Colloid particle transport in a microcapillary: NMR study of particle and suspending fluid dynamics
Introduction
The transport dynamics of colloid particles (diameter (2a): 1 nm to 10 μm (Russel, 1981)) suspended in a liquid, is important in many industrial and environmental processes and has therefore received significant attention in the scientific literature (Brady and Vicic, 1995, Vermant and Solomon, 2005). Precise manipulation of the hydrodynamic interaction between particles is important for operation of microfluidic devices (Stone et al., 2004); shear induced migration of the suspended particles being particularly important (Reddig and Stark, 2013). Microfluidic applications of shear induced migration include generation and manipulation of emulsion droplets (Christopher and Anna, 2007), polystyrene microspheres (Sochol et al., 2011) and biological cells (Yun et al., 2013). Flow induced migration gives rise to dynamical patterns which have been observed in a range of systems. These include coiling of semi-flexible polymers (Chelakkot et al., 2012, Harasim et al., 2013), anomalous crystal phonon modes (Beatus et al., 2007), collective dynamics (Janssen et al., 2012), inertial migration (Di Carlo et al., 2009) and shear induced migration (Semwogerere et al., 2007, Snijkers et al., 2013).
An important example is the Segre–Silberberg effect caused by inertial forces acting on the particles in non-zero Reynolds number (Re) flow (Leal, 1980) where rigid spheres assemble on an annulus at approximately 0.6 of the internal radii of a circular tube during laminar flow (Segre and Silberberg, 1962). When non-zero Re bounded shear flow is introduced to sphere trajectories a rich class of solutions is observed (Subramanian and Koch, 2006), while at non-inertial conditions a threshold for irreversibility and chaos is observed in many body particle suspensions where time reversible equations of motion should govern (Pine et al., 2005).
Forces which determine the particle dynamics are hydrodynamic, Brownian and interparticle (Brady, 1993). The hydrodynamic forces are due to the presence of fluid between particles which allows the propagation of particle interactions including those due to the application of a linear external shear field. Brownian forces are due to the stochastic motion of the suspending fluid molecules impacting the suspended particle. In colloidal suspensions, the particles in a suspending fluid are small enough that Brownian forces affect their dynamics (Brown, 1828, Einstein, 1906, Smoluchowski, 1906). Interparticle forces can be divided into those due to the excluded volume repulsion, electrostatic interaction, van der Waals forces (short-range and attractive), entropic forces and steric forces (either steric repulsion or attractive depletion) (Russel et al., 1989). If a colloidal suspension is unstable it can flocculate, i.e. form aggregates of colloidal particles due to the removal of the electrostatic barrier separating particles, due to addition of flocculants (charged polymer), depletants (non-adsorbed polymers) or colloid deformation (Russel et al., 1989). Mono-disperse hard-sphere colloidal suspensions are the simplest type of colloidal suspension, where the particles interact through hydrodynamic and Brownian forces, and can be fully characterized by the volume fraction (ϕ) and the particle Péclet number (Pep) (Brady and Vicic, 1995). They can also be used to form the building blocks for understanding more complex colloid suspensions (Brady, 1996, Yurkovetsky and Morris, 2008).
Detailed experimental, analytical and simulation studies have been conducted to investigate the behavior of hard sphere colloidal suspensions over the full range of volume fraction (ϕ) from dilute to close packed and for Pep numbers encompassing the rheological behavior from weak flow conditions (Pep ∼1) to strong flow conditions (Pep>>1) (Bergenholtz et al., 2002, Foss and Brady, 2000). In this paper, we focus on the dynamics in the shear flow dominated regime (Pep>>1) for a =0.22 hard sphere suspension (Wassenius et al., 2003), where Pep and are defined as:
Here is the viscosity of the suspending fluid, is the averaged shear rate, a is the mean radius of the colloidal spheres, kB is the Boltzmann constant, T is the absolute temperature and n is the number density. The averaged shear rate is defined as , where is the maximum velocity in the μ-capillary and R is the radius of the μ-capillary. Additional dimensionless numbers used to characterise the flow are the tube Péclet number (Pet), particle Reynolds number (Rep) and the tube Reynolds number (Ret):
In which is the average velocity in the capillary, Dw is the diffusion coefficient of the suspending fluid and ρ is the density of the suspending fluid in the capillary.
In this study pulsed gradient spin echo (PGSE) nuclear magnetic resonance (NMR) techniques are used to independently measure the transport properties of the suspending fluid phase and particle phase by using oil filled hard sphere core shell particles. These NMR “active” particles have previously been studied with NMR to measure the diffusion characteristics of the internal oil (Wassenius et al., 2003) and velocimetry (Wassenius and Callaghan, 2004, Wassenius and Callaghan, 2005). They have been used to demonstrate irreversibility of particle motion at dilute concentrations (Brown et al., 2007), shear induced migration in capillaries (Brown et al., 2009) and hydrodynamic dispersion in microcapillaries (Fridjonsson et al., 2014b). They have also been used to study deposition in porous media (Fridjonsson et al., 2014a), flow partitioning in bifurcations (Fridjonsson et al., 2011), effects of oscillatory flow (Evertz et al., 2012) and transport dynamics in open cell polymer foams (Brosten et al., 2010).
