Comparison of vial heat transfer coefficients during the primary and secondary drying stages of freeze-drying

This study uses a heat flux sensor and temperature probes to directly measure vial heat transfer coefficients (K_v) during primary and secondary drying stages of lyophilization. It is observed that K_v is 40-80% smaller during secondary drying than primary drying, and this value exhibits a weaker dependence on chamber pressure than in primary drying. These observations arise because water vapor in the chamber significantly decreases between primary and secondary drying, which alters the gas conductivity between the shelf and vial. This study tabulates K_v values for secondary drying for different vials and different chamber pressures, and demarcates the contributions from gas conduction. Lastly, the study performs an energy budget analysis on two different vials (10R glass vial and 10 mL plastic vial) to determine the major factors that contribute to vial energy consumption. During primary drying, the majority of energy supplied goes towards sublimation, while for secondary drying, the majority of energy goes towards heating the vial wall rather than desorbing bound water. We discuss the consequences of this behavior for heat transfer modeling. During secondary drying, the heat of desorption can be neglected in thermal modeling for some materials (e.g., glass) but not others (e.g., plastic vials).

A forward reconstruction, holographic method to overcome the lens effect during 3D detection of semi-transparent, non-spherical particles

Suspensions of semi-transparent particles such as polystyrene microparticles are commonly used as model systems in the study of micro-rheology, biology, and microfluidics. Holography is a valuable tool that allows one to obtain 3-D information for particle position and orientation, but forward reconstruction techniques often struggle to infer this information accurately for semi-transparent spheroids with an O(1) aspect ratio, since the lens effect from the particle introduces complex patterns. We propose a reconstruction method that uses image moment information to generate a mask over the sharp patterns from the lens effect and gives reasonable estimation of the 3-D position and orientation of the particle. The method proposed in this work uses the average particle geometry information to determine the process parameters and identify the appropriate detection zone. The average detection error for z_c is less than 25% of the average particle thickness, and the average errors in the in-plane and out-of-plane orientations ϕ and θ are 2° and 4°, respectively. Our method provides comparable accuracy in the detection of the particle center of mass (x_c, y_c, z_c) and in-plane orientation ϕ as a recent forward reconstruction method for semi-transparent particles proposed by Byeon et al. (H. Byeon, T. Go and S. J. Lee, Appl. Opt., 2016, 54, 2106-2112; H. Byeon, T. Go and S. J. Lee, Opt. Express, 2016, 24, 598-610). This method provides a clearly defined framework for identifying the particle's out-of-plane tilt angle θ. We finally demonstrate the applicability of the method to opaque, slender (aspect ratio A_R ≫ 1) particles by analyzing the 3-D motion of E. coli cells from holographic video footage.

Experimental and theoretical studies of cross-stream migration of non-spherical particles in a quadratic flow of a viscoelastic fluid

We experimentally investigate the cross-stream migration of spherical, prolate, and oblate particles in a circular tube flow of a weakly viscoelastic fluid (De = O(10^-2)) with negligible inertia (Re ≈ 0). From our previous theoretical studies, we developed mathematical models based on a second order fluid (i.e., retarded expansion for De ≪ 1) to characterize the migration trajectory of the particles in the absence of wall effects. The theory shows that the particle migration speed is proportional to the length the particle spans in the shear gradient direction (L_sg), and furthermore quantifies how particle shape alters the migration timescale. For particles with identical volume, spherical particles show the fastest migration speed among all the particles. The distinctive orientation behavior of prolate and oblate spheroids leads to a faster migration speed for an oblate particle compared to a prolate particle of the same aspect ratio. In this work, we verify our theory with microfluidic flow experiments using a model suspension of polystyrene (PS) micro-particles in a density-matched polyvinylpyrrolidone (PVP) solution (a Boger fluid). The experimental results show good qualitative and quantitative agreement with the theoretically predicted particle migration speed, indicating that the theory is able to provide reasonable predictions for real microfluidic systems.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.

