Xác định tham số phân nhánh (λ) theo hàm thời gian trong quá trình điện phân sử dụng phương trình Bratu

Ivan Patiño Montoya1,2, Juan Ramón Castro-Rodríguez2, Eduardo Alberto López-Maldonado2, Luis Jesús Villarreal-Gómez2,1
1Facultad de Ciencias de la Ingeniería y Tecnología, Universidad Autónoma de Baja California, Tijuana, México
2Facultad de Ciencias Químicas e Ingeniería, Universidad Autónoma de Baja California, Tijuana, México

Tóm tắt

Sợi nano polyme thu được từ quá trình điện phân có tiềm năng ứng dụng trong nhiều lĩnh vực như lọc chất lỏng, y sinh, hỗ trợ chất xúc tác, phát thuốc, kỹ thuật mô, sợi nano và nhiều hơn nữa. Tuy nhiên, mô hình lý thuyết của quá trình điện phân vẫn là một vấn đề cần được giải quyết, vì sự thiếu hiểu biết về bản chất vật lý của quá trình này hạn chế nghiêm trọng việc cải thiện chất lượng của các sợi cũng như hiệu quả của quá trình. Về mặt toán học, một hệ thống phi tuyến là một hệ thống mà các phương trình tiến hóa của nó là phi tuyến. Đối với các loại hệ thống này, một sự thay đổi nhỏ về một tham số có thể kích hoạt một sự thay đổi đột ngột và mạnh mẽ (hoặc phân nhánh) trong các thuộc tính định lượng và định tính của hệ thống, có thể dẫn tới việc tổ chức của hệ thống biểu hiện tính hỗn loạn. Nghiên cứu này thiết lập một mô hình toán học để thu được một xấp xỉ về vận tốc trục của dòng polyme điện phân ra ngoài, được mô phỏng trong MATLAB, chỉ sử dụng khoảng cách giữa đầu kim và bộ thu (10 và 20 cm) làm biến duy nhất trong mô hình toán học. Điều này không có nghĩa là các tham số khác như độ nhớt dung dịch, trọng lượng phân tử, và các tham số khác là không cần thiết. Tuy nhiên, nghiên cứu này đã xem xét khoảng cách giữa đầu kim và bộ thu như là biến khởi đầu, tiếp theo là đánh giá thực nghiệm để kiểm tra mối quan hệ giữa vận tốc theo trục và hình dạng cũng như đường kính sợi thu được. Lực điện được đánh giá là tham số chi phối hơn các lực khác và phương trình Bratu, có thể giải thích sự không ổn định (phân nhánh) trong quá trình điện phân. Kết quả của phương trình vi phân không gian-thời gian cho thấy vận tốc trục xuất hiện hỗn loạn khi thế năng vượt qua căng thẳng bề mặt của giọt polyme, được quan sát ở các giá trị phân nhánh λ = 0.5. Cuối cùng, việc kiểm soát khoảng cách giữa 10 và 20 cm không đại diện cho một biến thiết yếu trong việc tìm kiếm khả năng tái sản xuất của đường kính sợi bằng mô hình toán học một chiều.

Từ khóa


Tài liệu tham khảo

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