Thin film modeling of crystal dissolution and growth in confinement

Gagliardi, Luca; Pierre-Louis, Olivier

doi:10.1103/physreve.97.012802

Cited by 7 publications

(30 citation statements)

References 61 publications

(102 reference statements)

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“…Finally, the value of the normalized repulsion strength Ā is chosen following the same lines as in [19]. For simplicity we assume A≈10 −20 J [20] to be the same for all materials considered here.…”

Section: Model and Methodsmentioning

confidence: 99%

Crystal growth in nano-confinement: subcritical cavity formation and viscosity effects

Gagliardi

Pierre-Louis

2018

New J. Phys.

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We report on the modeling of the formation of a cavity at the surface of crystals confined by a flat wall during growth in solution. Using a continuum thin film model, we discuss two phenomena that could be observed when decreasing the thickness of the liquid film between the crystal and the wall down to the nanoscale. First, in the presence of an attractive van der Waals contribution to the disjoining pressure, the formation of the cavity becomes subcritical, i.e., discontinuous. In addition, there is a minimum supersaturation required to form a cavity. Second, when the thickness of the liquid film between the crystal and the substrate reaches the nanoscale, viscosity becomes relevant and hinders the formation of the cavity. We demonstrate that there is a critical value of the viscosity above which no cavity will form. The critical viscosity increases as the square of the thickness of the liquid film. A quantitative discussion of model materials such as calcite, sodium chlorate, glucose and sucrose is provided.

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Section: Model and Methodsmentioning

confidence: 99%

Crystal growth in nano-confinement: subcritical cavity formation and viscosity effects

Gagliardi

Pierre-Louis

2018

New J. Phys.

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“…From Fick's law, the local diffusion flux in the liquid is −D∇c. When the film is thin, diffusion in the z-direction orthogonal to the substrate leads to fast relaxation of the concentration to a value that does not depend on z [13]. As a consequence, the total mass flux in the directions x, y parallel to the substrate is simply −Dζ∇ xy c, where ζ(x, y) is the local thickness of the thin liquid film between the crystal and the substrate, and ∇ xy = (∂ x , ∂ y ) is the gradient operator in the x, y plane.…”

Section: Surface Kineticsmentioning

confidence: 99%

“…Following the same lines as in Ref. [13], the dynamics within the contact is described by a thin film model based on the small slope limit (also called the lubrication limit) [20]. Details about the derivation of these equations are reported in appendix A.…”

Section: Model Equationsmentioning

confidence: 99%

“…Finally, the force balance between an external force F z , viscous dissipation, and disjoining pressure provides an additional relations which allows one to determine u z [13]…”

Section: Model Equationsmentioning

confidence: 99%

“…We start in sections 2 and 3 by extending the thin film model introduced in Ref. [13] to account for slow surface kinetics.…”

Section: Introductionmentioning

confidence: 99%

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Confined growth with slow surface kinetics: A thin film model approach