Mass Transport in High-Flux Hemodialysis: Application of Engineering Principles to Clinical Prescription

An understanding of the processes underlying mass transfer is paramount for the attainment of adequate solute removal in the dialytic treatment of patients with kidney failure. In this review, engineering principles are applied to characterize the physical mechanisms behind the two major modes of mass transfer during hemodialysis, namely diffusion and convection. The manner in which flow rate, dialyzer geometry, and membrane microstructure affect these processes is discussed, with concepts such as boundary layers, effective membrane diffusivity, and sieving coefficients highlighted as critical considerations. The objective is to improve clinicians' understanding of these concepts as important factors influencing the prescription and delivery of hemodialysis therapy.

Understanding Heat Transfer During the Secondary Drying Stage of Freeze Drying: Current Practice and Knowledge Gaps

Currently, there is a lack of robust models for secondary drying with comparable accuracy and flexibility as primary drying models. In order to better understand heat transfer during secondary drying, sucrose and mannitol solutions were freeze-dried in vials in a lab-scale lyophilizer under various drying conditions. Several distinct thermal characteristics for secondary drying were experimentally observed: (1) the vial heat transfer coefficient can change significantly between primary and secondary drying due to the change in water vapor content in the freeze dryer; (2) the thermal mass of the vial plays a major role in determining the cake temperature as roughly 95% of the heat supplied is absorbed by the vial walls. From a theoretical perspective, three different models of secondary drying were examined with varying degrees of complexity (full 3D simulation, 1D-averaged equations, and lumped-capacitance 0D approach). In these models, the desorption of bound water is treated as a one-way coupling with temperature. It is found that although a simple lumped-capacitance approach can capture many of the vital features of cake temperature and moisture profile, near quantitative agreement with experiments can be made by employing a 1D-averaged equation approach, where the effective thermal conductivities of the vial are determined by thermal circuits.

Exact sampling of polymer conformations using Brownian bridges

The equilibrium conformation of a polymer molecule in an external field is often used in field theories to calculate macroscopic polymer properties of melts and solutions. We use a mathematical method called a Brownian bridge to exactly sample continuous polymer chains to end in a given state. We show that one can systematically develop such processes to sample specific polymer topologies, to confine polymers in a given geometry for its entire path, to efficiently generate high-probability conformations by excluding small Boltzmann weights, or to simulate rare events in a rugged energy landscape. This formalism can improve the polymer sampling efficiency significantly compared to traditional methods (e.g., Monte Carlo or Rosenbluth).

Uremic Toxins and their Relation to Dialysis Efficacy

Toxin retention is felt to be a major contributor to the development of uremia in patients with advanced chronic kidney disease and end-stage renal disease (ESRD). Uremic retention compounds are classically divided into 3 categories: small solutes, middle molecules, and protein-bound toxins. Compounds comprising the first category, for which the upper molecular weight limit is generally considered to be 500 Da, possess a high degree of water solubility and minimal or absent protein binding. The second category of middle molecules has largely evolved now to be synonymous with peptides and proteins that accumulate in uremia. Although not precisely defined, low-molecular weight proteins as a class have a molecular weight spectrum ranging from approximately 500 to 60,000 daltons. The final category of uremic retention compounds is protein-bound uremic toxins (PBUTs). As opposed to the above small, highly water-soluble toxins, which are largely by-products of protein metabolism, PBUTs have diverse origins and possess chemical characteristics that preclude the possibility of circulation in an unbound form despite being of low molecular weight. This review is the first in a series of papers designed to provide the current state of the art for extracorporeal treatment of ESRD. Subsequent papers in this series will address membranes, mass transfer mechanisms, and future directions. For small solutes and middle molecules, particular emphasis is placed on the important clinical trials that comprise the evidence base regarding the influence of dialytic solute removal on outcome. Because such trials do not exist for PBUTs, the discussion here is instead focused on solute characteristics and renal elimination mechanisms.