The stochastic motion of colloidal suspension particles can be characterized by the Stokes–Einstein–Sutherland diffusivity,
Ideal hard-sphere colloids have short-range repulsive interparticle interactions and no long-range electrostatic interactions (Antl et al., 1986). To achieve hard-sphere colloidal interactions in experiments it is almost always required that the surface of the colloidal spheres be manipulated (Antl et al., 1986) and that some charge be present on the surface (Wassenius et al., 2003). For the colloidal particles used in this work the particles are charge stabilized by adding polyvinyl alcohol (PVA) to the suspending fluid which absorbs on the particle surface and generates short range repulsive forces. Further information on colloidal dynamics has been reviewed elsewhere (Russel et al., 1989, Stickel and Powell, 2005, Vermant and Solomon, 2005).
Section snippets
Materials and methods
NMR experiments were conducted using a Bruker 250 MHz superconducting magnet, a Mirco5 probe base and magnetic field gradient coil with gmax=1.7 T/m in three orthogonal (x, y, z) gradient directions. The flow setup is placed inside a 5 mm radiofrequency (rf) coil at a distance >2000R from the beginning of the microcapillary section of the flow setup so that all experiments are conducted on the steady state regime of colloidal migration due to shear induced migration (Semwogerere et al., 2007). To
Results and discussion
Fig. 3 shows a series of propagators obtained for water flowing at Q=0.25 mL/h for Δ=25, 50, 150, 250 and 500 ms with displacement measured in the axial-flow (z) direction. These show a narrowing in the probability distribution of displacement with increasing observation time Δ. The initial propagator (Δ=25 ms) has the shape of a Heaviside-hat function convoluted with a Gaussian function, corresponding to Poiseuille flow combined with diffusion (Codd et al. 1999). As displacement time increases (Δ
Conclusions
This work has demonstrated a useful experimental framework for the simultaneous interrogation of shear rheology of the suspending fluid and particle phases of colloidal suspensions inside a microcapillary using dynamic NMR techniques. The dynamic behavior of the suspending fluid has been shown to carry within it information about the structure of the colloidal particle ensembles on the time scales investigated (Δ=25 ms→250 ms) providing detailed experimental data for further investigation and
Acknowledgments
JDS acknowledges funding from NSF CAREER Award CTS-0348076. The M.J. Murdock. Charitable Trust and NSF MRI program provided equipment funding. EOF acknowledges support from University of Western Australia (UWA) and Research Collaboration Award (RCA).
References (55)
- et al.
The preparation of poly(methyl methacrylate) lattices in nonaqueous media
Colloids Surf.
(1986) Model hard-sphere dispersions: Statistical mechanical theory, simulations, and experiments
Curr. Opin. Colloid Interface Sci.
(1996)- et al.
NMR measurement of the transport dynamics of colloidal particles in an open cell polymer foam porous media
J. Colloid Interface Sci.
(2010) - et al.
Preparation of poly (methylmethacrylate) microcapsules with liquid cores
J. Colloid Interface Sci.
(1998) - et al.
Nanoscale NMR velocimetry by means of slowly diffusing tracer particles
J. Magn. Reson.
(2004) - et al.
NMR diffusion studies of translational properties of oil inside core-shell latex particles
J. Colloid Interface Sci.
(2003) - et al.
Modified iterative model based on data extrapolation method to reduce Gibbs ringing
J. Magn. Reson. Imaging
(1991) - et al.
Anomalous microfluidic phonons induced by the interplay of hydrodynamic screening and incompressibility
Phys. Rev. Lett.
(2007) - et al.
The non-Newtonian rheology of dilute colloidal suspensions
J. Fluid Mech.
(2002) - et al.
Dynamics of Polymeric Liquids Fluid Dynamics
(1987)
NMR Imaging of Materials
The rheological behavior of concentrated colloidal dispersions
J. Chem. Phys.
Normal stresses in colloidal dispersions
J. Rheol.
Nuclear magnetic resonance measurement of shear-induced particle migration in Brownian suspensions
Phys. Fluids
Dynamics of the solid and liquid phases in dilute sheared Brownian suspensions: irreversibility and particle migration
Phys. Rev. Lett.
A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants and on the general existence of active molecules in organic and inorganic bodies
Philos. Mag.
Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR
Principles of Nuclear Magnetic Resonance Microscopy
Flow-Induced Helical Coiling of Semiflexible Polymers in Structured Microchannels
Phys. Rev. Lett.
Microfluidic methods for generating continuous droplet streams
J. Phys. D: Appl. Phys.
Taylor dispersion and molecular displacements in Poiseuille flow
Phys. Rev. E
Particle segregation and dynamics in confined flows
Phys. Rev. Lett.
The theory of the Brownian motion
Ann. Phys.
Oscillatory flow phenomena in simple and complex fluids
Appl. Magn. Reson.
Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation
J. Fluid Mech.
Particle migration in pressure-driven flow of a Brownian suspension
J. Fluid Mech.
Application of PFG–NMR to study the impact of colloidal deposition on hydrodynamic dispersion in a porous medium
Transp. Porous Media
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Materializing opportunities for NMR of solids
2019, Journal of Magnetic ResonanceCitation Excerpt :Many of these are well-established methods that similarly benefit from the enhancements of signal sensitivity and spectral resolution discussed above. The dynamics of molecules, for example, are central to understanding the mechanical and rheological behaviors of polymers [51,52], inorganic glasses and melts [70], colloidal suspensions [71], as well as the diffusion of adsorbed molecules in porous solids [72,73], ion mobility in bulk solids [74,75], and transitions between phases [37,76]. Variable-temperature analyses feature prominently in such investigations, as do multinuclear techniques that probe and correlate the local environments and interactions of different component nuclei, providing a wealth of complementary information.