract: Many theories about the rheological behaviour of melts and concentrated solutions of high molecular weight polymers are based upon the transientnetwork model, originally developed by Green and Tobolsky [l], Lodge [2], and Yamamoto [ 31. Among these theories a model proposed by Marrucci and coworkers [4,5] turns out to be rather successful [6-111. The basic equations of this model, as formulated in ref. [ 51, are:

A new microstructure-based constitutive model for human blood

Abstract: A new constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. Each erythrocyte is represented by a dumbbell. The use of a linear spring law in the dumbbells leads to a multi-mode generalized Maxwell equation for the elastic stress and both the relaxation times and viscosities are functions of a time-dependent structure variable. An approximate constitutive equation is derived by choosing a single mode corresponding to the cell aggregate size where the largest number of cells are to be found. This size is identified in the case of steady flows. The model exhibits shear-thinning, viscoelasticity and thixotropy and these are clearly related to the microstructural properties of the fluid. Agreement with the experimental data of Bureau et al. [M. Bureau, J.C. Healy, D. Bourgoin, M. Joly, Rheological hysteresis of blood at low shear rate, Biorheology 17 (1980) 191–203] in the case of a simple triangular step shear rate flow is convincing.

Rheological modelling of complex fluids: IV: Thixotropic and “thixoelastic” behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles

Abstract: Structural rheological modelling of complex fluids developed in Part I of this series and applied to shear thickening systems (Parts II & III), is now used to improve such a modelling in the case of unsteady behaviour, that is, in the presence of thixotropy. The model is based on an explicit viscosity-structure relationship, η ( S ), between the viscosity and a structural variable S. Under unsteady conditions, characterized by a reduced shear, Γ ( t ), shear-induced structural change obeys a kinetic equation (through shear-dependent relaxation times). The general solution of this equation is a time-dependent function, S ( t ) ≡ S [ t, Γ ( t )]. Thixotropy is automatically modelled by introducing S [ t, Γ ( t )] into η ( S ) which leads directly to η ( t ) ≡ η [ t, Γ ( t )], without the need for any additional assumptions in the model. Moreover, whilst observation of linear elasticity requires small enough deformation i.e. no change in the structure, larger deformations cause structural buildup/breakdown, i.e. the presence of thixotropy, and hence leads to a special case of non-linear viscoelasticity that can be called “thixoelasticity”. Predictions of a modified Maxwell equation, obtained by using the above-defined η ( S ) and assuming G = G 0 S (where G 0 is the shear modulus in the resting state defined by S = 1) are discussed in the case of start-up and relaxation tests. Similarly modified Maxwell-Jeffreys and Burger equations are used to predict creep tests and hysteresis loops. Discussion of model predictions Maynly concerns (i) effects of varying model variables or/and applied shear rate conditions and (ii) comparison with some experimental data.

Theory of shear-induced crystallization of polymer melts

Abstract: In the presented model elements of polymer melt rheology and polymer crystallization kinetics are combined. In particular, the proneness of the melt to the special type of crystallization which is characteristic for shear treatment is supposed to emerge only gradually during shear flow. Following Avrami's early ideas on crystal growth, an induction time is introduced. In principle, the model can be applied to any flow and temperature history. The special case of isothermal flow at constant shear rate is covered in greater detail: A favorable comparison is made with experimental results, as published by Lagasse and Maxwell [10].

Constitutive equations based on the transient network concept

Abstract: A consitutive theory for polymetric liquids based on the transient network concept is developed, following Wiegel and Jongschaap. The Phan-Thien-Tanner equation is shown to follow from the general theory with two critical assumption, one of these is quasi-equilibrium of the internal structure, which preludes consistency of application in ”fast flows“. The Marrucci model can be made consistent with the general format with a small change in the kinetic equation that can be deduced from asymptotic behaviour and leaves the steady viscometric behavior unchanged. The simplest genaral formulation requires the linear viscoelastic spectrum and two parameters; the latter cannot be determined uniquely from steady viscometric flow data.

A numerical stochastic approach to network theories of polymeric fluids

Abstract: A new numerical approach is presented to exactly solve the convection equation arising in network theories. The method is based on a direct stochastic interpretation of the convection equation. We show that with this approach models can be studied extensively which are not solvable analytically. It turns out that a conceptually simple approach to network theories predicts a qualitatively satisfying rheological behavior.