Gagliardi

Pierre-Louis

2019

Journal of Crystal Growth

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Recent experimental and theoretical investigations of crystal growth from solution in the vicinity of an impermeable wall have shown that: (i) growth can be maintained within the contact region when a liquid film is present between the crystal and the substrate; (ii) a cavity can form in the center of the contact region due to insufficient supply of mass through the liquid film. Here, we investigate the influence of surface kinetics on these phenomena using a thin film model. First, we determine the growth rate within the confined region in the absence of a cavity. Growth within the contact induces a drift of the crystal away from the substrate. Our results suggest novel strategies to measure surface kinetic coefficients based on the observation of this drift. For the specific case where growth is controlled by surface kinetics outside the contact, we show that the total displacement of the crystal due to the growth in the contact is finite. As a consequence, the growth shape approaches asymptotically the free growth shape truncated by a plane passing through the center of the crystal. Second, we investigate the conditions under which a cavity forms. The critical supersaturation above which the cavity forms is found to be larger for slower surface kinetics. In addition, the critical supersaturation decays as a power law of the contact size. The asymptotic value of the critical supersaturation and the exponent of the decay are found to be different for attractive and repulsive disjoining pressures. Finally, our previous representation of the transition within a morphology diagram appears to be uninformative in the limit of slow surface kinetics. Crystal SUBSTRATE Crystal F z < l a t e x i t s h a 1 _ b a s e 6 4 = " P L S e 1 5 N D 2 W B x m S b u H F 6 1 A r 2 L P W o = " > A A A B 9 X i c b V D L S g N B E O z 1 G e M r 6 t H L Y B A 8 h V 0 R 9 C Q B Q T x G N A 9 I l j A 7 6 c Q h s w 9 m e p W 4 5 B O 8 6 s m b e P V 7 P P g v 7 q 5 7 0 M Q 6 F V X d d H V 5 k Z K G b P v T W l h c W l 5 Z L a 2 V 1 z c 2 t 7 Y r O 7 s t E 8 Z a Y F O E K t Q d j x t U M s A m S V L Y i T R y 3 1 P Y 9 s Y X m d + + R 2 1 k G N z S J E L X 5 6 N A D q X g l E o 3 l / 3 H f q V q 1 + w c b J 4 4 B a l C g U a / 8 t U b h C L 2 M S C h u D F d x 4 7 I T b g m K R R O y 7 3 Y Y M T F m I + w m 9 K A + 2 j c J I 8 6 Z Y e x 4 R S y C D W T i u U i / t 5 I u G / M x P f S S Z / T n Z n 1 M v E / r x v T 8 M x N Z B D F h I H I D p F U m B 8 y Q s u 0 A 2 Q D q Z G I Z 8 m R y Y A J r j k R a s m 4 E K k Y p 6 W U 0 z 6 c 2 e / n S e u 4 5 t g 1 5 / q k W j 8 v m i n B P h z A E T h w C n W 4 g g Y 0 Q c A I n u A Z X q w H 6 9 V 6 s 9 5 / R h e s Y m c P / s D 6 + A b U e J I 4 < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " P L S e 1 5 N D 2 W B x m S b u H F 6 1 A r 2 L P W o = " > A A A B 9 X i c b V D L S g N B E O z 1 G e M r 6 t H L Y B A 8 h V 0 R 9 C Q B Q T x G N A 9 I l j A 7 6 c Q h s w 9 m e p W 4 5 B O 8 6 s m b e P V 7 P P g v 7 q 5 7 0 Ma s m 4 E K k Y p 6 W U 0 z 6 c 2 e / n S e u 4 5 t g 1 5 / q k W ...

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Crystallization in Confinement

2020

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Many crystallization processes of great importance, including frost heave, biomineralization, the synthesis of nanomaterials, and scale formation, occur in small volumes rather than bulk solution. Here, the influence of confinement on crystallization processes is described, drawing together information from fields as diverse as bioinspired mineralization, templating, pharmaceuticals, colloidal crystallization, and geochemistry. Experiments are principally conducted within confining systems that offer well‐defined environments, varying from droplets in microfluidic devices, to cylindrical pores in filtration membranes, to nanoporous glasses and carbon nanotubes. Dramatic effects are observed, including a stabilization of metastable polymorphs, a depression of freezing points, and the formation of crystals with preferred orientations, modified morphologies, and even structures not seen in bulk. Confinement is also shown to influence crystallization processes over length scales ranging from the atomic to hundreds of micrometers, and to originate from a wide range of mechanisms. The development of an enhanced understanding of the influence of confinement on crystal nucleation and growth will not only provide superior insight into crystallization processes in many real‐world environments, but will also enable this phenomenon to be used to control crystallization in applications including nanomaterial synthesis, heavy metal remediation, and the prevention of weathering.

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Thin film modeling of crystal dissolution and growth in confinement

Cited by 7 publications

References 61 publications

Crystal growth in nano-confinement: subcritical cavity formation and viscosity effects

Crystal growth in nano-confinement: subcritical cavity formation and viscosity effects

Confined growth with slow surface kinetics: A thin film model approach

Crystallization in Confinement

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