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

Abstract

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 ...

The nonequilibrium crystallization force

“…The evolution of the crystal morphology due to growth or dissolution in the contact region is described by the thin film model introduced in Refs. [21,22], which accounts for disjoining pressure, surface tension, diffusion, and surface kinetics. For the sake of definiteness, we focus on a Hele-Shaw geometry, where an axisymmetric crystal grows between two flat and parallel walls with a purely p-1 arXiv:1909.00414v1 [cond-mat.soft] 1 Sep 2019 repulsive disjoining pressure.…”

“…Model. -We employ a thin film model [20][21][22][23] describing the evolution of a rigid crystal in a region, hereafter called the contact region, where the crystal is in the vicinity of a flat substrate. The model was derived in the small slope limit (also called the lubrication expansion) [24].…”

“…The reader interested in the full derivation of the model equations should refer to refs. [21,22]. In order to simplify the model we consider the case of equal densities between the crystal and the liquid.…”