Knots modify the coil-stretch transition in linear DNA polymers

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Steady-State and Transient Behavior of Knotted Chains in Extensional Fields

Recently, there has been a push to understand how molecular topology alters the nonequilibrium dynamics of polymer systems. In this paper, we probe how knotted polymers evolve in planar extensional fields using Brownian dynamics simulations and single-molecule experiments. In the first part of the study, we quantify the extension versus strain-rate curves of polymers and find that knots shift these curves to larger strain-rates. These trends can be quantitatively explained by Rouse-like scaling theories. In the second half of the study, we examine the consequences of knot untying on the time-dependent conformations of polymers in these external fields. We find that knot untying creates significant, transient changes in chain extension. If the topology is complex, the chain undergoes a wide range of time-dependent conformations since knot untying proceeds through many different stages. We provide examples of such untying trajectories over time.

Kinetics of the Change in Droplet Size during Nanoemulsion Formation

The evolution of droplet size during nanoemulsion formation is critical for the rational design of nanoemulsions in areas such as drug delivery and materials synthesis. In this article, we discuss the relative importance of various time scales involved in nanoemulsion formation and propose a population balance model for droplet breakup that takes into account the droplet's internal viscosity. The proposed model gives a qualitative agreement between average droplet size and polydispersity data for nanoemulsions prepared by high-pressure homogenization and ultrasonication. On the basis of these modeling results, we propose a correlation to obtain a parity plot for the droplet size data. We show that our model and correlation also work well with data from the existing literature. The proposed model and correlation can be used to guide future population balance studies and experimental preparation of nanoemulsions.

Translocation dynamics of knotted polymers under a constant or periodic external field

We perform Brownian dynamics simulations to examine how knots alter the dynamics of polymers moving through nanopores under an external field. In the first part of this paper, we study the situation when the field is constant. Here, knots halt translocation above a critical force with jamming occurring at smaller forces for twist topologies compared to non-twist topologies. Slightly below the jamming transition, the polymer's transit times exhibit large fluctuations. This phenomenon is an example of the knot's molecular individualism since the conformation of the knot plays a large role in the chain's subsequent dynamics. In the second part of the paper, we study the motion of the chain when one cycles the field on and off. If the off time is comparable to the knot's relaxation time, one can adjust the swelling of the knot at the pore and hence design strategies to ratchet the polymer in a controllable fashion. We examine how the off time affects the ratcheting dynamics. We also examine how this strategy alters the fluctuations in the polymer's transit time. We find that cycling the force field can reduce fluctuations near the knot's jamming transition, but can enhance the fluctuations at very high forces since knots get trapped in metastable states during the relaxation process. The latter effect appears to be more prominent for non-torus topologies than torus ones. We conclude by discussing the feasibility of this approach to control polymer motion in biotechnology applications such as sequencing.

Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow

Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, J. Fluid Mech., 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Phys. Rev. Lett., 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.

Singular perturbation theory for predicting extravasation of Brownian particles

Motivated by recent studies on tumor treatments using the drug delivery of nanoparticles, we provide a singular perturbation theory and perform Brownian dynamics simulations to quantify the extravasation rate of Brownian particles in a shear flow over a circular pore with a lumped mass transfer resistance. The analytic theory we present is an expansion in the limit of a vanishing Péclet number (P), which is the ratio of convective fluxes to diffusive fluxes on the length scale of the pore. We state the concentration of particles near the pore and the extravasation rate (Sherwood number) to O(P^1/2). This model improves upon previous studies because the results are valid for all values of the particle mass transfer coefficient across the pore, as modeled by the Damköhler number (κ), which is the ratio of the reaction rate to the diffusive mass transfer rate at the boundary. Previous studies focused on the adsorption-dominated regime (i.e., κ → ∞). Specifically, our work provides a theoretical basis and an interpolation-based approximate method for calculating the Sherwood number (a measure of the extravasation rate) for the case of finite resistance [κ ~ O(1)] at small Péclet numbers, which are physiologically important in the extravasation of nanoparticles. We compare the predictions of our theory and an approximate method to Brownian dynamics simulations with reflection-reaction boundary conditions as modeled by κ. They are found to agree well at small P and for the κ ≪ 1 and κ ≫ 1 asymptotic limits representing the diffusion-dominated and adsorption-dominated regimes, respectively. Although this model neglects the finite size effects of the particles, it provides an important first step toward understanding the physics of extravasation in the tumor vasculature.